From 4ebd6d4bff9ded3fd5ba8e5d59fabf4d28e82f6c Mon Sep 17 00:00:00 2001 From: Henry Gabryjelski Date: Sat, 2 Mar 2024 23:36:36 -0800 Subject: [PATCH] Add id48lib and second half of key recovery. --- client/CMakeLists.txt | 1 + client/Makefile | 17 + client/deps/CMakeLists.txt | 3 + client/deps/id48/LICENSE | 21 + client/deps/id48/Makefile | 13 + client/deps/id48/README.md | 50 + client/deps/id48/TECHNICAL.md | 777 +++ client/deps/id48/id48.h | 206 + client/deps/id48/id48_data.c | 8366 +++++++++++++++++++++++++++++ client/deps/id48/id48_generator.c | 894 +++ client/deps/id48/id48_internals.h | 53 + client/deps/id48/id48_recover.c | 439 ++ client/deps/id48lib.cmake | 9 + client/src/cmdlfem4x70.c | 256 +- client/src/cmdlfem4x70.h | 2 +- include/em4x70.h | 14 +- 16 files changed, 11107 insertions(+), 14 deletions(-) create mode 100644 client/deps/id48/LICENSE create mode 100644 client/deps/id48/Makefile create mode 100644 client/deps/id48/README.md create mode 100644 client/deps/id48/TECHNICAL.md create mode 100644 client/deps/id48/id48.h create mode 100644 client/deps/id48/id48_data.c create mode 100644 client/deps/id48/id48_generator.c create mode 100644 client/deps/id48/id48_internals.h create mode 100644 client/deps/id48/id48_recover.c create mode 100644 client/deps/id48lib.cmake diff --git a/client/CMakeLists.txt b/client/CMakeLists.txt index db20bcb8b..7b7bcaddd 100644 --- a/client/CMakeLists.txt +++ b/client/CMakeLists.txt @@ -758,6 +758,7 @@ target_link_libraries(proxmark3 PRIVATE pm3rrg_rdv4_amiibo pm3rrg_rdv4_reveng pm3rrg_rdv4_hardnested + pm3rrg_rdv4_id48 ${ADDITIONAL_LNK}) if (NOT SKIPPTHREAD EQUAL 1) diff --git a/client/Makefile b/client/Makefile index 10929ffca..942316726 100644 --- a/client/Makefile +++ b/client/Makefile @@ -71,6 +71,12 @@ HARDNESTEDLIBINC = -I$(HARDNESTEDLIBPATH) HARDNESTEDLIB = $(HARDNESTEDLIBPATH)/libhardnested.a HARDNESTEDLIBLD = +## ID48 +ID48LIBPATH = ./deps/id48 +ID48LIBINC = -I$(ID48LIBPATH) +ID48LIB = $(ID48LIBPATH)/libid48.a +ID48LIBLD = + ## Jansson JANSSONLIBPATH = ./deps/jansson JANSSONLIBINC = -I$(JANSSONLIBPATH) @@ -157,6 +163,12 @@ STATICLIBS += $(HARDNESTEDLIB) LDLIBS +=$(HARDNESTEDLIBLD) PM3INCLUDES += $(HARDNESTEDLIBINC) +## ID48 +# not distributed as system library +STATICLIBS += $(ID48LIB) +LDLIBS += $(ID48LIBLD) +PM3INCLUDES += $(ID48LIBINC) + ## Linenoise # wait to see if Readline is available @@ -850,6 +862,7 @@ clean: $(Q)$(MAKE) --no-print-directory -C $(AMIIBOLIBPATH) clean $(Q)$(MAKE) --no-print-directory -C $(CLIPARSERLIBPATH) clean $(Q)$(MAKE) --no-print-directory -C $(HARDNESTEDLIBPATH) clean + $(Q)$(MAKE) --no-print-directory -C $(ID48LIBPATH) clean $(Q)$(MAKE) --no-print-directory -C $(JANSSONLIBPATH) clean ifeq ($(LINENOISE_LOCAL_FOUND), 1) $(Q)$(MAKE) --no-print-directory -C $(LINENOISELIBPATH) clean @@ -902,6 +915,10 @@ $(HARDNESTEDLIB): .FORCE $(info [*] MAKE $@) $(Q)$(MAKE) --no-print-directory -C $(HARDNESTEDLIBPATH) all +$(ID48LIB): .FORCE + $(info [*] MAKE $@) + $(Q)$(MAKE) --no-print-directory -C $(ID48LIBPATH) all + $(JANSSONLIB): .FORCE ifneq ($(JANSSON_FOUND),1) $(info [*] MAKE $@) diff --git a/client/deps/CMakeLists.txt b/client/deps/CMakeLists.txt index 87613c0fe..99a843d66 100644 --- a/client/deps/CMakeLists.txt +++ b/client/deps/CMakeLists.txt @@ -7,6 +7,9 @@ endif() if (NOT TARGET pm3rrg_rdv4_hardnested) include(hardnested.cmake) endif() +if (NOT TARGET pm3rrg_rdv4_id48) + include(id48lib.cmake) +endif() if (NOT TARGET pm3rrg_rdv4_jansson) include(jansson.cmake) endif() diff --git a/client/deps/id48/LICENSE b/client/deps/id48/LICENSE new file mode 100644 index 000000000..58dbf90ba --- /dev/null +++ b/client/deps/id48/LICENSE @@ -0,0 +1,21 @@ +The MIT License (MIT) + +Copyright (c) 2024 by Henry Gabryjelski + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/client/deps/id48/Makefile b/client/deps/id48/Makefile new file mode 100644 index 000000000..2039bba5b --- /dev/null +++ b/client/deps/id48/Makefile @@ -0,0 +1,13 @@ +# Makefile for ID48LIB library +MYSRCPATHS = +MYINCLUDES = -I. +MYCFLAGS = -Wpedantic -Wall -Werror -O3 -Wno-unknown-pragmas -Wno-inline -Wno-unused-function +MYDEFS = +MYSRCS = \ + id48_data.c \ + id48_generator.c \ + id48_recover.c + +LIB_A = libid48.a + +include ../../../Makefile.host diff --git a/client/deps/id48/README.md b/client/deps/id48/README.md new file mode 100644 index 000000000..4c8eb4e65 --- /dev/null +++ b/client/deps/id48/README.md @@ -0,0 +1,50 @@ +# ID48LIB + +## Purpose + +Enable reliable and repeatable key-writing and verification +on ID48 RFID tags. Improve key recovery when the tag is +present and writable. + +### Why this is needed. + +Have you ever lost data when a computer shutdown unexpectedly? +This occurs when the program believes the data was written, +but the device did not actually store the data before power +was lost. + +With RFID tags, the same problem exists, except the power is +wirelessly provided, and may be only enough to read data +(writing takes more power). Thus, it's even more critical +for RFID tags to validate what was written. + +If you are bothered by unreliable processes, and enjoy a measure +of certainty, and need to write a new key to an ID48 tag, +then read on. + +### Problem background + +The ProxMark3 RFID research tool has had basic support for +reading and writing ID48-based RFID tags (aka em4x70). However, +although the code existed to write new 96-bit keys, there was no +way to verify that the keys were actually written to the tag. + +This is because the keys are not directly readable from the tag +(by design). The *only* way to verify that the key was successfully +stored on the tag is to perform an authentication against the tag, +using the new key that you had attempted to write, and verify that +the tag's response to the nonce and challenge matches. + +Obviously, this requires the ability to calculate, given a known +key and nonce, the challenge to send to the tag, and the expected +response from the tag. Without this, folks simply could not know +if the key was safely stored on the tag or not. + +## Capabilities + +This library provides the ability to calculate the challenge and +expected response for a known key and nonce. In addition, if +provided the first half of the key, and at least one successful +authentication trio of nonce, challenge, and response, then +the library can recover all potentially valid values for the +second half of the key. diff --git a/client/deps/id48/TECHNICAL.md b/client/deps/id48/TECHNICAL.md new file mode 100644 index 000000000..f663791ca --- /dev/null +++ b/client/deps/id48/TECHNICAL.md @@ -0,0 +1,777 @@ +# Technical background and details + +This is a collection of random notes and thoughts from the +original development process. Much may be rambling. +Information herein was **_not_** validated before release, +and errors are likely. + +## Background and Primary Research Paper + +The Usenix security conference 2013 was going to have a presentation +documenting the internals fully (as well as crytpanalysis). This +disclosure was delayed for two years. When it was released, the +paper omitted a non-linear output filter function at definition 3.8. + +This omitted function takes a 20-bit input, and returns a single bit. + +All other details of the cipher appeared to have been fully disclosed (even if +some errors existed). The largest error is that text description of +the successor function for `g` register was incorrect. However, the +diagram version showed the correct operation. + +## Variable and notations used + +### Common variables + +* `K` ==> a 96-bit shared key, known to both vehicle and transponder +* `N` ==> a 56-bit nonce value, generated by the vehicle, + and sent in cleartext to the transponder +* `Aᵥ` ==> a 28-bit authenticator value generated by a reader + (often a vehicle), and sent in cleartext to the + tag. (aka `frn`) +* `Aₜ` ==> a 20-bit authenticator value generated by a tag + and sent in cleartext to the reader (aka `grn`) +* `frn` ==> an alternate name for `Aᵥ` +* `grn` ==> an alternate name for `Aₜ` +* `g` ==> a 23-bit Galois linear feedback shift register +* `h` ==> a 13-bit non-linear feedback shift register +* `l` ==> a 7-bit feedback register +* `m` ==> a 7-bit feedback register +* `r` ==> a 7-bit feedback register +* `sₙ` ==> a 57-bit internal state of the cipher `=== ` +* at iteration `n` (where `0 ≤ n ≤ 55`) +* `s₀` ==> cipher initial state + +### Notation and Symbols + +For our purposes, the finite field `F` will **_always_** refer to +a binary finite field (each element ∈ `{0,1}`). Thus, as is useful +for current computers, we can treat these as bitstrings. + +Symbol | Meaning +----------|--------- +`^` | bitwise exclusive-or (XOR); the paper used `⊕` +`ε` | the empty bitstring +`0ⁿ` | bitstring of n zero-bits +`xⁿ` | a bitstring of length `n` +`x₀` | the first bit of a bitstring +`xᵢ` | the `i`th bit of a bitstring `xⁿ` (where `in`) +`x·y` | concatenation of bitstrings `x` and `y` +`~x` | bitwise complement of bitstring `x` (paper uses `x̄`) +`&&` | logical AND (conjunction) (research paper uses `∧`) +`||` | logical OR (disjunction) (research paper uses `∨`) +`x[i..j]` | The contiguous bits of `x` from subscript `i` to `j` + +### Notation Examples: + +If the value is stored in +Given: + +* `x⁸ = 00000011` + +Then: + +* `x⁸ === x₇ · x₆ · x₅ · x₄ · x₃ · x₂ · x₁ · x₀` +* `x[7..4] = 0000` +* `x[3..0] = 0011` +* `x[2..1] = 01` + +## Cipher data dependencies + +### Cipher Initial State s0 - Data Dependencies + +Evaluating the bits that influence the initial state, `s₀₀`, +as described in section 3.5: + +`p` ==> 56-bit value, depends only on `N` and `K[95..40]` +`q` ==> 44-bit value, depends only on `p` +`t` ==> 43-bit value, depends only on `q` + +Thus, all three of those variables depend only +upon `N` and `K[95..40]`. + +Notably, the input `i` to the successor function +for `g` is hard-coded to zero for the initialization. + +As reproduced below, the full initial state is shown +to depend **_only_** on three variables (`p`, `q`, `t`): + +``` +g : t(0..22) +h : 0 · p(0..11) +l : t(23..29) +m : t(30..36) +r : t(37..42) · q(43) +``` + +Therefore, `s₀₀` depends **_only_** on `N` +and `K[95..40]`. Stated differently, the low +40 bits of key `K` (aka `K[39..0]`) have +**_no effect_** on the calculation of `s₀₀`. + + +### Challenging the assumptions + +Generally, `K` remains constant, and `N` is +a random value generated by the reader. It +appears these presumptions were accepted as +always true in the creation of this cipher. + +However, the value of `N` can be fully controlled +during research, including choosing to make `N` +constant. Moreover, with a writable tag, `K` can +be modified to have specific relationships with +known-good authentication traces. Taken together, +these properties will (as to be described later) +enable recovery of an equivalent to the output +filter function. + +As noted earlier, the initial cipher state `s₀₀` +depends only upon `K[95..40]` and `N`. + +Therefore, if `N` is held constant, then the +the initial cipher state `s₀₀` will depend solely +upon `K[95..40]`. Put another way, this means +that all keys which share the most significant 56 +bits (or differ only in the least significant 40 bits) +will share the same initial state `s₀₀`. + +### Cipher State sₙ - Data Dependencies + +_NOTE: This has utility (value) when `K` is known, +even when the mapping of the output filter function +is not yet known for all `2²⁰` potential inputs._ + +TLDR: With a fixed `N`... + +* `s₀` <-- `K[40..95]` +* `s₁` <-- `K[39..95]` +* `s₂` <-- `K[38..95]` +* `sₙ` <-- `s(N-1)` + `K[40-N]` +* `sₙ` <-- `K[(40-N)..95]` + +### K₃₉..K₀₀ to output bits + + +Here's an exhaustive table that maps which bit +of the key influences a given output bit. +Start state + key bit --> output + + +| Start state | Key bit | Output | +|-------|-------|----------------| +| `s₀₀` | `K₃₉` | << hidden >> | +| `s₀₁` | `K₃₈` | << hidden >> | +| `s₀₂` | `K₃₇` | << hidden >> | +| `s₀₃` | `K₃₆` | << hidden >> | +| `s₀₄` | `K₃₅` | << hidden >> | +| `s₀₅` | `K₃₄` | << hidden >> | +| `s₀₆` | `K₃₃` | << hidden >> | +| `s₀₇` | `K₃₂` | `O₀₀ == frn₀₀` | +| `s₀₈` | `K₃₁` | `O₀₁ == frn₀₁` | +| `s₀₉` | `K₃₀` | `O₀₂ == frn₀₂` | +| `s₁₀` | `K₂₉` | `O₀₃ == frn₀₃` | +| `s₁₁` | `K₂₈` | `O₀₄ == frn₀₄` | +| `s₁₂` | `K₂₇` | `O₀₅ == frn₀₅` | +| `s₁₃` | `K₂₆` | `O₀₆ == frn₀₆` | +| `s₁₄` | `K₂₅` | `O₀₇ == frn₀₇` | +| `s₁₅` | `K₂₄` | `O₀₈ == frn₀₈` | +| `s₁₆` | `K₂₃` | `O₀₉ == frn₀₉` | +| `s₁₇` | `K₂₂` | `O₁₀ == frn₁₀` | +| `s₁₈` | `K₂₁` | `O₁₁ == frn₁₁` | +| `s₁₉` | `K₂₀` | `O₁₂ == frn₁₂` | +| `s₂₀` | `K₁₉` | `O₁₃ == frn₁₃` | +| `s₂₁` | `K₁₈` | `O₁₄ == frn₁₄` | +| `s₂₂` | `K₁₇` | `O₁₅ == frn₁₅` | +| `s₂₃` | `K₁₆` | `O₁₆ == frn₁₆` | +| `s₂₄` | `K₁₅` | `O₁₇ == frn₁₇` | +| `s₂₅` | `K₁₄` | `O₁₈ == frn₁₈` | +| `s₂₆` | `K₁₃` | `O₁₉ == frn₁₉` | +| `s₂₇` | `K₁₂` | `O₂₀ == frn₂₀` | +| `s₂₈` | `K₁₁` | `O₂₁ == frn₂₁` | +| `s₂₉` | `K₁₀` | `O₂₂ == frn₂₂` | +| `s₃₀` | `K₀₉` | `O₂₃ == frn₂₃` | +| `s₃₁` | `K₀₈` | `O₂₄ == frn₂₄` | +| `s₃₂` | `K₀₇` | `O₂₅ == frn₂₅` | +| `s₃₃` | `K₀₆` | `O₂₆ == frn₂₆` | +| `s₃₄` | `K₀₅` | `O₂₇ == frn₂₇` | +| `s₃₅` | `K₀₄` | `O₂₈ == grn₀₀` | +| `s₃₆` | `K₀₃` | `O₂₉ == grn₀₁` | +| `s₃₇` | `K₀₂` | `O₃₀ == grn₀₂` | +| `s₃₈` | `K₀₁` | `O₃₁ == grn₀₃` | +| `s₃₉` | `K₀₀` | `O₃₂ == grn₀₄` | +| `s₄₀` | `0₁₄` | `O₃₃ == grn₀₅` | +| `s₄₁` | `0₁₃` | `O₃₄ == grn₀₆` | +| `s₄₂` | `0₁₂` | `O₃₅ == grn₀₇` | +| `s₄₃` | `0₁₁` | `O₃₆ == grn₀₈` | +| `s₄₄` | `0₁₀` | `O₃₇ == grn₀₉` | +| `s₄₅` | `0₀₉` | `O₃₈ == grn₁₀` | +| `s₄₆` | `0₀₈` | `O₃₉ == grn₁₁` | +| `s₄₇` | `0₀₇` | `O₄₀ == grn₁₂` | +| `s₄₈` | `0₀₆` | `O₄₁ == grn₁₃` | +| `s₄₉` | `0₀₅` | `O₄₂ == grn₁₄` | +| `s₅₀` | `0₀₄` | `O₄₃ == grn₁₅` | +| `s₅₁` | `0₀₃` | `O₄₄ == grn₁₆` | +| `s₅₂` | `0₀₂` | `O₄₅ == grn₁₇` | +| `s₅₃` | `0₀₁` | `O₄₆ == grn₁₈` | +| `s₅₄` | `0₀₀` | `O₄₇ == grn₁₉` | + + + +## Branching ... from one trace to millions + +Given the ability to control the nonce `N`, and +in particular to use a constant `N`, it becomes +possible to generate many valid authentication +sequences (with different keys) from just a +single valid authentication with a known key. + +### Trivially getting 31 more traces + +With a static nonce value, an astute observer may +have noticed that `frn` does not rely on the least +significant five bits of the key ... those bits +influence `grn₀₀..grn₀₄`. + +Therefore, so long as the only bits of `K` that +differ are `K₀₄..K₀₀`, the `frn` value will remain +constant for a given nonce. + +This allows a single known-good key + nonce + frn +to be trivially expanded to 32x known-good sets, +for "nearby" consecutive keys. Another way to state +this is that each block of 32 consecutive keys will +share the same `Aᵥ` value. + +More formally, where `(K' ^ K) <= 0x1F`, +then `Aᵥ' = Aᵥ`. + +``` +REM using the key and auth values from the research paper +lf em 4x70 writekey --key A090A0A02080000000000000 +REM expect a tag response of `60 9D 6` +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +REM repeat using 31 additional keys in the same "block" +lf em 4x70 writekey --key A090A0A02080000000000001 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +lf em 4x70 writekey --key A090A0A02080000000000002 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +lf em 4x70 writekey --key A090A0A02080000000000003 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +REM ... and so on, for a total of 31 more keys +lf em 4x70 writekey --key A090A0A0208000000000001E +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +lf em 4x70 writekey --key A090A0A0208000000000001F +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +``` + +The tag will respond to all 32 authentications, +although its `grn` responses may differ for each key. + +### Moving one bit further... + +Walking the sequence backwards one additional bit, +where the last ***six*** bits of the key change, +what happens to `Aᵥ`? + +It turns out that `Aᵥ` will either remain identical, +or that the least significant bit of `Aᵥ` will flip. +Thus, there are exactly two possible values that +need to be tested for `Aᵥ`, and the tag will respond +to exactly one of them. + +Formally, where `(K' ^ K) <= 0x3F`, +then `Aᵥ' ^ Aᵥ <= 0x1`. + +``` +REM using the key and auth values from the research paper +lf em 4x70 writekey --key A090A0A02080000000000000 +REM expect a tag response of `60 9D 6` +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +REM repeat using 31 additional keys in the same "block" +lf em 4x70 writekey --key A090A0A02080000000000020 +REM 50% chance that this is the correct FRN value +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +REM 50% chance that this is the correct FRN value +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1B0 +``` + +### Expanding further... + +Each additional bit of the key that is changed +will double the number of `Aᵥ` values that need +to be tested to find the correct challenge. + +Using `K'' == K ^ 0x1FF` (nine lowest bits changed), +requires testing only 16 possible `Aᵥ''` values, +by permuting the least significant bits of `Aᵥ`. + +Thus, exactly one of the following should result +in a successful authentication: + +``` +REM modify the key's lowest nine bits +lf em 4x70 writekey --key A090A0A02080000000000100 +REM 1/16 chance for each of these to work: +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F100 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F110 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F120 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F130 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F140 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F150 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F160 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F170 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F180 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F190 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1B0 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1C0 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1D0 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1E0 +lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1F0 +REM hint: response will be `65 09 A` +``` + +### Table of search space per key change + +Depending on the most significant bit that changed in the key, +it can be trivially calculated how many variations of `Aᵥ` +need to be tested to find the correct challenge for that same +nonce. + +| msb changed | key bits changed mask| Values to test | 2^N | +|-------------|----------------------|------------------|------| +| `0` | `0x00'0000'0000` | `1` | `0` | +| `1` | `0x00'0000'0001` | `1` | `0` | +| `2` | `0x00'0000'0003` | `1` | `0` | +| `3` | `0x00'0000'0007` | `1` | `0` | +| `4` | `0x00'0000'000F` | `1` | `0` | +| `5` | `0x00'0000'001F` | `1` | `0` | +| `6` | `0x00'0000'003F` | `2` | `1` | +| `7` | `0x00'0000'007F` | `4` | `2` | +| `8` | `0x00'0000'00FF` | `8` | `3` | +| `9` | `0x00'0000'01FF` | `16` | `4` | +| `10` | `0x00'0000'03FF` | `32` | `5` | +| `11` | `0x00'0000'07FF` | `64` | `6` | +| `12` | `0x00'0000'0FFF` | `128` | `7` | +| `13` | `0x00'0000'1FFF` | `256` | `8` | +| `14` | `0x00'0000'3FFF` | `512` | `9` | +| `15` | `0x00'0000'7FFF` | `1,024` | `10` | +| `16` | `0x00'0000'FFFF` | `2,048` | `11` | +| `17` | `0x00'0001'FFFF` | `4,096` | `12` | +| `18` | `0x00'0003'FFFF` | `8,192` | `13` | +| `19` | `0x00'0007'FFFF` | `16,384` | `14` | +| `20` | `0x00'000F'FFFF` | `32,768` | `15` | +| `21` | `0x00'001F'FFFF` | `65,536` | `16` | +| `22` | `0x00'003F'FFFF` | `131,072` | `17` | +| `23` | `0x00'007F'FFFF` | `262,144` | `18` | +| `24` | `0x00'00FF'FFFF` | `524,288` | `19` | +| `25` | `0x00'01FF'FFFF` | `1,048,576` | `20` | +| `26` | `0x00'03FF'FFFF` | `2,097,152` | `21` | +| `27` | `0x00'07FF'FFFF` | `4,194,304` | `22` | +| `28` | `0x00'0FFF'FFFF` | `8,388,608` | `23` | +| `29` | `0x00'1FFF'FFFF` | `16,777,216` | `24` | +| `30` | `0x00'3FFF'FFFF` | `33,554,432` | `25` | +| `31` | `0x00'7FFF'FFFF` | `67,108,864` | `26` | +| `32` | `0x00'FFFF'FFFF` | `134,217,728` | `27` | +| `33` | `0x01'FFFF'FFFF` | `268,435,456` | `28` | +| `34` | `0x03'FFFF'FFFF` | `536,870,912` | `29` | +| `35` | `0x07'FFFF'FFFF` | `1,073,741,824` | `30` | +| `36` | `0x0F'FFFF'FFFF` | `2,147,483,648` | `31` | +| `37` | `0x1F'FFFF'FFFF` | `4,294,967,296` | `32` | +| `38` | `0x3F'FFFF'FFFF` | `8,589,934,592` | `33` | +| `39` | `0x7F'FFFF'FFFF` | `17,179,869,184` | `34` | +| `40` | `0xFF'FFFF'FFFF` | `34,359,738,368` | `35` | +| `> 40` | ... more ... | changes s₀₀ ... | `56` | + +### Branching of keys + +Thus, it becomes almost trivial to generate millions of +valid authentication sequences for a given nonce, `frn`, +and `K' ~= K`. Each of these authentication sequences +has the potential to generate at least twenty distinct +internal cipher states from `Aₜ`. + +While trivial, this takes time. Millions of traces were +generated over the course of multiple months using multiple +PM3 Easy devices 24/7, each one writing keys and +brute-forcing the `frn` values. + +## Creating equivalent to the "Output Filter Function" + +While the **_mechanics and computation_** of the output +filter function is not known, the **_inputs_** are +defined in Definition 3.9, and the output is a single bit. + +Therefore, if the entire cipher except for the internal +computations of the output filter are known, given a +known valid authentication trace, all twenty of the +input bits passed to the output filter function can be +calculated for each of the 48 output bits (`Aᵥ` and `Aₜ`). + +When using branched traces (from above), the first 36 +internal cipher states (give or take) are shared, and +thus do not provide "new" information. This still +provides up to 12 bits of "new" information per trace, +or up to ~192 bits of "new" information per block of +32 consecutive keys that share the same `frn` value. + +Treating the 20-bit parameter as an index to a bitmap, +the full mapping requires only a 128k bitmap. +Initially, when there remain unknown mappings, a +second 128k bitmap is used to tracks if the output bit +for that 20-bit parameter has already been found. + +As the table become more filled, it becomes easier to +generate new authentication sequences using entirely +random values for `N` and `K`, especially where the +most significant bits of `frn` are known. Thus, the +brute force space for key branching never becomes +overwhelmingly large. + +As an exercise for the reader, and as it is important +to finish filling the last values in the table, an +astute reader can realize optimizations that improve +finding a "targeted" 20-bit input, especially where +the cipher states from current branching had been +archived. + +In summary, these traces can thus be used to (slowly) +fill in a 128k bitmap indicating all possible output +values for any of the `2²⁰` inputs, without ever +needing to replicate or know the internal functioning +of the output filter function. + +## Which bits of K .... + +Given a static value for `N`, what bits in `K` +influence a given output bit? + +| sₙ | Output Bit | Bits in `K` | Delta from s(N-1) | Hex Value | +|-------|-------------|-------------|-------------------|------------------| +| `s₁` | ` ` | `K[39..95]` | `K₃₉` | `0x80_0000_0000` | +| `s₂` | ` ` | `K[38..95]` | `K₃₈` | `0x40_0000_0000` | +| `s₃` | ` ` | `K[37..95]` | `K₃₇` | `0x20_0000_0000` | +| `s₄` | ` ` | `K[36..95]` | `K₃₆` | `0x10_0000_0000` | +| `s₅` | ` ` | `K[35..95]` | `K₃₅` | `0x08_0000_0000` | +| `s₆` | ` ` | `K[34..95]` | `K₃₄` | `0x04_0000_0000` | +| `s₇` | `Aᵥ₂₇` | `K[33..95]` | `K₃₃` | `0x02_0000_0000` | +| `s₈` | `Aᵥ₂₆` | `K[32..95]` | `K₃₂` | `0x01_0000_0000` | +| `s₉` | `Aᵥ₂₅` | `K[31..95]` | `K₃₁` | `0x00_8000_0000` | +| `s₁₀` | `Aᵥ₂₄` | `K[30..95]` | `K₃₀` | `0x00_4000_0000` | +| `s₁₁` | `Aᵥ₂₃` | `K[29..95]` | `K₂₉` | `0x00_2000_0000` | +| `s₁₂` | `Aᵥ₂₂` | `K[28..95]` | `K₂₈` | `0x00_1000_0000` | +| `s₁₃` | `Aᵥ₂₁` | `K[27..95]` | `K₂₇` | `0x00_0800_0000` | +| `s₁₄` | `Aᵥ₂₀` | `K[26..95]` | `K₂₆` | `0x00_0400_0000` | +| `s₁₅` | `Aᵥ₁₉` | `K[25..95]` | `K₂₅` | `0x00_0200_0000` | +| `s₁₆` | `Aᵥ₁₈` | `K[24..95]` | `K₂₄` | `0x00_0100_0000` | +| `s₁₇` | `Aᵥ₁₇` | `K[23..95]` | `K₂₃` | `0x00_0080_0000` | +| `s₁₈` | `Aᵥ₁₆` | `K[22..95]` | `K₂₂` | `0x00_0040_0000` | +| `s₁₉` | `Aᵥ₁₅` | `K[21..95]` | `K₂₁` | `0x00_0020_0000` | +| `s₂₀` | `Aᵥ₁₄` | `K[20..95]` | `K₂₀` | `0x00_0010_0000` | +| `s₂₁` | `Aᵥ₁₃` | `K[19..95]` | `K₁₉` | `0x00_0008_0000` | +| `s₂₂` | `Aᵥ₁₂` | `K[18..95]` | `K₁₈` | `0x00_0004_0000` | +| `s₂₃` | `Aᵥ₁₁` | `K[17..95]` | `K₁₇` | `0x00_0002_0000` | +| `s₂₄` | `Aᵥ₁₀` | `K[16..95]` | `K₁₆` | `0x00_0001_0000` | +| `s₂₅` | `Aᵥ₉` | `K[15..95]` | `K₁₅` | `0x00_0000_8000` | +| `s₂₆` | `Aᵥ₈` | `K[14..95]` | `K₁₄` | `0x00_0000_4000` | +| `s₂₇` | `Aᵥ₇` | `K[13..95]` | `K₁₃` | `0x00_0000_2000` | +| `s₂₈` | `Aᵥ₆` | `K[12..95]` | `K₁₂` | `0x00_0000_1000` | +| `s₂₉` | `Aᵥ₅` | `K[11..95]` | `K₁₁` | `0x00_0000_0800` | +| `s₃₀` | `Aᵥ₄` | `K[10..95]` | `K₁₀` | `0x00_0000_0400` | +| `s₃₁` | `Aᵥ₃` | `K[ 9..95]` | `K₉` | `0x00_0000_0200` | +| `s₃₂` | `Aᵥ₂` | `K[ 8..95]` | `K₈` | `0x00_0000_0100` | +| `s₃₃` | `Aᵥ₁` | `K[ 7..95]` | `K₇` | `0x00_0000_0080` | +| `s₃₄` | `Aᵥ₀` | `K[ 6..95]` | `K₆` | `0x00_0000_0040` | +| `s₃₅` | `Aₜ₁₉` | `K[ 5..95]` | `K₅` | `0x00_0000_0020` | +| `s₃₆` | `Aₜ₁₈` | `K[ 4..95]` | `K₄` | `0x00_0000_0010` | +| `s₃₇` | `Aₜ₁₇` | `K[ 3..95]` | `K₃` | `0x00_0000_0008` | +| `s₃₈` | `Aₜ₁₆` | `K[ 2..95]` | `K₂` | `0x00_0000_0004` | +| `s₃₉` | `Aₜ₁₅` | `K[ 1..95]` | `K₁` | `0x00_0000_0002` | +| `s₄₀` | `Aₜ₁₄` | `K[ 0..95]` | `K₀` | `0x00_0000_0001` | +| `s₄₁` | `Aₜ₁₃` | `K[ 0..95]` | ... | | +| `s₄₂` | `Aₜ₁₂` | `K[ 0..95]` | ... | | +| `s₄₃` | `Aₜ₁₁` | `K[ 0..95]` | ... | | +| `s₄₄` | `Aₜ₁₀` | `K[ 0..95]` | ... | | +| `s₄₅` | `Aₜ₉` | `K[ 0..95]` | ... | | +| `s₄₆` | `Aₜ₈` | `K[ 0..95]` | ... | | +| `s₄₇` | `Aₜ₇` | `K[ 0..95]` | ... | | +| `s₄₈` | `Aₜ₆` | `K[ 0..95]` | ... | | +| `s₄₉` | `Aₜ₅` | `K[ 0..95]` | ... | | +| `s₅₀` | `Aₜ₄` | `K[ 0..95]` | ... | | +| `s₅₁` | `Aₜ₃` | `K[ 0..95]` | ... | | +| `s₅₂` | `Aₜ₂` | `K[ 0..95]` | ... | | +| `s₅₃` | `Aₜ₁` | `K[ 0..95]` | ... | | +| `s₅₄` | `Aₜ₀` | `K[ 0..95]` | ... | | + +## 128k table ... too large to fit in IoT flash memory + +Although too large to fit, there are various two-level (boolean) logic +reduction techniques that can migrate from a truth table (e.g., the bitmap) +to a reduced set of logical operations that will obtain the same result. +(ref: Espresso) + +With the 128k bitmap converted to a truth table, a much more reduced set +of tables was found to generate the same results. There is no assurance +that this is the most optimal way to generate the results, but it is +an acceptably small solution ... small enough to even be implemented in +FPGA logic if desired. + +## Appendix of random notes (not organized) + +### EM4x70 Chip Memory Layout + +There are sixteen (`16x`) blocks of memory, each storing a 16-bit value. +Blocks may be protected (`P` column) as read-only (`RO`) or write-only (`WO`). +`Lock₀` === Disable writingPermanent write-prevention when set to 1. +`Lock₁` === Pin-code lock + +| `Block` | `P` | `Purpose` | Bits (LSB first) | Bits (MSB first) | +|---------|------|--------------|----------------------------|-----------------------------| +| ` 0` | ` ` | `user memory | bits 0..15` | `bits 15.. 0` | +| ` 1` | ` ` | `user memory | bits 16..29, lock0, lock1` | `lock₁, lock₀, bits 29..16` | +| ` 2` | `RO` | `id | bits 0..15` | `bits 15.. 0` | +| ` 3` | `RO` | `id | bits 16..31` | `bits 31..16` | +| ` 4` | `wo` | `crypto key | bits 0..15` | `bits 15.. 0` | +| ` 5` | `wo` | `crypto key | bits 16..31` | `bits 31..16` | +| ` 6` | `wo` | `crypto key | bits 32..47` | `bits 47..32` | +| ` 7` | `wo` | `crypto key | bits 48..63` | `bits 63..48` | +| ` 8` | `wo` | `crypto key | bits 64..79` | `bits 79..64` | +| ` 9` | `wo` | `crypto key | bits 80..95` | `bits 95..80` | +| `10` | `wo` | `pin code | bits 0..15` | `bits 15.. 0` | +| `11` | `wo` | `pin code | bits 16..31` | `bits 31..16` | +| `12` | ` ` | `user memory | bits 30..45` | `bits 45..30` | +| `13` | ` ` | `user memory | bits 46..61` | `bits 61..46` | +| `14` | ` ` | `user memory | bits 62..77` | `bits 77..62` | +| `15` | ` ` | `user memory | bits 78..93` | `bits 93..78` | + +### Vehicle authentication value - Data dependency + +Given: +* An EM4x70 (ID48) Transponder with a writable key +* The output filter `OF(X²⁰) -> r¹` function is a black box: + * The internal workings are not, themselves, known + * The 20-bit input for the output filter function `OF(X²⁰)` + can be calculated for `s₀..s₅₄`, given only `N` and `K` +* Exists a bitmap `OF_Known[2²⁰]` (128kb) indicating if, for + a given 20-bit input, the result `r¹` is known + * Initially, this is all set to zero (false). +* Exists a bitmap `OF_Result[2²⁰]` (128kb) indicating, for a given + 20-bit input, a known result `r¹`. + * Values are valid only when corresponding bit in `OF_Known` is set to one (true) + +The, starting with a single known valid trace: `K` + `[ N, Aᵥ, Aₜ]`: + +1. The starting valid trace fills in ~48 entries in `OF_Known`/`OF_Result` +2. By cycling through all `K''` having the same upper 91 bits, + 31 additional traces `[K'', N, Aᵥ]` are trivially created. + Each `K''` will share the first 28 output bits (`Aᵥ` is the same), + but have potentially 20 more unique internal states. + a. 31 instances x 20 bits per instance == 620 more potential entries + b. Subtotal: 668 entries known (0.06%) +3. By cycling through all `K'` having the same upper 80 bits, + with least significant 5 bits set to zero: + a. Brute-forcing the required value of `N'` takes at most 512 attempts + because `N(55..9) = N'(55..9)`. + b. On average, this takes 256 attempts. + b. As above, all other 31 values for `K''` will use the same `N'`, + allowing 668 additional output values to be potentially filled +4. Over time, `OF_Known` will trend towards being mostly populated + +### more random thoughts + +Can leave multiple pm3 running 24/7, logging results. + +Note that the initial state `S₀` is also known +(for that nonce) for ALL OTHER 2^40 keys that +share the same bits in `K[95..40]`. (!!!) + + +### earliest notes on branching technique + +Similar to Partial Key-Update Aₜtack, for creating mapping +of the output filter function `OF( x²⁰ ) --> bool` + +Given: +* Known private key `K` +* Known working data: { `Nonce[55..0]` , `AuthV[27..0]`, `AuthT²⁰` } +* ID48 Transponder with Rewritable Key +* Output bit does not alter any other cryptographic state + +* s₀ depends ONLY on { N, K[40..95] } +* sₙ depends ONLY on s(N-1) and K(40-N) --> { N, K[(40-N)..95] } + +* `s₀` depends ONLY on --> { `N`, `K[40..95]` } +* `s₁` --> { `N`, `K[39..95]` } +* `s₂` --> { `N`, `K[38..95]` } +* `s₃` --> { `N`, `K[37..95]` } +* `s₄` --> { `N`, `K[36..95]` } +* `s₅` --> { `N`, `K[35..95]` } +* `s₆` --> { `N`, `K[34..95]` } +* `s₇` `Aᵥ₂₇` --> { `N`, `K[33..95]` } +* `s₈` `Aᵥ₂₆` --> { `N`, `K[32..95]` } +* `s₉` `Aᵥ₂₅` --> { `N`, `K[31..95]` } +* `s₁₀` `Aᵥ₂₄` --> { `N`, `K[30..95]` } +* `s₁₁` `Aᵥ₂₃` --> { `N`, `K[29..95]` } +* `s₁₂` `Aᵥ₂₂` --> { `N`, `K[28..95]` } +* `s₁₃` `Aᵥ₂₁` --> { `N`, `K[27..95]` } +* `s₁₄` `Aᵥ₂₀` --> { `N`, `K[26..95]` } +* `s₁₅` `Aᵥ₁₉` --> { `N`, `K[25..95]` } +* `s₁₆` `Aᵥ₁₈` --> { `N`, `K[24..95]` } +* `s₁₇` `Aᵥ₁₇` --> { `N`, `K[23..95]` } +* `s₁₈` `Aᵥ₁₆` --> { `N`, `K[22..95]` } +* `s₁₉` `Aᵥ₁₅` --> { `N`, `K[21..95]` } +* `s₂₀` `Aᵥ₁₄` --> { `N`, `K[20..95]` } +* `s₂₁` `Aᵥ₁₃` --> { `N`, `K[19..95]` } +* `s₂₂` `Aᵥ₁₂` --> { `N`, `K[18..95]` } +* `s₂₃` `Aᵥ₁₁` --> { `N`, `K[17..95]` } +* `s₂₄` `Aᵥ₁₀` --> { `N`, `K[16..95]` } +* `s₂₅` `Aᵥ₉` --> { `N`, `K[15..95]` } +* `s₂₆` `Aᵥ₈` --> { `N`, `K[14..95]` } +* `s₂₇` `Aᵥ₇` --> { `N`, `K[13..95]` } +* `s₂₈` `Aᵥ₆` --> { `N`, `K[12..95]` } +* `s₂₉` `Aᵥ₅` --> { `N`, `K[11..95]` } +* `s₃₀` `Aᵥ₄` --> { `N`, `K[10..95]` } +* `s₃₁` `Aᵥ₃` --> { `N`, `K[ 9..95]` } +* `s₃₂` `Aᵥ₂` --> { `N`, `K[ 8..95]` } +* `s₃₃` `Aᵥ₁` --> { `N`, `K[ 7..95]` } +* `s₃₄` `Aᵥ₀` --> { `N`, `K[ 6..95]` } + +Therefore, if we write `K'` to a second transponder, +where `K' == K ^ 0x20` (flip bit 6) +then `Aᵥ'` == `Aᵥ[27..1]` + one random bit + +Therefore, by carefully selecting derived keys to +be written to transponders, it becomes trivial to +generate many successful authentication traces. + +Example: +Known valid trace: +[ K, N, Aᵥ ] == [ F32AA98CF5BE4ADFA6D3480B, 45F54ADA252AAC, 4866BB70 ] --> 9B D1 80 + +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3482B, 45F54ADA252AAC, 4866BB60 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3482B, 45F54ADA252AAC, 4866BB70 ] --> 4E BB D0 + +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3486B, 45F54ADA252AAC, 4866BB40 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3486B, 45F54ADA252AAC, 4866BB50 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3486B, 45F54ADA252AAC, 4866BB60 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3486B, 45F54ADA252AAC, 4866BB70 ] --> 39 55 90 + +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3484B, 45F54ADA252AAC, 4866BB60 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D3484B, 45F54ADA252AAC, 4866BB70 ] --> E8 60 D0 + +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB70 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB60 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB50 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB40 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB30 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB20 ] --> Fail +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB10 ] --> ED 9C 20 +[ K', N, Aᵥ' ] == [ F32AA98CF5BE4ADFA6D348DB, 45F54ADA252AAC, 4866BB00 ] --> Fail + +This has been CONFIRMED WORKING using actual hardware. + +See https://github.com/dorssel/usbipd-win/wiki/Automation#json + +This can avoid having to swap to Windows to re-connect if the +device disconnects/reconnects for any reason. + +### Branching Logic + +Function ExpandBy32() takes as input: +* 96-bit private key `K` +* 56-bit nonce `N` +* 28-bit valid vehicle auth `Aᵥ` + +Step 1. Write the private key `K` +Step 2. Validate authentication works with `N` and `Aᵥ` +Step 3. Set lowest 5 bits of `K` to zero +Step 4. For `i` in (0..31): + 4a. Set temporary key `K'` as `K+i` (set some of lowest 5 bits) + 4b. Write private key `K'` + 4c. Validate authentication works with `N` and `Aᵥ` + 4d. Verify received 20-bit response, `Aₜ` + 4e. For each success, print the set: { `K'`, `N`, `Aᵥ`, `Aₜ` } + + + +Function Branch() takes as input: +* 96-bit private key `K` +* 56-bit nonce `N` +* 28-bit valid vehicle auth `Aᵥ` (just `A` in below) + +VERIFY VALID INPUTS: +* Write the private key +* Validate authentication works with `N` and `Aᵥ` + +Then (using 2^16) potential authentications as maximum +Select a target key `K'`, where `K'[95..()]` + + +This is when the private key ***IS*** already known, +and you have a starting point. + + + +### My vehicle + +My 2004 Volvo S60 key originally had a pin code of 'AAAAAAAA'. + +Updating the pin code: +1. Get info: + In this example, block 1 data == `ED08`, (0b1110...) + + `lf em 4x70 info` + +2. Because Lockbit 0 was set, send the PIN to unlock: + + `lf em 4x70 unlock --pin AAAAAAAA` + +3. Verify successful unlock by checking LockBit0: + In this example, block 1 data == `AD08`, (0b1010...) + so LockBit1 = 1, LockBit0 = 0 == success. + + `lf em 4x70 info` + +4. Write the new pin code as DEADBEEF + + `lf em 4x70 writepin --pin DEADBEEF` + +5. Set lockbit0 to 1 (based on existing data in block1): + e.g, `AD08 | 4000 == ED08` + + `lf em 4x70 write --block 1 --data ED08` + + +[=] ------+----------+----------------------------- +[=] 3 | xx xx | ID (redacted) +[=] 2 | xx xx | ID (redacted) +[=] ------+----------+----------------------------- +[=] 1 | ED 08 | UM1 +[=] 0 | 87 7D | UM1 +[=] ------+----------+----------------------------- +[=] +[=] Tag ID: DB 4F B2 E8 +[=] Lockbit 0: 1 +[=] Lockbit 1: 1 +[=] Tag is LOCKED. + +### Demodulating the traces + +To be written. Generally, save as WAV file, +and then use more powerful tools than the data +viewer that is built into PM3 client. + + + +### fancy characters + +Symbols, subscripts, superscripts... + +``` +X₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎ₐₑₒₓₔₕₖₗₘₙₚₛₜⱼᵢᵣᵤᵥᵦᵧᵨᵩᵪ. +X⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾ⁿⁱ +⊕εx̄∧∨ +``` \ No newline at end of file diff --git a/client/deps/id48/id48.h b/client/deps/id48/id48.h new file mode 100644 index 000000000..1aa0002cc --- /dev/null +++ b/client/deps/id48/id48.h @@ -0,0 +1,206 @@ +/** + * The MIT License (MIT) + * + * Copyright (c) 2024 by Henry Gabryjelski + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in all + * copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + * + */ +#if !defined(ID48_H__) +#define ID48_H__ + +// This file defines only the structs and API surface. +// There are no dependencies on any external code. +#include +#include +#include +#if defined(NDEBUG) + #define ASSERT(x) ((void)0) +#elif defined(ID48_NO_STDIO) + #define ASSERT(x) ((void)0) +#else // neither NDEBUG nor ID48_NO_STDIO defined + #include + #include + #define ASSERT(x) assert((x)) +#endif + + +#if defined(__cplusplus) +extern "C" { +#endif + +/// +/// [0..11] stores K₉₅..K₀₀ +/// +/// +/// Big-endian, "native" bit order, when viewed linearly from k[ 0..11] +/// Mapping to the indices used in the research paper: +/// k[ 0] :== K₉₅..K₈₈ +/// k[ 1] :== K₈₇..K₈₀ +/// k[ 2] :== K₇₉..K₇₂ +/// k[ 3] :== K₇₁..K₆₄ +/// k[ 4] :== K₆₃..K₅₆ +/// k[ 5] :== K₅₅..K₄₈ +/// k[ 6] :== K₄₇..K₄₀ +/// k[ 7] :== K₃₉..K₃₂ +/// k[ 8] :== K₃₁..K₂₄ +/// k[ 9] :== K₂₃..K₁₆ +/// k[10] :== K₁₅..K₀₈ +/// k[11] :== K₀₇..K₀₀ +/// +typedef struct _ID48LIB_KEY { // 96-bit + uint8_t k[12]; +} ID48LIB_KEY; +/// +/// [0..6] stores N₅₅..N₀₀ +/// +/// +/// Big-endian, "native" bit order, when viewed linearly from rn[0..6] +/// Mapping to the indices used in the research paper: +/// rn[ 0] :== N₅₅..N₄₈ +/// rn[ 1] :== N₄₇..N₄₀ +/// rn[ 2] :== N₃₉..N₃₂ +/// rn[ 3] :== N₃₁..N₂₄ +/// rn[ 4] :== N₂₃..N₁₆ +/// rn[ 5] :== N₁₅..N₀₈ +/// rn[ 6] :== N₀₇..N₀₀ +/// +typedef struct _ID48LIB_NONCE { // 56-bit + uint8_t rn[7]; +} ID48LIB_NONCE; +/// +/// [0..3] stores O₀₀..O₂₇ 0000 +/// +/// +/// Big-endian, "bitstream" bit order, when viewed linearly from frn[0..3] +/// This is the order in which the research paper typically lists the bits. +/// Mapping to the indices used in the research paper, +/// where ( O₀₀ .. O₂₇ ) :== output(s₀₇,k₃₂..k₀₅ ) +/// then: +/// frn[ 0] :== O₀₀..O₀₇ +/// frn[ 1] :== O₀₈..O₁₅ +/// frn[ 2] :== O₁₆..O₂₃ +/// frn[ 3] :== O₂₄..O₂₇ 0000 +/// +typedef struct _ID48LIB_FRN { + uint8_t frn[4]; +} ID48LIB_FRN; +/// +/// [0..3] stores O₂₈..O₄₇ (12x 0) +/// +/// +/// Native format if viewed linearly from frn[0..6]. +/// Mapping to the indices used in the research paper, +/// where ( O₂₈ .. O₅₅ ) :== output( s₃₅, k₀₄..k₀₀ (15x 0) ) == grn +/// +/// then: +/// rn[ 0] :== O₂₈ .. O₃₅ +/// rn[ 1] :== O₃₆ .. O₄₃ +/// rn[ 2] :== O₄₄..O₄₇ 0000 +/// rn[ 3] :== 0000 0000 +/// +typedef struct _ID48LIB_GRN { + uint8_t grn[3]; +} ID48LIB_GRN; + +/// +/// When provided a key and nonce, will calculate +/// the frn and grn values and store in caller-provided +/// output parameters. +/// +/// +/// Note: In C++, each parameter would be a reference (not pointer). +/// +void id48lib_generator( + const ID48LIB_KEY* key_96bit, + const ID48LIB_NONCE* nonce_56bit, + ID48LIB_FRN* frn28_out, + ID48LIB_GRN* grn20_out + ); + +/// +/// Initializes to allow iterative recovery +/// of multiple potential keys. After calling +/// this init() function, can repeatedly call +/// the next() function until it returns false +/// to obtain all potential keys. +/// +/// +/// Top 48 bits of the key, such as those discovered +/// using the proxmark3 command `lf em 4x70 brute`. +/// Only k[0..5] are used from this parameter, +/// corresponding to K₉₅..K₄₈. +/// +/// +/// The nonce value. +/// Typically from a sniffed authentication. +/// +/// +/// The challenge sent from the reader (e.g., car) +/// to the tag (e.g., key). +/// Typically from a sniffed authentication. +/// +/// +/// The response sent from the tag (e.g., key) +/// to the car (e.g., car). +/// Typically from a sniffed authentication. +/// +/// +/// Note: In C++, each parameter would be a reference (not pointer). +/// +void id48lib_key_recovery_init( + const ID48LIB_KEY* input_partial_key, + const ID48LIB_NONCE* input_nonce, + const ID48LIB_FRN* input_frn, + const ID48LIB_GRN* input_grn +); +/// +/// This can be repeated called (after calling init()) +/// to find the next potential key for the given +/// partial key + nonce + frn + grn values. +/// I've seen combinations that have up to six +/// potential keys available, although typically +/// there are 1-3 results. +/// Each call to this function will return a single +/// value. Call repeatedly until the function returns +/// false to get all potential keys. +/// +/// +/// When the function returns true, this caller-provided +/// value will be filled with the 96-bit key that, when +/// programmed to the tag, should authenticate against +/// the nonce+frn values, with tag returning the grn value. +/// +/// +/// true when another potential key has been found. +/// false if no additional potential keys have been found. +/// +/// +/// Note: In C++, each parameter would be a reference (not pointer). +/// +bool id48lib_key_recovery_next( + ID48LIB_KEY* potential_key_output +); + +#if defined(__cplusplus) +} +#endif + +#endif // !defined(ID48_H__) + diff --git a/client/deps/id48/id48_data.c b/client/deps/id48/id48_data.c new file mode 100644 index 000000000..227dc348d --- /dev/null +++ b/client/deps/id48/id48_data.c @@ -0,0 +1,8366 @@ +/** + * The MIT License (MIT) + * + * Copyright (c) 2024 by Henry Gabryjelski + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in all + * copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + * + */ + +#include "id48_internals.h" + +#define LARGE_LUT_BIT_COUNT (0x100000ul) // thus the lookup parameter is uint20_t... +#define LARGE_LUT_ELEMENT_COUNT ( 0x20000ul) // LARGE_LUT_BIT_COUNT / 8u <-- causes compilation error? + +//_Static_assert((LARGE_LUT_BIT_COUNT % 8) == 0, ""); +static const uint8_t large_output_lut[LARGE_LUT_ELEMENT_COUNT] = { + 0x5a, 0x69, 0x69, 0x5a, 0xa5, 0x96, 0x96, 0xa5, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0x2e, 0xe2, 0xd1, + 0x5a, 0x96, 0x69, 0xa5, 0xa5, 0x69, 0x96, 0x5a, 0xe2, 0x2e, 0x1d, 0xd1, 0x1d, 0xd1, 0xe2, 0x2e, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0x5a, 0x69, 0x69, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0x2e, 0xe2, 0xd1, + 0xa5, 0x5a, 0x96, 0x69, 0x5a, 0xa5, 0x69, 0x96, 0xe2, 0x2e, 0x1d, 0xd1, 0x1d, 0xd1, 0xe2, 0x2e, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0xd1, 0xe2, 0x2e, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0x2e, 0x1d, 0xd1, + 0xa5, 0x96, 0x96, 0xa5, 0x5a, 0x69, 0x69, 0x5a, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0xd1, 0x1d, 0x2e, + 0xa5, 0x69, 0x96, 0x5a, 0x5a, 0x96, 0x69, 0xa5, 0x1d, 0xd1, 0xe2, 0x2e, 0xe2, 0x2e, 0x1d, 0xd1, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0xa5, 0x96, 0x96, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0xd1, 0x1d, 0x2e, + 0x5a, 0xa5, 0x69, 0x96, 0xa5, 0x5a, 0x96, 0x69, 0x1d, 0xd1, 0xe2, 0x2e, 0xe2, 0x2e, 0x1d, 0xd1, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0x2e, 0x1d, 0xd1, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0xd1, 0xe2, 0x2e, + 0x69, 0x69, 0x5a, 0x5a, 0x96, 0x96, 0xa5, 0xa5, 0xd1, 0xd1, 0x2e, 0x2e, 0x2e, 0x2e, 0xd1, 0xd1, + 0x69, 0x96, 0x5a, 0xa5, 0x96, 0x69, 0xa5, 0x5a, 0xd1, 0x2e, 0x2e, 0xd1, 0x2e, 0xd1, 0xd1, 0x2e, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0x69, 0x69, 0x5a, 0x5a, 0x96, 0x96, 0xa5, 0xa5, 0xd1, 0xd1, 0x2e, 0x2e, 0x2e, 0x2e, 0xd1, 0xd1, + 0x69, 0x96, 0x5a, 0xa5, 0x96, 0x69, 0xa5, 0x5a, 0xd1, 0x2e, 0x2e, 0xd1, 0x2e, 0xd1, 0xd1, 0x2e, + 0x69, 0x69, 0x5a, 0x5a, 0x96, 0x69, 0xa5, 0x5a, 0xd1, 0xd1, 0x2e, 0x2e, 0x2e, 0xd1, 0xd1, 0x2e, + 0x96, 0x96, 0xa5, 0xa5, 0x69, 0x96, 0x5a, 0xa5, 0x2e, 0x2e, 0xd1, 0xd1, 0xd1, 0x2e, 0x2e, 0xd1, + 0x96, 0x96, 0xa5, 0xa5, 0x69, 0x69, 0x5a, 0x5a, 0x2e, 0x2e, 0xd1, 0xd1, 0xd1, 0xd1, 0x2e, 0x2e, + 0x96, 0x69, 0xa5, 0x5a, 0x69, 0x96, 0x5a, 0xa5, 0x2e, 0xd1, 0xd1, 0x2e, 0xd1, 0x2e, 0x2e, 0xd1, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0x96, 0x96, 0xa5, 0xa5, 0x69, 0x69, 0x5a, 0x5a, 0x2e, 0x2e, 0xd1, 0xd1, 0xd1, 0xd1, 0x2e, 0x2e, + 0x96, 0x69, 0xa5, 0x5a, 0x69, 0x96, 0x5a, 0xa5, 0x2e, 0xd1, 0xd1, 0x2e, 0xd1, 0x2e, 0x2e, 0xd1, + 0x96, 0x96, 0xa5, 0xa5, 0x69, 0x96, 0x5a, 0xa5, 0x2e, 0x2e, 0xd1, 0xd1, 0xd1, 0x2e, 0x2e, 0xd1, + 0x69, 0x69, 0x5a, 0x5a, 0x96, 0x69, 0xa5, 0x5a, 0xd1, 0xd1, 0x2e, 0x2e, 0x2e, 0xd1, 0xd1, 0x2e, + 0x5a, 0x69, 0x69, 0x5a, 0xa5, 0x96, 0x96, 0xa5, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0x2e, 0xe2, 0xd1, + 0x5a, 0x96, 0x69, 0xa5, 0xa5, 0x69, 0x96, 0x5a, 0xe2, 0x2e, 0x1d, 0xd1, 0x1d, 0xd1, 0xe2, 0x2e, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0xa5, 0x96, 0x96, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0xd1, 0x1d, 0x2e, + 0x5a, 0xa5, 0x69, 0x96, 0xa5, 0x5a, 0x96, 0x69, 0x1d, 0xd1, 0xe2, 0x2e, 0xe2, 0x2e, 0x1d, 0xd1, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0x2e, 0x1d, 0xd1, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0xe2, 0xd1, 0x1d, 0x2e, 0x1d, 0xd1, 0xe2, 0x2e, + 0xa5, 0x96, 0x96, 0xa5, 0x5a, 0x69, 0x69, 0x5a, 0x1d, 0x2e, 0xe2, 0xd1, 0xe2, 0xd1, 0x1d, 0x2e, + 0xa5, 0x69, 0x96, 0x5a, 0x5a, 0x96, 0x69, 0xa5, 0x1d, 0xd1, 0xe2, 0x2e, 0xe2, 0x2e, 0x1d, 0xd1, + 0x5a, 0x5a, 0x69, 0x69, 0xa5, 0x5a, 0x96, 0x69, 0xe2, 0xe2, 0x1d, 0x1d, 0x1d, 0xe2, 0xe2, 0x1d, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0xa5, 0x69, 0x96, 0x1d, 0x1d, 0xe2, 0xe2, 0xe2, 0x1d, 0x1d, 0xe2, + 0xa5, 0xa5, 0x96, 0x96, 0x5a, 0x5a, 0x69, 0x69, 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0xcf, 0x4f, 0xcc, 0xff, 0xcc, 0x44, + 0x00, 0x00, 0x0f, 0x0f, 0x55, 0x55, 0x55, 0x55, + 0xcc, 0x00, 0xcf, 0x0f, 0xcc, 0x00, 0xcc, 0x00, +}; +/// g1_idx = (a << 4) | (l2 << 3) | (l3 << 2) | (l0 << 1) | (l6 << 0) +static const uint8_t small_lut_group1[4] = { // aka 32 bits + 0x4f, 0x92, 0xa1, 0x7c, +}; +/// g2_idx = (l5 << 4) | (b << 3) | (m0 << 2) | (l4 << 1) | (m1 << 0) +static const uint8_t small_lut_group2[4] = { // aka 32 bits + 0x8f, 0x52, 0x61, 0xbc, +}; +/// g3_idx = (m5 << 4) | (c << 3) | (r1 << 2) | (m3 << 1) | (r3 << 0) +static const uint8_t small_lut_group3[4] = { // aka 32 bits + 0x8f, 0x34, 0x61, 0xda, +}; +/// g4_idx = (r2 << 4) | (r4 << 3) | (r6 << 2) | (r0 << 1) | (r5 << 0) +static const uint8_t small_lut_group4[4] = { // aka 32 bits + 0x8f, 0x34, 0x52, 0xe9, +}; + +static inline bool get_bit(const uint8_t* table_start, uint32_t