-Caveat Lector-
from:
http://jya