bit_idx) { + const uint32_t byte = bit_idx / 8u; + const uint8_t mask = 1u << (bit_idx % 8u); + return (table_start[byte] & mask) != 0; +} + +// +// NOTE: Additional optimizations possible, but not pursued. +// Could spend a lot of time to define more optimized version that directly +// takes ID48LIBX_STATE_REGISTERS as input. These optimizations may include +// changing the order of the bits in each intermediate lookup index (indices). +// Optimizations may also include modifying where a/b/c are stored in the +// ID48LIBX_STATE_REGISTER, such as shifting a/b/c from being stored at +// bits [03,02,01] to being stored at bit [61,60,59]. +// +// Q: Maybe move a/b/c to upper 32 bits? +// This would allow all bits and bitshifting to occur using only upper 32-bits. +// +// Note: Each set of bits for the lookup tables can be in any order, +// so long as the lookup tables are adjusted accordingly. +// +// Which bits are used for which small lookup table indixes? +// +// Bit: ₆₃ ₆₂ ₆₁ ₆₀ ₅₉ ₅₈ ₅₇ ₅₆ ₅₅ ₅₄ ₅₃ ₅₂ ₅₁ ₅₀ ₄₉ ₄₈ ₄₇ ₄₆ ₄₅ ₄₄ ₄₃ ₄₂ ₄₁ ₄₀ ₃₉ ₃₈ ₃₇ ₃₆ ₃₅ ₃₄ ₃₃ ₃₂ +// Reg: i j r₀₆ r₀₅ r₀₄ r₀₃ r₀₂ r₀₁ r₀₀ m₀₆ m₀₅ m₀₄ m₀₃ m₀₂ m₀₁ m₀₀ l₀₆ l₀₅ l₀₄ l₀₃ l₀₂ l₀₁ l₀₀ g₂₂ g₂₁ g₂₀ g₁₉ g₁₈ g₁₇ g₁₆ g₁₅ g₁₄ +// i_v i_v i_v i_v i_v i_v i_v i_v +// AAA AAA AAA AAA +// BBB BBB BBB BBB +// CCC CCC CCC CCC +// DDD DDD DDD DDD DDD +// +// Bit: ₃₁ ₃₀ ₂₉ ₂₈ ₂₇ ₂₆ ₂₅ ₂₄ ₂₃ ₂₂ ₂₁ ₂₀ ₁₉ ₁₈ ₁₇ ₁₆ ₁₅ ₁₄ ₁₃ ₁₂ ₁₁ ₁₀ ₀₉ ₀₈ ₀₇ ₀₆ ₀₅ ₀₄ ₀₃ ₀₂ ₀₁ ₀₀ +// Reg: g₁₃ g₁₂ g₁₁ g₁₀ g₀₉ g₀₈ g₀₇ g₀₆ g₀₅ g₀₄ g₀₃ g₀₂ g₀₁ g₀₀ h₁₂ h₁₁ h₁₀ h₀₉ h₀₈ h₀₇ h₀₆ h₀₅ h₀₄ h₀₃ h₀₂ h₀₁ h₀₀ _ a b c 0 +// AAA BBB CCC +// +// Example minor optimization of initial 8-bit lookup: +// =================================================== +// i_v depends on ==> r₀₅ ... r₀₃ ... ... r₀₀ ... ... ... m₀₃ ... m₀₁ ... l₀₆ ... ... l₀₄ ... ... ... l₀₀ +// So can reduce the number of operations somewhat as follows: +// ... r₀₅ ... r₀₃ ... ... ... ... +// r₀₀ ... ... ... m₀₃ ... ... ... +// ... ... ... ... ... m₀₁ ... l₀₆ +// ... ... l₀₄ ... ... ... l₀₀ ... +// Resulting in the following (slightly-improved) bit order for the lookup table index: +// r₀₀ r₀₅ l₀₄ r₀₃ m₀₃ m₀₁ l₀₀ l₀₆ +// +// alt_initial_v = // r₀₀ r₀₅ l₀₄ r₀₃ m₀₃ m₀₁ l₀₀ l₀₆ +// ((uint8_t)((r & (R05_BIT | R03_BIT)) >> (58 - 4))) | +// ((uint8_t)((r & (R00_BIT | M03_BIT)) >> (51 - 3))) | +// ((uint8_t)((r & (M01_BIT | L06_BIT)) >> (47 - 0))) | +// ((uint8_t)((r & (L04_BIT | L00_BIT)) >> (41 - 1))) ; +// + +static bool output_lookup_large_lut(uint32_t output_index) { + if (output_index >= LARGE_LUT_BIT_COUNT) { return false; } + return get_bit(large_output_lut, output_index); +} +static bool output_lookup_small_lut(uint32_t output_index) { + if (output_index >= LARGE_LUT_BIT_COUNT) { return false; } + // 1 1 1 1 1 1 1 1 1 1 + // 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 + // Fₒ( a b c l₀ l₂ l₃ l₄ l₅ l₆ m₀ m₁ m₃ m₅ r₀ r₁ r₂ r₃ r₄ r₅ r₆ ) + + const uint8_t initial_v = // i_v + ((output_index >> 9) & 0x80u) | // (l0 << 7) + ((output_index >> 7) & 0x40u) | // (l4 << 6) + ((output_index >> 6) & 0x20u) | // (l6 << 5) + ((output_index >> 5) & 0x10u) | // (m1 << 4) + ((output_index >> 5) & 0x08u) | // (m3 << 3) + ((output_index >> 4) & 0x04u) | // (r0 << 2) + ((output_index >> 2) & 0x02u) | // (r3 << 1) + ((output_index >> 1) & 0x01u) ; // (r5 << 0) + const uint8_t g1_v = // AAA + ((output_index >> 15) & 0x10u) | // ( a << 4) | + ((output_index >> 12) & 0x08u) | // (l2 << 3) | + ((output_index >> 12) & 0x04u) | // (l3 << 2) | + ((output_index >> 15) & 0x02u) | // (l0 << 1) | + ((output_index >> 11) & 0x01u) ; // (l6 << 0) ; + const uint8_t g2_v = // BBB + ((output_index >> 8) & 0x10u) | // (l5 << 4) | + ((output_index >> 15) & 0x08u) | // ( b << 3) | + ((output_index >> 8) & 0x04u) | // (m0 << 2) | + ((output_index >> 12) & 0x02u) | // (l4 << 1) | + ((output_index >> 9) & 0x01u) ; // (m1 << 0) ; + const uint8_t g3_v = // CCC + ((output_index >> 3) & 0x10u) | // (m5 << 4) | + ((output_index >> 14) & 0x08u) | // ( c << 3) | + ((output_index >> 3) & 0x04u) | // (r1 << 2) | + ((output_index >> 7) & 0x02u) | // (m3 << 1) | + ((output_index >> 3) & 0x01u) ; // (r3 << 0) ; + const uint8_t g4_v = // DDD + ((output_index >> 0) & 0x10u) | // (r2 << 4) | + ((output_index << 1) & 0x08u) | // (r4 << 3) | + ((output_index << 2) & 0x04u) | // (r6 << 2) | + ((output_index >> 5) & 0x02u) | // (r0 << 1) | + ((output_index >> 1) & 0x01u) ; // (r5 << 0) ; + bool result = get_bit(small_lut_initial, initial_v); + if (get_bit(small_lut_group1, g1_v)) result = !result; + if (get_bit(small_lut_group2, g2_v)) result = !result; + if (get_bit(small_lut_group3, g3_v)) result = !result; + if (get_bit(small_lut_group4, g4_v)) result = !result; + return result; +} + +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// +// ******************************************************************************************************************** // +// *** Everything above this line in the file is declared static, *** // +// *** which avoids polluting the global namespace. *** // +// *** Everything below is technically visible, but not necessarily an exported API. *** // +// *** In C++, this separation is much more easily achieved using an anonymous namespace. C'est la vie! *** // +// ******************************************************************************************************************** // +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + +bool id48libx_output_lookup(uint32_t output_index) { + //return output_lookup_large_lut(output_index); + return output_lookup_small_lut(output_index); +} diff --git a/client/deps/id48/id48_generator.c b/client/deps/id48/id48_generator.c new file mode 100644 index 000000000..7ae0e52a7 --- /dev/null +++ b/client/deps/id48/id48_generator.c @@ -0,0 +1,894 @@ +/** + * The MIT License (MIT) + * + * Copyright (c) 2024 by Henry Gabryjelski + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in all + * copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + * + */ +#include "id48_internals.h" + +typedef struct _INPUT_BITS2 { + // least significant 55 bits are valid/used; lsb == input₀₀ + uint64_t Raw; +} INPUT_BITS2; +typedef struct _OUTPUT_BITS2 { + // least significant 55 bits valid + // Raw₅₄..Raw₄₈ == ignored bits to get to s₀₇ + // Raw₄₇..Raw₂₀ == 28-bit challenge value frn + // Raw₁₉..Raw₀₀ == 20-bit response value grn + uint64_t Raw; +} OUTPUT_BITS2; +typedef struct _OUTPUT_INDEX2 { + // Opaque value for use in lookup of the output bit + // only least significant 20 bits are valid + uint32_t Raw; +} OUTPUT_INDEX2; + +#if !defined(nullptr) +#define nullptr ((void*)0) +#endif + +#pragma region // reverse_bits() +static inline uint8_t reverse_bits_08(uint8_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint8_t mask = (uint8_t)(~((uint8_t)(0u))); // equivalent to uint32_t mask = 0b11111111111111111111111111111111; + + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); // will convert mask to 0b00000000000000001111111111111111; + n = (uint8_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); // divide and conquer + } + return n; +} +static inline uint16_t reverse_bits_16(uint16_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint16_t mask = (uint16_t)(~((uint16_t)(0u))); // equivalent to uint32_t mask = 0b11111111111111111111111111111111; + + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); // will convert mask to 0b00000000000000001111111111111111; + n = (uint16_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); // divide and conquer + } + return n; +} +static inline uint32_t reverse_bits_32(uint32_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint32_t mask = (uint32_t)(~((uint32_t)(0u))); // equivalent to uint32_t mask = 0b11111111111111111111111111111111; + + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); // will convert mask to 0b00000000000000001111111111111111; + n = (uint32_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); // divide and conquer + } + return n; +} +static inline uint64_t reverse_bits_64(uint64_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint64_t mask = (uint64_t)(~((uint64_t)(0u))); // equivalent to uint32_t mask = 0b11111111111111111111111111111111; + + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); // will convert mask to 0b00000000000000001111111111111111; + n = (uint64_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); // divide and conquer + } + return n; +} +#pragma endregion // reverse_bits() + +#pragma region // id48lib state register +// Bit: ₆₃ ₆₂ ₆₁ ₆₀ ₅₉ ₅₈ ₅₇ ₅₆ ₅₅ ₅₄ ₅₃ ₅₂ ₅₁ ₅₀ ₄₉ ₄₈ ₄₇ ₄₆ ₄₅ ₄₄ ₄₃ ₄₂ ₄₁ ₄₀ ₃₉ ₃₈ ₃₇ ₃₆ ₃₅ ₃₄ ₃₃ ₃₂ +// Reg: x x x r₀₆ r₀₅ r₀₄ r₀₃ r₀₂ r₀₁ r₀₀ m₀₆ m₀₅ m₀₄ m₀₃ m₀₂ m₀₁ m₀₀ l₀₆ l₀₅ l₀₄ l₀₃ l₀₂ l₀₁ l₀₀ g₂₂ g₂₁ g₂₀ g₁₉ g₁₈ g₁₇ g₁₆ g₁₅ +// +// Bit: ₃₁ ₃₀ ₂₉ ₂₈ ₂₇ ₂₆ ₂₅ ₂₄ ₂₃ ₂₂ ₂₁ ₂₀ ₁₉ ₁₈ ₁₇ ₁₆ ₁₅ ₁₄ ₁₃ ₁₂ ₁₁ ₁₀ ₀₉ ₀₈ ₀₇ ₀₆ ₀₅ ₀₄ ₀₃ ₀₂ ₀₁ ₀₀ +// Reg: g₁₄ g₁₃ g₁₂ g₁₁ g₁₀ g₀₉ g₀₈ g₀₇ g₀₆ g₀₅ g₀₄ g₀₃ g₀₂ g₀₁ g₀₀ h₁₂ h₁₁ h₁₀ h₀₉ h₀₈ h₀₇ h₀₆ h₀₅ h₀₄ h₀₃ h₀₂ h₀₁ h₀₀ x x x 1 +#pragma endregion // id48lib state register +#pragma region // bit definitions for the (stable) id48lib state register +// 63 +// #define SSR_BIT_i 62 -- could do this ... one fewer parameter +// 61 +#define SSR_BIT_R06 60 +#define SSR_BIT_R05 59 +#define SSR_BIT_R04 58 +#define SSR_BIT_R03 57 +#define SSR_BIT_R02 56 +#define SSR_BIT_R01 55 +#define SSR_BIT_R00 54 +#define SSR_BIT_M06 53 +#define SSR_BIT_M05 52 +#define SSR_BIT_M04 51 +#define SSR_BIT_M03 50 +#define SSR_BIT_M02 49 +#define SSR_BIT_M01 48 +#define SSR_BIT_M00 47 +#define SSR_BIT_L06 46 +#define SSR_BIT_L05 45 +#define SSR_BIT_L04 44 +#define SSR_BIT_L03 43 +#define SSR_BIT_L02 42 +#define SSR_BIT_L01 41 +#define SSR_BIT_L00 40 +#define SSR_BIT_G22 39 +#define SSR_BIT_G21 38 +#define SSR_BIT_G20 37 +#define SSR_BIT_G19 36 +#define SSR_BIT_G18 35 +#define SSR_BIT_G17 34 +#define SSR_BIT_G16 33 +#define SSR_BIT_G15 32 +#define SSR_BIT_G14 31 +#define SSR_BIT_G13 30 +#define SSR_BIT_G12 29 +#define SSR_BIT_G11 28 +#define SSR_BIT_G10 27 +#define SSR_BIT_G09 26 +#define SSR_BIT_G08 25 +#define SSR_BIT_G07 24 +#define SSR_BIT_G06 23 +#define SSR_BIT_G05 22 +#define SSR_BIT_G04 21 +#define SSR_BIT_G03 20 +#define SSR_BIT_G02 19 +#define SSR_BIT_G01 18 +#define SSR_BIT_G00 17 +#define SSR_BIT_H12 16 +#define SSR_BIT_H11 15 +#define SSR_BIT_H10 14 +#define SSR_BIT_H09 13 +#define SSR_BIT_H08 12 +#define SSR_BIT_H07 11 +#define SSR_BIT_H06 10 +#define SSR_BIT_H05 9 +#define SSR_BIT_H04 8 +#define SSR_BIT_H03 7 +#define SSR_BIT_H02 6 +#define SSR_BIT_H01 5 +#define SSR_BIT_H00 4 +// 3 // used only when unstable (during calculations) +// 2 // used only when unstable (during calculations) +// 1 // used only when unstable (during calculations) +// 0 // 1 == stable, 0 == unstable (during calculations) +#pragma endregion // bit definitions for the (stable) id48lib state register +#pragma region // Unstable (during calculations) id48lib state register +// Bit: ₆₃ ₆₂ ₆₁ ₆₀ ₅₉ ₅₈ ₅₇ ₅₆ ₅₅ ₅₄ ₅₃ ₅₂ ₅₁ ₅₀ ₄₉ ₄₈ ₄₇ ₄₆ ₄₅ ₄₄ ₄₃ ₄₂ ₄₁ ₄₀ ₃₉ ₃₈ ₃₇ ₃₆ ₃₅ ₃₄ ₃₃ ₃₂ +// Reg: i j r₀₆ r₀₅ r₀₄ r₀₃ r₀₂ r₀₁ r₀₀ m₀₆ m₀₅ m₀₄ m₀₃ m₀₂ m₀₁ m₀₀ l₀₆ l₀₅ l₀₄ l₀₃ l₀₂ l₀₁ l₀₀ g₂₂ g₂₁ g₂₀ g₁₉ g₁₈ g₁₇ g₁₆ g₁₅ g₁₄ +// +// Bit: ₃₁ ₃₀ ₂₉ ₂₈ ₂₇ ₂₆ ₂₅ ₂₄ ₂₃ ₂₂ ₂₁ ₂₀ ₁₉ ₁₈ ₁₇ ₁₆ ₁₅ ₁₄ ₁₃ ₁₂ ₁₁ ₁₀ ₀₉ ₀₈ ₀₇ ₀₆ ₀₅ ₀₄ ₀₃ ₀₂ ₀₁ ₀₀ +// Reg: g₁₃ g₁₂ g₁₁ g₁₀ g₀₉ g₀₈ g₀₇ g₀₆ g₀₅ g₀₄ g₀₃ g₀₂ g₀₁ g₀₀ h₁₂ h₁₁ h₁₀ h₀₉ h₀₈ h₀₇ h₀₆ h₀₅ h₀₄ h₀₃ h₀₂ h₀₁ h₀₀ _ a b c 0 +#pragma endregion // Unstable (during calculations) id48lib state register +// +// Summary of XOR baseline that can be excluded because they are part of a single 64-bit `<< 1` operation: +// g₀₀ <-- h₁₂ +// l₀₀ <-- g₂₂ +// m₀₀ <-- l₀₆ +// r₀₀ <-- m₀₆ +// +#pragma region // bit definitions for the (unstable) id48lib state register +#define SSR_UNSTABLE_BIT_i 63 +#define SSR_UNSTABLE_BIT_j 62 +#define SSR_UNSTABLE_OLD_BIT_R06 61 // valid only during calculations aka R07 ... just has to have a name... doesn't matter what +#define SSR_UNSTABLE_OLD_BIT_R05 60 +#define SSR_UNSTABLE_OLD_BIT_R04 59 +#define SSR_UNSTABLE_OLD_BIT_R03 58 +#define SSR_UNSTABLE_OLD_BIT_R02 57 +#define SSR_UNSTABLE_OLD_BIT_R01 56 +#define SSR_UNSTABLE_OLD_BIT_R00 55 +#define SSR_UNSTABLE_OLD_BIT_M06 54 +#define SSR_UNSTABLE_OLD_BIT_M05 53 +#define SSR_UNSTABLE_OLD_BIT_M04 52 +#define SSR_UNSTABLE_OLD_BIT_M03 51 +#define SSR_UNSTABLE_OLD_BIT_M02 50 +#define SSR_UNSTABLE_OLD_BIT_M01 49 +#define SSR_UNSTABLE_OLD_BIT_M00 48 +#define SSR_UNSTABLE_OLD_BIT_L06 47 +#define SSR_UNSTABLE_OLD_BIT_L05 46 +#define SSR_UNSTABLE_OLD_BIT_L04 45 +#define SSR_UNSTABLE_OLD_BIT_L03 44 +#define SSR_UNSTABLE_OLD_BIT_L02 43 +#define SSR_UNSTABLE_OLD_BIT_L01 42 +#define SSR_UNSTABLE_OLD_BIT_L00 41 +#define SSR_UNSTABLE_OLD_BIT_G22 40 +#define SSR_UNSTABLE_OLD_BIT_G21 39 +#define SSR_UNSTABLE_OLD_BIT_G20 38 +#define SSR_UNSTABLE_OLD_BIT_G19 37 +#define SSR_UNSTABLE_OLD_BIT_G18 36 +#define SSR_UNSTABLE_OLD_BIT_G17 35 +#define SSR_UNSTABLE_OLD_BIT_G16 34 +#define SSR_UNSTABLE_OLD_BIT_G15 33 +#define SSR_UNSTABLE_OLD_BIT_G14 32 +#define SSR_UNSTABLE_OLD_BIT_G13 31 +#define SSR_UNSTABLE_OLD_BIT_G12 30 +#define SSR_UNSTABLE_OLD_BIT_G11 29 +#define SSR_UNSTABLE_OLD_BIT_G10 28 +#define SSR_UNSTABLE_OLD_BIT_G09 27 +#define SSR_UNSTABLE_OLD_BIT_G08 26 +#define SSR_UNSTABLE_OLD_BIT_G07 25 +#define SSR_UNSTABLE_OLD_BIT_G06 24 +#define SSR_UNSTABLE_OLD_BIT_G05 23 +#define SSR_UNSTABLE_OLD_BIT_G04 22 +#define SSR_UNSTABLE_OLD_BIT_G03 21 +#define SSR_UNSTABLE_OLD_BIT_G02 20 +#define SSR_UNSTABLE_OLD_BIT_G01 19 +#define SSR_UNSTABLE_OLD_BIT_G00 18 +#define SSR_UNSTABLE_OLD_BIT_H12 17 +#define SSR_UNSTABLE_OLD_BIT_H11 16 +#define SSR_UNSTABLE_OLD_BIT_H10 15 +#define SSR_UNSTABLE_OLD_BIT_H09 14 +#define SSR_UNSTABLE_OLD_BIT_H08 13 +#define SSR_UNSTABLE_OLD_BIT_H07 12 +#define SSR_UNSTABLE_OLD_BIT_H06 11 +#define SSR_UNSTABLE_OLD_BIT_H05 10 +#define SSR_UNSTABLE_OLD_BIT_H04 9 +#define SSR_UNSTABLE_OLD_BIT_H03 8 +#define SSR_UNSTABLE_OLD_BIT_H02 7 +#define SSR_UNSTABLE_OLD_BIT_H01 6 +#define SSR_UNSTABLE_OLD_BIT_H00 5 +#define SSR_UNSTABLE_NEW_BIT_H00 4 // ... new value of H00 goes here ... +#define SSR_UNSTABLE_BIT_a 3 // valid only during calculations (ssr & 0b1 == 0b0), else ??? +#define SSR_UNSTABLE_BIT_b 2 // valid only during calculations (ssr & 0b1 == 0b0), else ??? +#define SSR_UNSTABLE_BIT_c 1 // valid only during calculations (ssr & 0b1 == 0b0), else ??? +// 0 // == 0 value defines as unstable state +#pragma endregion // bit definitions for the (stable) id48lib state register +#pragma region // single bit test/set/clear/flip/assign +static inline bool is_ssr_state_stable (const ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(ssr != nullptr); return ((ssr->Raw & 1u) == 1u); } +static inline bool test_single_ssr_bit (const ID48LIBX_STATE_REGISTERS* ssr, size_t bit_index) { ASSERT(ssr != nullptr); ASSERT(bit_index < (sizeof(uint64_t) * 8)); return ((ssr->Raw) >> bit_index) & 1; } +static inline void set_single_ssr_bit ( ID48LIBX_STATE_REGISTERS* ssr, size_t bit_index) { ASSERT(ssr != nullptr); ASSERT(bit_index < (sizeof(uint64_t) * 8)); ssr->Raw |= ((uint64_t)(1ull << bit_index)); } +static inline void clear_single_ssr_bit ( ID48LIBX_STATE_REGISTERS* ssr, size_t bit_index) { ASSERT(ssr != nullptr); ASSERT(bit_index < (sizeof(uint64_t) * 8)); ssr->Raw &= ~((uint64_t)(1ull << bit_index)); } +static inline void flip_single_ssr_bit ( ID48LIBX_STATE_REGISTERS* ssr, size_t bit_index) { ASSERT(ssr != nullptr); ASSERT(bit_index < (sizeof(uint64_t) * 8)); ssr->Raw ^= ((uint64_t)(1ull << bit_index)); } +static inline void assign_single_ssr_bit ( ID48LIBX_STATE_REGISTERS* ssr, size_t bit_index, bool value) { + ASSERT(ssr != nullptr); + ASSERT(bit_index < (sizeof(uint64_t) * 8)); + if (value) { + set_single_ssr_bit(ssr, bit_index); + } + else { + clear_single_ssr_bit(ssr, bit_index); + } +} +#pragma endregion // single bit test/set/clear/flip/assign +#pragma region // test/assign of temporaries a/b/c/i/j +static inline void test_temporary_a(ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(!is_ssr_state_stable(ssr)); test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a); } +static inline void test_temporary_b(ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(!is_ssr_state_stable(ssr)); test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b); } +static inline void test_temporary_c(ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(!is_ssr_state_stable(ssr)); test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c); } +static inline void test_temporary_i(ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(!is_ssr_state_stable(ssr)); test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i); } +static inline void test_temporary_j(ID48LIBX_STATE_REGISTERS* ssr) { ASSERT(!is_ssr_state_stable(ssr)); test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j); } + +static inline void assign_temporary_a(ID48LIBX_STATE_REGISTERS* ssr, bool v) { ASSERT(!is_ssr_state_stable(ssr)); assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a, v); } +static inline void assign_temporary_b(ID48LIBX_STATE_REGISTERS* ssr, bool v) { ASSERT(!is_ssr_state_stable(ssr)); assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b, v); } +static inline void assign_temporary_c(ID48LIBX_STATE_REGISTERS* ssr, bool v) { ASSERT(!is_ssr_state_stable(ssr)); assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c, v); } +static inline void assign_temporary_i(ID48LIBX_STATE_REGISTERS* ssr, bool v) { ASSERT(!is_ssr_state_stable(ssr)); assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i, v); } +static inline void assign_temporary_j(ID48LIBX_STATE_REGISTERS* ssr, bool v) { ASSERT(!is_ssr_state_stable(ssr)); assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j, v); } +#pragma endregion // test/assign of temporaries a/b/c/i/j + +#pragma region // Mask & Macro to get registers (in minimal bit form) +// ------------------------> 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 0 +// | | | | | | | | | | | | | | | | +#define SSR_BITMASK_REG_H (0x000000000001FFF0ull) // (0b0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0001'1111'1111'1111'0000ull) +#define SSR_BITMASK_REG_G (0x000000FFFFFE0000ull) // (0b0000'0000'0000'0000'0000'0000'1111'1111'1111'1111'1111'1110'0000'0000'0000'0000ull) +#define SSR_BITMASK_REG_L (0x00007F0000000000ull) // (0b0000'0000'0000'0000'0111'1111'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000ull) +#define SSR_BITMASK_REG_M (0x003F100000000000ull) // (0b0000'0000'0011'1111'1000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000ull) +#define SSR_BITMASK_REG_R (0x1FC0000000000000ull) // (0b0001'1111'1100'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000'0000ull) +#define SSR_BITMASK_REG_ALL (0x1FFFFFFFFFFFFFF0ull) // (0b0001'1111'1111'1111'1111'1111'1111'1111'1111'1111'1111'1111'1111'1111'1111'0000ull) +// | | | | | | | | | | | | | | | | +// ------------------------> 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 0 + +#define SSR_BITMASK_WITHOUT_REG_H (~(SSR_BITMASK_REG_H)) +#define SSR_BITMASK_WITHOUT_REG_G (~(SSR_BITMASK_REG_G)) +#define SSR_BITMASK_WITHOUT_REG_L (~(SSR_BITMASK_REG_L)) +#define SSR_BITMASK_WITHOUT_REG_M (~(SSR_BITMASK_REG_M)) +#define SSR_BITMASK_WITHOUT_REG_R (~(SSR_BITMASK_REG_R)) +#define SSR_BITMASK_WITHOUT_ANY_REGS (~(SSR_BITMASK_REG_ALL)) +#define SSR_SHIFT_COUNT_REG_H ( 4) +#define SSR_SHIFT_COUNT_REG_G (17) +#define SSR_SHIFT_COUNT_REG_L (40) +#define SSR_SHIFT_COUNT_REG_M (47) +#define SSR_SHIFT_COUNT_REG_R (54) +#define SSR_VALUE_MASK_REG_H (0x001FFFu) // 13 bits +#define SSR_VALUE_MASK_REG_G (0x7FFFFFu) // 23 bits +#define SSR_VALUE_MASK_REG_L (0x00007Fu) // 7 bits +#define SSR_VALUE_MASK_REG_M (0x00007Fu) // 7 bits +#define SSR_VALUE_MASK_REG_R (0x00007Fu) // 7 bits + +static inline uint16_t get_register_h(const ID48LIBX_STATE_REGISTERS* ssr) { return ((uint16_t)(ssr->Raw >> SSR_SHIFT_COUNT_REG_H)) & (SSR_VALUE_MASK_REG_H); } +static inline uint32_t get_register_g(const ID48LIBX_STATE_REGISTERS* ssr) { return ((uint32_t)(ssr->Raw >> SSR_SHIFT_COUNT_REG_G)) & (SSR_VALUE_MASK_REG_G); } +static inline uint8_t get_register_l(const ID48LIBX_STATE_REGISTERS* ssr) { return ((uint8_t )(ssr->Raw >> SSR_SHIFT_COUNT_REG_L)) & (SSR_VALUE_MASK_REG_L); } +static inline uint8_t get_register_m(const ID48LIBX_STATE_REGISTERS* ssr) { return ((uint8_t )(ssr->Raw >> SSR_SHIFT_COUNT_REG_M)) & (SSR_VALUE_MASK_REG_M); } +static inline uint8_t get_register_r(const ID48LIBX_STATE_REGISTERS* ssr) { return ((uint8_t )(ssr->Raw >> SSR_SHIFT_COUNT_REG_R)) & (SSR_VALUE_MASK_REG_R); } + +static inline void set_register_h(ID48LIBX_STATE_REGISTERS* ssr, uint16_t v) { ASSERT((v & SSR_VALUE_MASK_REG_H) == v); ssr->Raw = (ssr->Raw & SSR_BITMASK_WITHOUT_REG_H) | (((uint64_t)(v & SSR_VALUE_MASK_REG_H)) << SSR_SHIFT_COUNT_REG_H); } +static inline void set_register_g(ID48LIBX_STATE_REGISTERS* ssr, uint32_t v) { ASSERT((v & SSR_VALUE_MASK_REG_G) == v); ssr->Raw = (ssr->Raw & SSR_BITMASK_WITHOUT_REG_G) | (((uint64_t)(v & SSR_VALUE_MASK_REG_G)) << SSR_SHIFT_COUNT_REG_G); } +static inline void set_register_l(ID48LIBX_STATE_REGISTERS* ssr, uint8_t v) { ASSERT((v & SSR_VALUE_MASK_REG_L) == v); ssr->Raw = (ssr->Raw & SSR_BITMASK_WITHOUT_REG_L) | (((uint64_t)(v & SSR_VALUE_MASK_REG_L)) << SSR_SHIFT_COUNT_REG_L); } +static inline void set_register_m(ID48LIBX_STATE_REGISTERS* ssr, uint8_t v) { ASSERT((v & SSR_VALUE_MASK_REG_M) == v); ssr->Raw = (ssr->Raw & SSR_BITMASK_WITHOUT_REG_M) | (((uint64_t)(v & SSR_VALUE_MASK_REG_M)) << SSR_SHIFT_COUNT_REG_M); } +static inline void set_register_r(ID48LIBX_STATE_REGISTERS* ssr, uint8_t v) { ASSERT((v & SSR_VALUE_MASK_REG_R) == v); ssr->Raw = (ssr->Raw & SSR_BITMASK_WITHOUT_REG_R) | (((uint64_t)(v & SSR_VALUE_MASK_REG_R)) << SSR_SHIFT_COUNT_REG_R); } +#pragma endregion // Mask & Macro to get registers (in minimal bit form) + +/// +/// Calculates and returns 56-bit value p₅₅..p₀₀ +/// per Definition 3.11: +/// p = p₀₀..p₅₅ = ( K₄₀..K₉₅ ) + ( N₀₀..N₅₅ ) +/// +/// key in pm3 order +/// nonce in pm3 order +/// 56-bit value p₅₅..p₀₀ +static inline uint64_t calculate__p55_p00(const ID48LIB_KEY* k96, const ID48LIB_NONCE* n56) { + // messy ... have to reverse the bits AND shift them into position, + // perform the addition, and then reverse bits again to return to + // native bit order (subscript is same as bit position). + // + // 1. for each byte, reverse bit order and shift into 64-bit tmp + // 2. add the two 56-bit tmp values + // 3. keeping only low 56-bit bits... reverse the bits + ASSERT(k96 != nullptr); + ASSERT(n56 != nullptr); + uint64_t k40_k95 = 0; + uint64_t n00_n55 = 0; + // + // k [ 6] :== K₄₇..K₄₀ + // ... + // k [ 0] :== K₉₅..K₈₈ + // + // rn[ 6] :== N₀₇..N₀₀ + // ... + // rn[ 0] :== N₅₅..N₄₈ + // + for (int8_t i = 6; i >= 0; --i) { + k40_k95 <<= 8; + n00_n55 <<= 8; + uint8_t t1 = reverse_bits_08(k96->k[i]); + k40_k95 |= t1; + uint8_t t2 = reverse_bits_08(n56->rn[i]); + n00_n55 |= t2; + } + uint64_t result = k40_k95 + n00_n55; + // shift so msb == p₀₀ (p₀₀..p₅₅0⁸) + result <<= 8; + // reverse the 64-bit value to get: 0⁸p₅₅..p₀₀ + result = reverse_bits_64(result); + return result; +} +/// +/// Calculate and return q₄₃..q₀₀ +/// per Definition 3.11: +/// bitstream_q = (p₀₂ ... p₄₅) ⊕ (p₀₈ ... p₅₁) ⊕ (p₁₂ ... p₅₅) +/// <-- 44b --> <-- 44b --> <-- 44b --> +/// q43_q00 = (p₄₅ ... p₀₂) ⊕ (p₅₁ ... p₀₈) ⊕ (p₅₅ ... p₁₂) +/// +/// 56 bit value: p₅₅..p₀₀ +/// 44-bit value: q₄₃..q₀₀ +static inline uint64_t calculate__q43_q00(const uint64_t* p55_p00) { + ASSERT(p55_p00 != nullptr); + static const uint64_t C_BITMASK44 = (1ull << 44) - 1u; + uint64_t result = (*p55_p00 >> 2); + result ^= (*p55_p00 >> 8); + result ^= (*p55_p00 >> 12); + result &= C_BITMASK44; + return result; +} + + +/// +/// Relies on old g22 bit (now in L00). +/// May modify G00, G03, G04, G05, G06, G13, G16 +/// +static inline void g_successor(ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + ASSERT(!is_ssr_state_stable(ssr)); + assign_single_ssr_bit(ssr, SSR_BIT_G00, test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j)); + //alternatively: set to zero, because `j` includes the start bit state + //if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j)) { + // flip_single_ssr_bit(ssr, SSR_BIT_G00); + //} + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G22)) { + // taps ==> [ n, 16, 13, 6, 5, 3, 0 ] + // 0b000'0001'0010'0000'0110'1001 == 0x012069 + static const uint64_t G22_XOR_MASK = 0x0000000240D20000ull; + // static assert is only available in C11 (or C++11) and later... + // _Static_assert(G22_XOR_MASK == (0x012069ull << SSR_SHIFT_COUNT_REG_G), "G22 XOR Mask invalid"); + ssr->Raw ^= G22_XOR_MASK; + } + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i)) { + flip_single_ssr_bit(ssr, SSR_BIT_G04); + } +} + +static inline ID48LIBX_STATE_REGISTERS init_id48libx_state_register(const ID48LIB_KEY* k96, const ID48LIB_NONCE* n56) { + ASSERT(k96 != nullptr); + ASSERT(n56 != nullptr); + ID48LIBX_STATE_REGISTERS result; result.Raw = 0; + ID48LIBX_STATE_REGISTERS* const ssr = &result; // the pointer is constant ... not the value it points to + + const uint64_t p55_p00 = calculate__p55_p00(k96, n56); + // p55_p00 is used to set initial value of register l + if (true) { + static const uint8_t C_BITMASK7 = ((1u << 7) - 1u); + const uint8_t l = ( + ((uint8_t)(p55_p00 >> 55)) ^ // 0 0 0 0 0 0 p55 + ((uint8_t)(p55_p00 >> 51)) ^ // 0 0 p55 p54 p53 p52 p51 + ((uint8_t)(p55_p00 >> 45)) // p51 p50 p49 p48 p47 p46 p45 + ) & C_BITMASK7; + set_register_l(ssr, l); + ASSERT(l == get_register_l(ssr)); + } + + // p is used to calculate q + const uint64_t q43_q00 = calculate__q43_q00(&p55_p00); + + // init( q₂₀..q₄₂, q₀₀..q₁₉ ) + // ===> G(q₂₀..q₄₂, 0, q₀₀..q₁₉) + // ===> g₀₀..g₂₂ :=== q₂₀..q₄₂ + // and j₀₀..j₁₉ :=== q₀₀..q₁₉ + // + // But, since I'm storing the register with g₀₀ as lsb: + // ===> g₂₂..g₀₀ :=== q₄₂..q₂₀ + if (true) { + static const uint32_t C_BITMASK23 = ((1u << 23) - 1u); + const uint32_t g = ((uint32_t)(q43_q00 >> 20)) & C_BITMASK23; + set_register_g(ssr, g); + ASSERT(g == get_register_g(ssr)); + } + + // input bits for `j` during init are q00..q19, with q19 used first + // For ease of use, I'll generate this as q00..q19, so the loop + // can test the lsb (and then shift it right one bit) + uint32_t q00_q19 = reverse_bits_32( ((uint32_t)q43_q00) << 12 ); + uint32_t q_lsb_next = q00_q19; + ssr->Raw |= 1u; + + // G(g,0,j) twenty times, using q19, q18, ... q00 for `j` + for (uint8_t ix = 0; ix < 20; ++ix) + { + ASSERT(is_ssr_state_stable(ssr)); + ssr->Raw <<= 1; // starts the process ... it's now an unstable value + ASSERT(!is_ssr_state_stable(ssr)); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j, (q_lsb_next & 1u) != 0); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i, 0); + q_lsb_next >>= 1; + + g_successor(ssr); + // save only the register bits + ssr->Raw &= SSR_BITMASK_REG_ALL; + // mark this as a stable value + ssr->Raw |= 1u; + } + + // h00..h12 is defined as 0 p00..p11 + // but since we're storing h as h12..h00: p11..p00 0 + if (true) { + // NOTE: delay `h` until loops done, else low bits + // will shift into / break calculation of g() above + static const uint16_t C_BITMASK_H_INIT = (1u << 13) - 2u; // 0b1'1111'1111'1110 + const uint16_t h = (((uint16_t)p55_p00) << 1) & C_BITMASK_H_INIT; + set_register_h(ssr, h); + ASSERT(h == get_register_h(ssr)); + } + return result; +} + +/// +/// H(h) matches the research paper, definition 3.3 +/// +/// Reads bits H01, H08, H09, H11, H12. +/// +/// +/// If ssr is in unstable state, caller is responsible for ensuring +/// the values have not changed. +/// +static inline bool calculate_feedback_h(const ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + // ( h₀₁ && h₀₈ ) || ( h₀₉ && h₁₁ ) || (!h₁₂ ) + // \____ a1 ____/ \____ a2 ____/ \____ a3 ____/ + // result == xor(a1,a2,a3) + bool a1 = is_ssr_state_stable(ssr) ? + test_single_ssr_bit(ssr, SSR_BIT_H01) && test_single_ssr_bit(ssr, SSR_BIT_H08) : + test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H01) && test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H08); + bool a2 = is_ssr_state_stable(ssr) ? + test_single_ssr_bit(ssr, SSR_BIT_H09) && test_single_ssr_bit(ssr, SSR_BIT_H11) : + test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H09) && test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H11); + bool a3 = is_ssr_state_stable(ssr) ? + !test_single_ssr_bit(ssr, SSR_BIT_H12) : + !test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H12); + bool result = false; + if (a1) result = !result; + if (a2) result = !result; + if (a3) result = !result; + return result; +} + +/// +/// fₗ(...) matches the research paper, definition 3.4 +/// hard-coded to use bits for calculation of 'a' +/// +static inline bool calculate_feedback_l(const ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + // a = fₗ( g00 g04 g06 g13 g18 h03 ) ⊕ g22 ⊕ r02 ⊕ r06 + // fₗ( x₀ x₁ x₂ x₃ x₄ x₅ ) + bool x0 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G00 : SSR_UNSTABLE_OLD_BIT_G00); + bool x1 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G04 : SSR_UNSTABLE_OLD_BIT_G04); + bool x2 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G06 : SSR_UNSTABLE_OLD_BIT_G06); + bool x3 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G13 : SSR_UNSTABLE_OLD_BIT_G13); + bool x4 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G18 : SSR_UNSTABLE_OLD_BIT_G18); + bool x5 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H03 : SSR_UNSTABLE_OLD_BIT_H03); + + bool line1 = !x0 && !x2 && x3; + bool line2 = x2 && x4 && !x5; + bool line3 = x0 && !x1 && !x4; + bool line4 = x1 && !x3 && x5; + + bool result = line1 || line2 || line3 || line4; + return result; +} + +/// +/// fₘ(...) matches the research paper, definition 3.5 +/// hard-coded to use bits for calculation of 'b' +/// +static inline bool calculate_feedback_m(const ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + // b = fₘ( g01 g05 g10 g15 h00 h07 ) ⊕ l00 ⊕ l03 ⊕ l06 + // fₘ( x₀ x₁ x₂ x₃ x₄ x₅ ) + bool x0 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G01 : SSR_UNSTABLE_OLD_BIT_G01); + bool x1 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G05 : SSR_UNSTABLE_OLD_BIT_G05); + bool x2 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G10 : SSR_UNSTABLE_OLD_BIT_G10); + bool x3 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_G15 : SSR_UNSTABLE_OLD_BIT_G15); + bool x4 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H00 : SSR_UNSTABLE_OLD_BIT_H00); + bool x5 = test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H07 : SSR_UNSTABLE_OLD_BIT_H07); + + bool line1 = x1 && !x2 && !x4; + bool line2 = x0 && x2 && !x3; + bool line3 = !x1 && x3 && x5; + bool line4 = !x0 && x4 && !x5; + + bool result = line1 || line2 || line3 || line4; + return result; +} + +/// +/// fᵣ(...) matches the research paper, definition 3.6 +/// hard-coded to use bits for calculation of 'c' +/// +static inline bool calculate_feedback_r(const ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + ASSERT(!is_ssr_state_stable(ssr)); + // c = fᵣ( g02 g03⊕i g09 g14 g16 h01 ) ⊕ m00 ⊕ m03 ⊕ m06 + // fᵣ( x₀ x₁ x₂ x₃ x₄ x₅ ) + bool x0 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G02); + bool x1 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G03); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i)) { x1 = !x1; } + bool x2 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G09); + bool x3 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G14); + bool x4 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G16); + bool x5 = test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_H01); + + bool line1 = x1 && x3 && !x5; + bool line2 = x2 && !x3 && !x4; + bool line3 = !x0 && !x2 && x5; + bool line4 = x0 && !x1 && x4; + bool result = line1 || line2 || line3 || line4; + return result; +} + +/// +/// Matches the research paper, definition 3.7 +/// See also Definition 3.2, defining that parameter as `j`. +/// +static inline bool calculate_j(const ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); + // g′ := G(g, i, l₀₁ ⊕ m₀₆ ⊕ h₀₂ ⊕ h₀₈ ⊕ h₁₂) + // ^^^^^^^^^^^^^^^^^^^^^^^^^^^------ calculates `j` + bool result = 0; + if (test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_L01 : SSR_UNSTABLE_OLD_BIT_L01)) result = !result; + if (test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_M06 : SSR_UNSTABLE_OLD_BIT_M06)) result = !result; + if (test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H02 : SSR_UNSTABLE_OLD_BIT_H02)) result = !result; + if (test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H08 : SSR_UNSTABLE_OLD_BIT_H08)) result = !result; + if (test_single_ssr_bit(ssr, is_ssr_state_stable(ssr) ? SSR_BIT_H12 : SSR_UNSTABLE_OLD_BIT_H12)) result = !result; + return result; +} + + +/// +/// REQUIRES INPUT BIT `i` TO BE VALID. +/// Calculates a, b, c, j and new value for H₀₀. +/// These are the only bits changed by this function. +/// +static inline void calculate_temporaries(ID48LIBX_STATE_REGISTERS* ssr) { + ASSERT(ssr != nullptr); +#pragma region // to be removed after all is validated + static const uint64_t bits_must_remain_same_mask = + ~( + (1ull << SSR_UNSTABLE_BIT_a) | + (1ull << SSR_UNSTABLE_BIT_b) | + (1ull << SSR_UNSTABLE_BIT_c) | + (1ull << SSR_UNSTABLE_BIT_j) | + (1ull << SSR_UNSTABLE_NEW_BIT_H00) + ); + + const uint64_t backup = ssr->Raw & bits_must_remain_same_mask; +#pragma endregion // to be removed after all is validated + + // Only bits that change value: H00, a, b, c, j + + ASSERT(!is_ssr_state_stable(ssr)); // assigning temp values directly in ssr, so... + assign_single_ssr_bit(ssr, SSR_UNSTABLE_NEW_BIT_H00, calculate_feedback_h(ssr)); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a, calculate_feedback_l(ssr)); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b, calculate_feedback_m(ssr)); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c, calculate_feedback_r(ssr)); + assign_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_j, calculate_j(ssr)); + + // NOTE: Could scramble the below nine lines into any order desired. + // If start by setting the outputs all to zero, could also scramble the above into this mix + // + // a = fₗ() ⊕ g22 ⊕ r02 ⊕ r06 + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_G22)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R02)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R06)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a); + // b = fₘ() ⊕ l00 ⊕ l03 ⊕ l06 + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L00)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L03)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L06)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b); + // c = fᵣ() ⊕ m00 ⊕ m03 ⊕ m06 + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M00)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M03)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M06)) flip_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c); + +#pragma region // to be removed after all is validated + const uint64_t chk = ssr->Raw & bits_must_remain_same_mask; + ASSERT(chk == backup); +#pragma endregion // to be removed after all is validated + + return; +} + + +static inline OUTPUT_INDEX2 calculate_output_index(const ID48LIBX_STATE_REGISTERS* ssr) { + // Fₒ( abc l₀l₂l₃l₄l₅l₆ m₀m₁m₃m₅ r₀r₁r₂r₃r₄r₅r₆ ) + // msb 19 ---^ lsb 00 ---^^ + ASSERT(ssr != nullptr); + ASSERT(!is_ssr_state_stable(ssr)); + OUTPUT_INDEX2 result; result.Raw = 0; + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a )) result.Raw |= (1u << 19); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b )) result.Raw |= (1u << 18); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c )) result.Raw |= (1u << 17); + //bool bit17 = test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c); + //if (test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_i) ) bit17 = !bit17; + //if (bit17 ) result.Raw |= (1u << 17); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L00)) result.Raw |= (1u << 16); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L02)) result.Raw |= (1u << 15); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L03)) result.Raw |= (1u << 14); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L04)) result.Raw |= (1u << 13); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L05)) result.Raw |= (1u << 12); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_L06)) result.Raw |= (1u << 11); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M00)) result.Raw |= (1u << 10); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M01)) result.Raw |= (1u << 9); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M03)) result.Raw |= (1u << 8); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_M05)) result.Raw |= (1u << 7); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R00)) result.Raw |= (1u << 6); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R01)) result.Raw |= (1u << 5); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R02)) result.Raw |= (1u << 4); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R03)) result.Raw |= (1u << 3); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R04)) result.Raw |= (1u << 2); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R05)) result.Raw |= (1u << 1); + if (test_single_ssr_bit(ssr, SSR_UNSTABLE_OLD_BIT_R06)) result.Raw |= (1u << 0); + return result; +} + +// returns a single bit corresponding to the output bit for this transition +static inline bool calculate_successor_state(ID48LIBX_STATE_REGISTERS* ssr, bool i) { + ASSERT(ssr != nullptr); + ASSERT(is_ssr_state_stable(ssr)); + + + // HACK -- ORDER OF THESE OPERATIONS MATTERS ... + // to avoid overwriting bits needed for calculation of temporaries + // Thus: + // 1. ssr_new = ssr_old << 1; // all prior values still available (even r₀₆) + // 2. store input bit `i` // required many places + // 3. calculate and store a/b/c/j h'00 // can use SSR_UNSTABLE_OLD_BIT_... to get old values + // 4. calculate and save output index // relies on a/b/c AND the bits that get modified using a/b/c, + // // so must be after calculate a/b/c and before setting new L00,M00,R00 values + // 5. G(g, i, j) // relies on SSR_UNSTABLE_OLD_BIT_G22, which is now L00 ... aka must do before L() + // 6. L() // overwrite L00 with `a` + // 7. M() // overwrite M00 with `b` + // 8. R() // overwrite R00 with `c` + // + + + // 1. ssr_new = ssr_old << 1; + ssr->Raw <<= 1; // begin! + + // 2. store input bit `i` + assign_temporary_i(ssr, i); + + // 3. calculate and store a/b/c/j and new H00 bits + calculate_temporaries(ssr); // updates new H00, stores a/c/c and j + + // 4. calculate and save output index + OUTPUT_INDEX2 output_index = calculate_output_index(ssr); // note: does *NOT* rely on new H00 value + bool output_result = id48libx_output_lookup(output_index.Raw); + + // 5. g --> g', aka G(g, i, j) + g_successor(ssr); + + // 6. l --> l' + assign_single_ssr_bit(ssr, SSR_BIT_L00, test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_a)); + + // 7. m --> m' + assign_single_ssr_bit(ssr, SSR_BIT_M00, test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_b)); + + // 8. r --> r' + assign_single_ssr_bit(ssr, SSR_BIT_R00, test_single_ssr_bit(ssr, SSR_UNSTABLE_BIT_c)); + + // Done! Clear temporaries and indicate this is a final state + + // Keep only the registers (no temporaries) + ssr->Raw &= SSR_BITMASK_REG_ALL; + + // Mark as stable view of the SSR + ssr->Raw |= 1u; + + return output_result; +} + +/// +/// Returns a value where the least significant bit is the +/// first input bit, so that the value can be right-shifted +/// by one bit each iteration (allowing least significant bit +/// to always be the input bit). +/// +static inline INPUT_BITS2 get_key_input_bits(const ID48LIB_KEY* k) { + ASSERT(k != nullptr); + + // Per research paper, key bit 39 is used first. + // So, what should end up in result is: 0²⁴ k₀₀..K₃₉ + // This allows simply shifting the lsb out each cycle.... + + INPUT_BITS2 result; result.Raw = 0; + + // k[ 0] :== K₉₅..K₈₈ + // ... + // k[ 7] :== K₃₉..K₃₂ + // ... + // k[11] :== K₀₇..K₀₀ + for (uint8_t i = 0; i < 5; ++i) { + result.Raw <<= 8; + uint8_t tmp = k->k[11 - i]; // e.g., first loop will contain K₀₇..K₀₀ + tmp = reverse_bits_08(tmp); // e.g., first loop will contain K₀₀..K₀₇ + result.Raw |= tmp; + } + + static const uint64_t INPUT_MASK = (1ull << 40) - 1u; + ASSERT((result.Raw & (~INPUT_MASK)) == 0ull); + return result; +} + +static inline bool shift_out_next_input_bit(INPUT_BITS2* inputs) { + ASSERT(inputs != nullptr); + bool result = inputs->Raw & 1ull; + inputs->Raw >>= 1; + return result; +} +static inline void shift_in_next_output_bit(OUTPUT_BITS2* outputs, bool v) { + ASSERT(outputs != nullptr); + outputs->Raw <<= 1; + if (v) outputs->Raw |= 1ull; +} + +static inline void extract_frn(const OUTPUT_BITS2* outputs, ID48LIB_FRN* frn28_out) { + ASSERT(outputs != nullptr); + ASSERT(frn28_out != nullptr); + + static const uint64_t C_MASK28 = (1ull << 28) - 1u; + uint64_t tmp = outputs->Raw; + tmp >>= 20; // remove the 20 bit grn (but still has 7 ignored bits) + tmp &= C_MASK28; // tmp now has exactly 28 valid bits + tmp <<= 4; // align to 32-bits for easier assignment to output + // tmp now :== O₀₀..O₂₇ 0000 + frn28_out->frn[0] = (uint8_t)((tmp >> (8 * 3)) & 0xFFu); + frn28_out->frn[1] = (uint8_t)((tmp >> (8 * 2)) & 0xFFu); + frn28_out->frn[2] = (uint8_t)((tmp >> (8 * 1)) & 0xFFu); + frn28_out->frn[3] = (uint8_t)((tmp >> (8 * 0)) & 0xFFu); +} +static inline void extract_grn(const OUTPUT_BITS2* outputs, ID48LIB_GRN* grn20_out) { + ASSERT(outputs != nullptr); + ASSERT(grn20_out != nullptr); + memset(grn20_out, 0, sizeof(ID48LIB_GRN)); + + static const uint64_t C_MASK20 = (1ull << 20) - 1u; + uint64_t tmp = outputs->Raw; + tmp &= C_MASK20; // tmp now has exactly 20 valid bits + tmp <<= 4; // align to 24-bits for easier assignment to output + grn20_out->grn[0] = (uint8_t)((tmp >> (8 * 2)) & 0xFFu); + grn20_out->grn[1] = (uint8_t)((tmp >> (8 * 1)) & 0xFFu); + grn20_out->grn[2] = (uint8_t)((tmp >> (8 * 0)) & 0xFFu); +} + +static void retro_generator_impl( + const ID48LIB_KEY* k, + const ID48LIB_NONCE* n, + ID48LIB_FRN* frn28_out, + ID48LIB_GRN* grn20_out + ) +{ + ASSERT(k != nullptr); + ASSERT(n != nullptr); + ASSERT(frn28_out != nullptr); + ASSERT(grn20_out != nullptr); + memset(frn28_out, 0, sizeof(ID48LIB_FRN)); + memset(grn20_out, 0, sizeof(ID48LIB_GRN)); + + ID48LIBX_STATE_REGISTERS ssr = init_id48libx_state_register(k, n); + + // get 55-bit successor state input + INPUT_BITS2 inputs = get_key_input_bits(k); + OUTPUT_BITS2 outputs; outputs.Raw = 0ull; + for (uint8_t ix = 0; ix < 55; ix++) { + ASSERT(is_ssr_state_stable(&ssr)); + + // input bit `i` is not valid in stable state... + bool input_bit = shift_out_next_input_bit(&inputs); + // calculate the next state... (note: logs calculations for this state) + bool output_bit = calculate_successor_state(&ssr, input_bit); + ASSERT(is_ssr_state_stable(&ssr)); + + // store the output bit + shift_in_next_output_bit(&outputs, output_bit); + } + + // convert the output bits into frn/grn + extract_frn(&outputs, frn28_out); + extract_grn(&outputs, grn20_out); + return; +} + + +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// +// ******************************************************************************************************************** // +// *** Everything above this line in the file is declared static, *** // +// *** which avoids polluting the global namespace. *** // +// *** Everything below is technically visible, but not necessarily an exported API. *** // +// *** In C++, this separation is much more easily achieved using an anonymous namespace. C'est la vie! *** // +// ******************************************************************************************************************** // +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + +// internal function +ID48LIBX_SUCCESSOR_RESULT id48libx_retro003_successor(const ID48LIBX_STATE_REGISTERS* initial_state, uint8_t input_bit) { + ASSERT(initial_state != nullptr); + ID48LIBX_SUCCESSOR_RESULT r; memset(&r, 0, sizeof(ID48LIBX_SUCCESSOR_RESULT)); + ID48LIBX_STATE_REGISTERS s = *initial_state; + bool output_bit = calculate_successor_state(&s, !!input_bit); + r.state.Raw = s.Raw; + r.output = output_bit; + return r; +} +// internal function +ID48LIBX_STATE_REGISTERS id48libx_retro003_init(const ID48LIB_KEY* key, const ID48LIB_NONCE* nonce) { + ASSERT(key != nullptr); + ASSERT(nonce != nullptr); + + ID48LIBX_STATE_REGISTERS ssr = init_id48libx_state_register(key, nonce); + ID48LIBX_STATE_REGISTERS result; memset(&result, 0, sizeof(ID48LIBX_STATE_REGISTERS)); + result.Raw = ssr.Raw; + return result; +} + +// public API +void id48lib_generator( + const ID48LIB_KEY* k, + const ID48LIB_NONCE* n, + ID48LIB_FRN* frn28_out, + ID48LIB_GRN* grn20_out +) +{ + retro_generator_impl(k, n, frn28_out, grn20_out); +} diff --git a/client/deps/id48/id48_internals.h b/client/deps/id48/id48_internals.h new file mode 100644 index 000000000..918494650 --- /dev/null +++ b/client/deps/id48/id48_internals.h @@ -0,0 +1,53 @@ +/** + * The MIT License (MIT) + * + * Copyright (c) 2024 by Henry Gabryjelski + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in all + * copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + * + */ +//----------------------------------------------------------------------------- +// NOTE: This file describes internal details used by the ID48 library. +// Changes to this file are unannounced, and may break any code that +// is relying on it. Nothing in this file is considered part of the +// public API. +// The public API can be found in id48.h +//----------------------------------------------------------------------------- + +#if !defined(ID48_INTERNALS_H__) +#define ID48_INTERNALS_H__ + +#include "id48.h" + +typedef struct _ID48LIBX_STATE_REGISTERS { + uint64_t Raw; +} ID48LIBX_STATE_REGISTERS; + +typedef struct _ID48LIBX_SUCCESSOR_RESULT { + ID48LIBX_STATE_REGISTERS state; + bool output; +} ID48LIBX_SUCCESSOR_RESULT; + +// the following are used in key recovery but implemented in id48.c +ID48LIBX_SUCCESSOR_RESULT id48libx_retro003_successor(const ID48LIBX_STATE_REGISTERS* initial_state, uint8_t input_bit); +ID48LIBX_STATE_REGISTERS id48libx_retro003_init (const ID48LIB_KEY* key, const ID48LIB_NONCE* nonce); + +bool id48libx_output_lookup(uint32_t output_index); + +#endif // !defined(ID48_INTERNALS_H__) diff --git a/client/deps/id48/id48_recover.c b/client/deps/id48/id48_recover.c new file mode 100644 index 000000000..2bb19df40 --- /dev/null +++ b/client/deps/id48/id48_recover.c @@ -0,0 +1,439 @@ +/** + * The MIT License (MIT) + * + * Copyright (c) 2024 by Henry Gabryjelski + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in all + * copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + * + */ + +#include +#include +#include +#include +#include // memset() +#include + +#include "id48_internals.h" + +#ifndef nullptr +#define nullptr ((void*)0) +#endif + +#pragma region // reverse_bits() +static inline uint8_t reverse_bits_08(uint8_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint8_t mask = (uint8_t)(~((uint8_t)(0u))); + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); + n = (uint8_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); + } + return n; +} +static inline uint16_t reverse_bits_16(uint16_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint16_t mask = (uint16_t)(~((uint16_t)(0u))); + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); + n = (uint16_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); + } + return n; +} +static inline uint32_t reverse_bits_32(uint32_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint32_t mask = (uint32_t)(~((uint32_t)(0u))); + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); + n = (uint32_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); + } + return n; +} +static inline uint64_t reverse_bits_64(uint64_t n) { + uint8_t bitsToSwap = sizeof(n) * 8; + uint64_t mask = (uint64_t)(~((uint64_t)(0u))); + while (bitsToSwap >>= 1) { + mask ^= mask << (bitsToSwap); + n = (uint64_t)(((n & ~mask) >> bitsToSwap) | ((n & mask) << bitsToSwap)); + } + return n; +} +#pragma endregion // reverse_bits() + +#define MAXIMUM_STATE_HISTORY (56u) + +typedef struct _EXPECTED_OUTPUT_BITS { + uint64_t Raw; // s07: 1ull << 0, s08: 1ull << 1, s09: 1ull << 2, ... s55: 1ull << 47 +} EXPECTED_OUTPUT_BITS; +typedef struct _KEY_BITS_K47_TO_K00 { + uint64_t Raw; +} KEY_BITS_K47_TO_K00; +typedef struct _RECOVERY_STATE { + /// + /// What are the 48 expected output bits? + /// Stored as 0¹⁶·O₄₇..O₀₀. + /// + EXPECTED_OUTPUT_BITS expected_output_bits; // const once initialized + /// + /// The value of the low 48-bits most recently + /// returned to the caller as a potential match. + /// + KEY_BITS_K47_TO_K00 last_returned_potential_key; + /// + /// State history. Overwritten during testing + /// of input bits (next bit of possible key). + /// Storing the full history allows backtracking + /// without re-computing the state. + /// + ID48LIBX_STATE_REGISTERS states[MAXIMUM_STATE_HISTORY]; // history ... avoids re-computation when backtracking + /// + /// The 48-bit partial key to recover the remaining 48 bits of. + /// Constant after initialization. + /// + ID48LIB_KEY known_k95_to_k48; + /// + /// The 56-bit nonce corresponding to the frn/grn (output bits). + /// Constant after initialization. + /// + ID48LIB_NONCE known_nonce; + /// + /// boolean to identify first run after initialization (an edge case) + /// + bool is_fresh_initialization; + /// + /// boolean to identify that all keys have been tested. + /// If set, caller would need to call init() function again. + /// + bool more_keys_to_test; +} RECOVERY_STATE; + +// Need equivalent of the following two function pointers: +typedef ID48LIBX_SUCCESSOR_RESULT (*ID48LIB_SUCCESSOR_FN)(const ID48LIBX_STATE_REGISTERS* initial_state, uint8_t input_bit); +typedef ID48LIBX_STATE_REGISTERS(*ID48LIB_INIT_FN )(const ID48LIB_KEY* key, const ID48LIB_NONCE* nonce); + +static const ID48LIB_INIT_FN init_fn = id48libx_retro003_init; +static const ID48LIB_SUCCESSOR_FN successor_fn = id48libx_retro003_successor; + +/// +/// Creates PM3-formatted key with K₉₅..K₄₈ from the provided partial key, +/// and with K₄₇..K₃₃ from bit-reversed `more_bits`. +/// +/// Key with K₉₅..K₄₈, in PM3 compatible layout +/// 0 K₃₃..K₄₇ (to support simple incrementing input) +/// PM3-formatted key: K₉₅..K₃₃ 0³³ +static ID48LIB_KEY create_partial_key56(const ID48LIB_KEY * input_partial_key, uint8_t k47_to_k40) { + ID48LIB_KEY result; + result.k[ 0] = input_partial_key->k[0]; // k[ 0] :== K₉₅..K₈₈ + result.k[ 1] = input_partial_key->k[1]; // k[ 1] :== K₈₇..K₈₀ + result.k[ 2] = input_partial_key->k[2]; // k[ 2] :== K₇₉..K₇₂ + result.k[ 3] = input_partial_key->k[3]; // k[ 3] :== K₇₁..K₆₄ + result.k[ 4] = input_partial_key->k[4]; // k[ 4] :== K₆₃..K₅₆ + result.k[ 5] = input_partial_key->k[5]; // k[ 5] :== K₅₅..K₄₈ + result.k[ 6] = k47_to_k40; // k[ 6] :== K₄₇..K₄₀ + result.k[ 7] = 0; // k[ 7] :== K₃₉..K₃₂ + result.k[ 8] = 0; // k[ 8] :== K₃₁..K₂₄ + result.k[ 9] = 0; // k[ 9] :== K₂₃..K₁₆ + result.k[10] = 0; // k[10] :== K₁₅..K₀₈ + result.k[11] = 0; // k[11] :== K₀₇..K₀₀ + return result; +} +/// +/// Returns 48-bit value (using 64-bits of storage): 0¹⁶ O₄₇..O₀₀. +/// This allows simple calculation of the relevant bit to review, +/// or simply shifting the value right each time a bit is used and using lsb. +/// +/// PM3 compatible input for frn +/// PM3 compatible input for grn +/// +static EXPECTED_OUTPUT_BITS create_expected_output_bits(const ID48LIB_FRN* input_frn, const ID48LIB_GRN* input_grn) { + // inputs: + // frn[ 0] :== O₀₀..O₀₇ + // frn[ 1] :== O₀₈..O₁₅ + // frn[ 2] :== O₁₆..O₂₃ + // frn[ 3] :== O₂₄..O₂₇ 0000 + // grn[ 0] :== O₂₈ .. O₃₅ + // grn[ 1] :== O₃₆ .. O₄₃ + // grn[ 2] :== O₄₄..O₄₇ 0000 + EXPECTED_OUTPUT_BITS result; result.Raw = 0u; + result.Raw <<= 4; result.Raw |= reverse_bits_08(input_grn->grn[2] & 0xF0u); // adds grn₁₉..grn₁₆ aka O₄₇..O₄₄ + result.Raw <<= 8; result.Raw |= reverse_bits_08(input_grn->grn[1] & 0xFFu); // adds grn₁₅..grn₀₈ aka O₄₃..O₃₆ + result.Raw <<= 8; result.Raw |= reverse_bits_08(input_grn->grn[0] & 0xFFu); // adds grn₀₇..grn₀₀ aka O₃₅..O₂₈ + + result.Raw <<= 4; result.Raw |= reverse_bits_08(input_frn->frn[3] & 0xF0u); // adds frn₂₇..frn₂₄ aka O₂₇..O₂₄ + result.Raw <<= 8; result.Raw |= reverse_bits_08(input_frn->frn[2] & 0xFFu); // adds frn₂₃..frn₁₆ aka O₂₃..O₁₆ + result.Raw <<= 8; result.Raw |= reverse_bits_08(input_frn->frn[1] & 0xFFu); // adds frn₁₅..frn₀₈ aka O₁₅..O₀₈ + result.Raw <<= 8; result.Raw |= reverse_bits_08(input_frn->frn[0] & 0xFFu); // adds frn₀₇..frn₀₀ aka O₀₇..O₀₀ + return result; +} +/// +/// For a current state, get the expected output bit. +/// This is used to determine which value(s) the key bit +/// may be valid, allowing early pruning of the search space. +/// +/// A value in the range [0,55] +/// Zero or non-zero (boolean) corresponding to the expected output. +static bool get_expected_output_bit(const RECOVERY_STATE* recovery_state, uint8_t current_state_index) { + assert(recovery_state != nullptr); + assert(current_state_index >= 7); + assert(current_state_index <= 55); + uint64_t shifted = recovery_state->expected_output_bits.Raw >> (current_state_index - 7u); + return !!(shifted & 0x1u); // return the single bit result +} + +static void restart_and_calculate_s00(RECOVERY_STATE* s, const KEY_BITS_K47_TO_K00* k_low) { + assert(s != nullptr); + assert(k_low != nullptr); + memset(&(s->states[0]), 0xAA, sizeof(ID48LIBX_STATE_REGISTERS) * MAXIMUM_STATE_HISTORY); + uint8_t k47_to_k40 = (uint8_t)(k_low->Raw >> 40); + const ID48LIB_KEY start_56b_key = create_partial_key56(&(s->known_k95_to_k48), k47_to_k40); + s->states[0] = init_fn(&start_56b_key, &(s->known_nonce)); +} + +static bool validate_output_from_additional_fifteen_zero_bits(RECOVERY_STATE* s) { + bool all_still_match = true; + for (uint8_t i = 0; all_still_match && i < 15; i++) { + const uint8_t src_idx = 40 + i; + const ID48LIBX_STATE_REGISTERS* state = &(s->states[src_idx]); + ID48LIBX_SUCCESSOR_RESULT r = successor_fn(state, 0); + bool expected_result = get_expected_output_bit(s, src_idx); + if (expected_result != (!!r.output)) { + all_still_match = false; + } + s->states[src_idx + 1] = r.state; + } + return all_still_match; +} + + +// intentionally declare this global state only here, as a way +// of forcing the above functions to act on a pointer. Ensuring +// the above routines don't inadvertently use the global state +// makes it easier to enable a multi-threaded version. +RECOVERY_STATE g_S = { 0 }; + +static void init( + const ID48LIB_KEY * input_partial_key, + const ID48LIB_NONCE * input_nonce, + const ID48LIB_FRN * input_frn, + const ID48LIB_GRN * input_grn + ) +{ + memset(&g_S, 0, sizeof(RECOVERY_STATE)); + memset(&(g_S.states[0]), 0xAA, sizeof(ID48LIBX_STATE_REGISTERS) * MAXIMUM_STATE_HISTORY); + g_S.known_k95_to_k48.k[0] = input_partial_key->k[0]; + g_S.known_k95_to_k48.k[1] = input_partial_key->k[1]; + g_S.known_k95_to_k48.k[2] = input_partial_key->k[2]; + g_S.known_k95_to_k48.k[3] = input_partial_key->k[3]; + g_S.known_k95_to_k48.k[4] = input_partial_key->k[4]; + g_S.known_k95_to_k48.k[5] = input_partial_key->k[5]; + g_S.known_nonce = *input_nonce; + g_S.expected_output_bits = create_expected_output_bits(input_frn, input_grn); + g_S.more_keys_to_test = true; + g_S.is_fresh_initialization = true; +} +static bool get_next_potential_key( + ID48LIB_KEY* potential_key_output +) { + memset(potential_key_output, 0, sizeof(ID48LIB_KEY)); + + // Three possible states when this function enters: + // 1. Never initialized / finished enumerating keys + // --> returns false immediately + // 2. First time after initialization + // --> key starts at zero, with zero current bits + // 3. After a key was provided as a potential match + // --> If that last reported potential match was + // all one-bits, then early-exit with false + // because the whole keyspace was exhausted. + // --> Since state stores the last key reported, + // setup to continue search at the first + // bit that was zero. + + // Early exit when no more keys to test + if (!g_S.more_keys_to_test) { + return false; + } + + KEY_BITS_K47_TO_K00 k_low; + int8_t current_key_bit_shift; + + // Setup the next key to be tested. + if (g_S.is_fresh_initialization) { + // first-time init is easy: key is zero, and zero bits set + g_S.is_fresh_initialization = false; + k_low.Raw = 0ull; + current_key_bit_shift = 47; + } + else { + // by definition, a returned potential key had all the bits defined + current_key_bit_shift = 0; + k_low = g_S.last_returned_potential_key; + + // edge case: returned potential key 0xFFFFFFFFFFFFull, so no more keys to be tested! + if (k_low.Raw == 0xFFFFFFFFFFFFull) { + g_S.more_keys_to_test = false; + return false; + } + + // backtrack to first zero value, flipping bits... + if (1) { + uint64_t mask = (1ull << current_key_bit_shift); + while ((mask & k_low.Raw) != 0) { + k_low.Raw ^= mask; + mask <<= 1; + ++current_key_bit_shift; + } + // and flip that next bit also + k_low.Raw ^= mask; + } + } + + // TODO: move above setup to re-use code in below loop ... + // especially since backtracking logic is duplicated? + // may require re-arranging the order in which things + // occur in the while loop? + + + // Two exit conditions from this point on: + // 1. potential key was found (and thus returned) + // 2. no more keys to be tested (returns false) + while (1) { + // Currently, at loop start, ready to test the current bit vs. expected value + + assert(current_key_bit_shift < 48); + // Anytime bit shift is 40+, changes would affect s00 ... + if (current_key_bit_shift > 39) { + restart_and_calculate_s00(&g_S, &k_low); + current_key_bit_shift = 39; // k47..k40 used to get to s00 + } + + assert(current_key_bit_shift < 40); + // Anytime bit shift is 33+, unconditionally calculate through s07, + // because the output bits are not exposed, and thus cannot be validated. + while (current_key_bit_shift > 32) { // k39..k33 used to move from s00-->s07 + uint8_t src_idx = 39 - current_key_bit_shift; + bool input_bit = !!(((uint8_t)(k_low.Raw >> current_key_bit_shift)) & 0x1u); + ID48LIBX_SUCCESSOR_RESULT r = successor_fn(&(g_S.states[src_idx]), input_bit); + g_S.states[src_idx + 1] = r.state; + --current_key_bit_shift; + } + + + assert(current_key_bit_shift <= 32); // K₃₂ is used with s₀₇ to generate first output bit O₀₀ + assert(current_key_bit_shift >= 0); // K₀₀ is a special case ... so negative is unexpected + + // Check if the current state + current key bit (as stored) gives expected result. + const uint8_t src_idx = 39 - current_key_bit_shift; + bool input_bit = !!(((uint8_t)(k_low.Raw >> current_key_bit_shift)) & 0x1u); + ID48LIBX_SUCCESSOR_RESULT r = successor_fn(&(g_S.states[src_idx]), input_bit); + // can unconditionally overwrite next state... + g_S.states[src_idx + 1] = r.state; + + bool expected_result = get_expected_output_bit(&g_S, src_idx); + bool matched = expected_result == (!!r.output); + // when matched the last bit, actually check the next 15x inputs (all zero) as well + if (matched && current_key_bit_shift == 0) { + // that was the last bit to be checked in this potential key + // but, must also test 15x additional zero bit inputs before + // reporting that this may be a potential key + assert(src_idx == 39); + matched = validate_output_from_additional_fifteen_zero_bits(&g_S); + } + + // Exit point ... found a potential key! + if (matched && current_key_bit_shift == 0) { + g_S.last_returned_potential_key = k_low; + potential_key_output->k[ 0] = g_S.known_k95_to_k48.k[0]; + potential_key_output->k[ 1] = g_S.known_k95_to_k48.k[1]; + potential_key_output->k[ 2] = g_S.known_k95_to_k48.k[2]; + potential_key_output->k[ 3] = g_S.known_k95_to_k48.k[3]; + potential_key_output->k[ 4] = g_S.known_k95_to_k48.k[4]; + potential_key_output->k[ 5] = g_S.known_k95_to_k48.k[5]; + potential_key_output->k[ 6] = (uint8_t)(k_low.Raw >> (8 * 5)); + potential_key_output->k[ 7] = (uint8_t)(k_low.Raw >> (8 * 4)); + potential_key_output->k[ 8] = (uint8_t)(k_low.Raw >> (8 * 3)); + potential_key_output->k[ 9] = (uint8_t)(k_low.Raw >> (8 * 2)); + potential_key_output->k[10] = (uint8_t)(k_low.Raw >> (8 * 1)); + potential_key_output->k[11] = (uint8_t)(k_low.Raw >> (8 * 0)); + return true; + } + // that bit of the key was OK, but there are more to check + else if (matched) { + --current_key_bit_shift; + } + // wrong output generated with that bit. + // Backtrack to find next one to be tested. + else { + // not required ... but makes debugging easier + memset(&g_S.states[src_idx + 1], 0xAA, sizeof(ID48LIBX_STATE_REGISTERS)); + + // that bit of the key results in wrong output. + // backtrack until the next zero bit, flip it to one, and + // continue testing from there... + if (1) { + // This is ***NOT*** the same as simply adding 1. + // (Consider, for example, when current_key_bit_shift == 3.) + uint64_t mask = 1ull << current_key_bit_shift; + while ((mask & k_low.Raw) != 0) { + k_low.Raw ^= mask; + mask <<= 1; + ++current_key_bit_shift; + } + // found a zero bit, so flip it + // this is the next key to test + k_low.Raw ^= mask; + } + + // EXIT CONDITION: k_low wraps to invalid value + if (current_key_bit_shift >= 48) { + // no more results available ... return! + g_S.more_keys_to_test = false; + return 0u; + } + + } + } // end while(1) loop +} + + + + +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// +// ******************************************************************************************************************** // +// *** Everything above this line in the file is declared static, *** // +// *** which avoids polluting the global namespace. *** // +// *** Everything below is technically visible, but not necessarily an exported API. *** // +// *** In C++, this separation is much more easily achieved using an anonymous namespace. C'est la vie! *** // +// ******************************************************************************************************************** // +////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// + + +void id48lib_key_recovery_init( + const ID48LIB_KEY * input_partial_key, + const ID48LIB_NONCE * input_nonce, + const ID48LIB_FRN * input_frn, + const ID48LIB_GRN * input_grn + ) +{ + init(input_partial_key, input_nonce, input_frn, input_grn); +} +bool id48lib_key_recovery_next( + ID48LIB_KEY* potential_key_output +) { + return get_next_potential_key(potential_key_output); +} diff --git a/client/deps/id48lib.cmake b/client/deps/id48lib.cmake new file mode 100644 index 000000000..97e31e57c --- /dev/null +++ b/client/deps/id48lib.cmake @@ -0,0 +1,9 @@ +add_library(pm3rrg_rdv4_id48 STATIC + id48/id48_data.c + id48/id48_generator.c + id48/id48_recover.c +) +target_compile_options( pm3rrg_rdv4_id48 PRIVATE -Wpedantic -Wall -Werror -O3 -Wno-unknown-pragmas -Wno-inline -Wno-unused-function) +target_include_directories(pm3rrg_rdv4_id48 PRIVATE id48) +target_include_directories(pm3rrg_rdv4_id48 INTERFACE id48) +set_property(TARGET pm3rrg_rdv4_id48 PROPERTY POSITION_INDEPENDENT_CODE ON) diff --git a/client/src/cmdlfem4x70.c b/client/src/cmdlfem4x70.c index a91550a4d..7ccfbf4f0 100644 --- a/client/src/cmdlfem4x70.c +++ b/client/src/cmdlfem4x70.c @@ -23,6 +23,8 @@ #include "fileutils.h" #include "commonutil.h" #include "em4x70.h" +#include "id48.h" +#include "time.h" #define LOCKBIT_0 BITMASK(6) #define LOCKBIT_1 BITMASK(7) @@ -31,6 +33,15 @@ static int CmdHelp(const char *Cmd); +static void fill_buffer_prng_bytes(void* buffer, size_t byte_count) { + if (byte_count <= 0) return; + srand((unsigned) time(NULL)); + for (size_t i = 0; i < byte_count; i++) { + ((uint8_t*)buffer)[i] = (uint8_t)rand(); + } +} + + static void print_info_result(const uint8_t *data) { PrintAndLogEx(NORMAL, ""); @@ -52,7 +63,7 @@ static void print_info_result(const uint8_t *data) { } PrintAndLogEx(INFO, "------+----------+-----------------------------"); - // Print Crypt Key (will never have data) + // Print Key (will never have data) for (int i = 12; i < 24; i += 2) { PrintAndLogEx(INFO, " %2d | -- -- | KEY write-only", INDEX_TO_BLOCK(i)); } @@ -109,6 +120,13 @@ bool detect_4x70_block(void) { return em4x70_info() == PM3_SUCCESS; } +// TODO: split the below functions, so can use them as building blocks for more complex interactions +// without generating fake `const char *Cmd` strings. First targets: +// Auth +// Write +// WriteKey +// Together, they will allow writekey to verify the key was written correctly. + int CmdEM4x70Info(const char *Cmd) { // envoke reading of a EM4x70 tag which has to be on the antenna because @@ -388,8 +406,10 @@ int CmdEM4x70Auth(const char *Cmd) { CLIParserInit(&ctx, "lf em 4x70 auth", "Authenticate against an EM4x70 by sending random number (RN) and F(RN)\n" - " If F(RN) is incorrect based on the tag crypt key, the tag will not respond", - "lf em 4x70 auth --rnd 45F54ADA252AAC --frn 4866BB70 --> Test authentication, tag will respond if successful\n" + " If F(RN) is incorrect based on the tag key, the tag will not respond\n" + " If F(RN) is correct based on the tag key, the tag will give a 20-bit response\n", + "lf em 4x70 auth --rnd 45F54ADA252AAC --frn 4866BB70 --> (using pm3 test key)\n" + "lf em 4x70 auth --rnd 3FFE1FB6CC513F --frn F355F1A0 --> (using research paper key)\n" ); void *argtable[] = { @@ -499,20 +519,21 @@ int CmdEM4x70WritePIN(const char *Cmd) { int CmdEM4x70WriteKey(const char *Cmd) { - // Write new crypt key to tag + // Write new key to tag em4x70_data_t etd = {0}; CLIParserContext *ctx; CLIParserInit(&ctx, "lf em 4x70 writekey", "Write new 96-bit key to tag\n", - "lf em 4x70 writekey -k F32AA98CF5BE4ADFA6D3480B\n" + "lf em 4x70 writekey -k F32AA98CF5BE4ADFA6D3480B (pm3 test key)\n" + "lf em 4x70 writekey -k A090A0A02080000000000000 (research paper key)\n" ); void *argtable[] = { arg_param_begin, arg_lit0(NULL, "par", "Add parity bit when sending commands"), - arg_str1("k", "key", "", "Crypt Key as 12 hex bytes"), + arg_str1("k", "key", "", "Key as 12 hex bytes"), arg_param_end }; @@ -526,7 +547,7 @@ int CmdEM4x70WriteKey(const char *Cmd) { CLIParserFree(ctx); if (key_len != 12) { - PrintAndLogEx(FAILED, "Crypt key length must be 12 bytes instead of %d", key_len); + PrintAndLogEx(FAILED, "Key length must be 12 bytes instead of %d", key_len); return PM3_EINVARG; } @@ -540,23 +561,236 @@ int CmdEM4x70WriteKey(const char *Cmd) { } if (resp.status) { - PrintAndLogEx(INFO, "Writing new crypt key: " _GREEN_("ok")); + PrintAndLogEx(INFO, "Writing new key: " _GREEN_("ok")); + + // TODO: use prng to generate a new nonce, calculate frn/grn, and authenticate with tag + return PM3_SUCCESS; } - PrintAndLogEx(FAILED, "Writing new crypt key: " _RED_("failed")); + PrintAndLogEx(FAILED, "Writing new key: " _RED_("failed")); return PM3_ESOFT; } +// largest seen "in the wild" was 6 +#define MAXIMUM_ID48_RECOVERED_KEY_COUNT 10 +typedef struct _em4x70_recovery_data_t { + ID48LIB_KEY key; + ID48LIB_NONCE nonce; + ID48LIB_FRN frn; + ID48LIB_GRN grn; + bool verify; // if true, tag must be present + bool parity; // if true, add parity bit to commands sent to tag + + uint8_t keys_found_count; + uint8_t keys_validated_count; + ID48LIB_KEY potential_keys[MAXIMUM_ID48_RECOVERED_KEY_COUNT]; + ID48LIB_NONCE alt_nonce; + ID48LIB_FRN alt_frn[MAXIMUM_ID48_RECOVERED_KEY_COUNT]; + ID48LIB_GRN alt_grn[MAXIMUM_ID48_RECOVERED_KEY_COUNT]; + bool potential_keys_validated[MAXIMUM_ID48_RECOVERED_KEY_COUNT]; +} em4x70_recovery_data_t; + +static int ValidateArgsForRecover(const char *Cmd, em4x70_recovery_data_t* out_results) { + memset(out_results, 0, sizeof(em4x70_recovery_data_t)); + + int result = PM3_SUCCESS; + + CLIParserContext *ctx; + CLIParserInit( + &ctx, + "lf em 4x70 recover", + "After obtaining key bits 95..48 (such as via 'lf em 4x70 brute'), this command will recover\n" + "key bits 47..00. By default, this process does NOT require a tag to be present.\n" + "\n" + "By default, the potential keys are shown (typically 1-6) along with a corresponding\n" + "'lf em 4x70 auth' command that will authenticate, if that potential key is correct.\n" + "The user can copy/paste these commands when the tag is present to manually check\n" + "which of the potential keys is correct.\n" + // "\n" + // "If the `--verify` option is provided, the tag must be present. The rnd/frn parameters will\n" + // "be used to authenticate against the tag, and then any potential keys will be automatically\n" + // "be checked for correctness against the tag, reducing manual steps.\n" + , + "lf em 4x70 recover --key F32AA98CF5BE --rnd 45F54ADA252AAC --frn 4866BB70 --grn 9BD180 (pm3 test key)\n" + "lf em 4x70 recover --key A090A0A02080 --rnd 3FFE1FB6CC513F --frn F355F1A0 --grn 609D60 (research paper key)\n" + ); + + void *argtable[] = { + arg_param_begin, + arg_lit0(NULL, "par", "Add parity bit when sending commands"), + arg_str1("k", "key", "", "Key as 6 hex bytes"), + arg_str1(NULL, "rnd", "", "Random 56-bit"), + arg_str1(NULL, "frn", "", "F(RN) 28-bit as 4 hex bytes"), + arg_str1(NULL, "grn", "", "G(RN) 20-bit as 3 hex bytes"), + //arg_lit0(NULL, "verify", "automatically use tag for validation"), + arg_param_end + }; + + // do the command line arguments even parse? + if (CLIParserParseString(ctx, Cmd, argtable, arg_getsize(argtable), true)) { + result = PM3_ESOFT; + } + int key_len = 0; // must be 6 bytes hex data + int rnd_len = 0; // must be 7 bytes hex data + int frn_len = 0; // must be 4 bytes hex data + int grn_len = 0; // must be 3 bytes hex data + + // if all OK so far, convert to internal data structure + if (PM3_SUCCESS == result) { + // magic number == index in argtable above. Fragile technique! + out_results->parity = arg_get_lit(ctx, 1); + if (CLIParamHexToBuf(arg_get_str(ctx, 2), &(out_results->key.k[0]), 12, &key_len)) { + result = PM3_ESOFT; + } + if (CLIParamHexToBuf(arg_get_str(ctx, 3), &(out_results->nonce.rn[0]), 7, &rnd_len)) { + result = PM3_ESOFT; + } + if (CLIParamHexToBuf(arg_get_str(ctx, 4), &(out_results->frn.frn[0]), 4, &frn_len)) { + result = PM3_ESOFT; + } + if (CLIParamHexToBuf(arg_get_str(ctx, 5), &(out_results->grn.grn[0]), 3, &grn_len)) { + result = PM3_ESOFT; + } + //out_results->verify = arg_get_lit(ctx, 6); + } + // if all OK so far, do additional parameter validation + if (PM3_SUCCESS == result) { + // Validate number of bytes read for hex data + if (key_len != 6) { + PrintAndLogEx(FAILED, "Key length must be 6 bytes instead of %d", key_len); + result = PM3_EINVARG; + } + if (rnd_len != 7) { + PrintAndLogEx(FAILED, "Random number length must be 7 bytes instead of %d", rnd_len); + result = PM3_EINVARG; + } + if (frn_len != 4) { + PrintAndLogEx(FAILED, "F(RN) length must be 4 bytes instead of %d", frn_len); + result = PM3_EINVARG; + } + if (grn_len != 3) { + PrintAndLogEx(FAILED, "G(RN) length must be 3 bytes instead of %d", grn_len); + result = PM3_EINVARG; + } + } + + if (PM3_SUCCESS == result) { + ID48LIB_NONCE alt_n; + fill_buffer_prng_bytes(&alt_n, sizeof(ID48LIB_NONCE)); + } + + // single exit point + CLIParserFree(ctx); + return result; +} +int CmdEM4x70Recover(const char *Cmd) { + // From paper "Dismantling Megamos Crypto", Roel Verdult, Flavio D. Garcia and Barıs¸ Ege. + // Partial Key-Update Attack -- final 48 bits (after optimized version gets k95..k48) + em4x70_recovery_data_t recover_ctx = {0}; + int result = PM3_SUCCESS; + + result = ValidateArgsForRecover(Cmd, &recover_ctx); + // recover the potential keys -- no more than a few seconds + if (PM3_SUCCESS == result) { + // The library is stateful. First must initialize its internal context. + id48lib_key_recovery_init(&recover_ctx.key, &recover_ctx.nonce, &recover_ctx.frn, &recover_ctx.grn); + + // repeatedly call id48lib_key_recovery_next() to get the next potential key + ID48LIB_KEY q; + while ((PM3_SUCCESS == result) && id48lib_key_recovery_next(&q)) { + if (recover_ctx.keys_found_count >= MAXIMUM_ID48_RECOVERED_KEY_COUNT) { + PrintAndLogEx(ERR, "ERROR: too many potential keys found. This is unexpected and likely a code failure."); + result = PM3_EFAILED; + } else { + recover_ctx.potential_keys[recover_ctx.keys_found_count] = q; + ++recover_ctx.keys_found_count; + } + } + if (recover_ctx.keys_found_count == 0) { + PrintAndLogEx(ERR, "No potential keys recovered. This is unexpected and likely a code failure."); + result = PM3_EFAILED; + } + } + // generate alternate authentication for each potential key -- sub-second execution, no error paths + if (PM3_SUCCESS == result) { + for (uint8_t i = 0; i < recover_ctx.keys_found_count; ++i) { + // generate the alternate frn/grn for the alternate nonce + id48lib_generator(&recover_ctx.potential_keys[i], &recover_ctx.alt_nonce, &recover_ctx.alt_frn[i], &recover_ctx.alt_grn[i]); + } + } + // display alternate authentication for each potential key -- no error paths + if (PM3_SUCCESS == result) { + PrintAndLogEx(NORMAL, "Recovered %d potential keys:", recover_ctx.keys_found_count); + for (uint8_t i = 0; i < recover_ctx.keys_found_count; ++i) { + // generate an alternative authentication based on the potential key + // and the alternate nonce. + ID48LIB_KEY q = recover_ctx.potential_keys[i]; + ID48LIB_FRN alt_frn = recover_ctx.alt_frn[i]; + ID48LIB_GRN alt_grn = recover_ctx.alt_grn[i]; + + // dump the results to screen, to enable the user to manually check validity + // PrintAndLogEx() automatically adds newline, forcing this large parameter count + PrintAndLogEx(NORMAL, + "Potential Key #%d: %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x" + " --> " _YELLOW_("lf em 4x70 auth --rnd %02X%02X%02X%02X%02X%02X%02X --frn %02X%02X%02X%02X") + " --> %02X%02X%02X\n", + i, + q.k[ 0], q.k[ 1], q.k[ 2], q.k[ 3], q.k[ 4], q.k[ 5], + q.k[ 6], q.k[ 7], q.k[ 8], q.k[ 9], q.k[10], q.k[11], + recover_ctx.alt_nonce.rn[0], + recover_ctx.alt_nonce.rn[1], + recover_ctx.alt_nonce.rn[2], + recover_ctx.alt_nonce.rn[3], + recover_ctx.alt_nonce.rn[4], + recover_ctx.alt_nonce.rn[5], + recover_ctx.alt_nonce.rn[6], + alt_frn.frn[0], + alt_frn.frn[1], + alt_frn.frn[2], + alt_frn.frn[3], + alt_grn.grn[0], + alt_grn.grn[1], + alt_grn.grn[2] + ); + } + printf("\n"); + } + if (PM3_SUCCESS == result && recover_ctx.verify) { + // TODO: automatic verification against a present tag. + // Updates ctx.potential_keys_validated[10] and ctx.keys_validated_count + PrintAndLogEx(WARNING, "Automatic verification against tag is not yet implemented."); + // 0. verify a tag is present + // 1. verify the parameters provided authenticate against the tag + // if not, print "Authentication failed. Verify the current tag matches parameters provided." + // print the authentication command used (allows user to easily copy/paste) + // SET ERROR + // 2. for each potential key: + // a. Attempt to authentic against the tag using alt_nonce and alt_frn[i] + // b. verify tag's response is alt_grn[i] + // c. if successful, set ctx.potential_keys_validated[i] = true and increment ctx.keys_validated_count + // + // All validation done... now just interpret the results.... + // + // 3. if ctx.keys_validated_count == 0, print "No keys recovered. Check tag for good coupling (position, etc)?" + // 4. if ctx.keys_validated_count >= 2, print "Multiple keys recovered. Run command again (will use different alt nonce)?" + // 5. if ctx.keys_validated_count == 1, print "Found key: " ... + } + + + return result; +} + static command_t CommandTable[] = { {"help", CmdHelp, AlwaysAvailable, "This help"}, - {"brute", CmdEM4x70Brute, IfPm3EM4x70, "Bruteforce EM4X70 to find partial Crypt Key"}, + {"brute", CmdEM4x70Brute, IfPm3EM4x70, "Bruteforce EM4X70 to find partial key"}, {"info", CmdEM4x70Info, IfPm3EM4x70, "Tag information EM4x70"}, {"write", CmdEM4x70Write, IfPm3EM4x70, "Write EM4x70"}, {"unlock", CmdEM4x70Unlock, IfPm3EM4x70, "Unlock EM4x70 for writing"}, {"auth", CmdEM4x70Auth, IfPm3EM4x70, "Authenticate EM4x70"}, {"writepin", CmdEM4x70WritePIN, IfPm3EM4x70, "Write PIN"}, - {"writekey", CmdEM4x70WriteKey, IfPm3EM4x70, "Write Crypt Key"}, + {"writekey", CmdEM4x70WriteKey, IfPm3EM4x70, "Write key"}, + {"recover", CmdEM4x70Recover, IfPm3EM4x70, "Recover remaining key from partial key"}, {NULL, NULL, NULL, NULL} }; diff --git a/client/src/cmdlfem4x70.h b/client/src/cmdlfem4x70.h index 3c9152f13..1158321a3 100644 --- a/client/src/cmdlfem4x70.h +++ b/client/src/cmdlfem4x70.h @@ -31,7 +31,7 @@ int CmdEM4x70Unlock(const char *Cmd); int CmdEM4x70Auth(const char *Cmd); int CmdEM4x70WritePIN(const char *Cmd); int CmdEM4x70WriteKey(const char *Cmd); -//int CmdEM4x70Recover(const char *Cmd); +int CmdEM4x70Recover(const char *Cmd); // for `lf search`: bool detect_4x70_block(void); diff --git a/include/em4x70.h b/include/em4x70.h index 734e83f48..0b9bcd2f2 100644 --- a/include/em4x70.h +++ b/include/em4x70.h @@ -13,12 +13,15 @@ // // See LICENSE.txt for the text of the license. //----------------------------------------------------------------------------- -// Low frequency EM4x70 structs +// Low frequency EM4x70 structs -- common to both ARM firmware and client //----------------------------------------------------------------------------- #ifndef EM4X70_H__ #define EM4X70_H__ +#include +#include + #define EM4X70_NUM_BLOCKS 16 // Common word/block addresses @@ -26,6 +29,12 @@ #define EM4X70_PIN_WORD_UPPER 11 typedef struct { + // ISSUE: `bool` type does not have a standard-defined size. + // therefore, compatibility between architectures / + // compilers is not guaranteed. + // ISSUE: C99 has no _Static_assert() ... was added in C11 + // TODO: add _Static_assert(sizeof(bool)==1); + // TODO: add _Static_assert(sizeof(em4x70_data_t)==36); bool parity; // Used for writing address @@ -36,8 +45,9 @@ typedef struct { uint32_t pin; // Used for authentication - uint8_t rnd[7]; uint8_t frnd[4]; + uint8_t grnd[3]; + uint8_t rnd[7]; // Used to write new key uint8_t crypt_key[12];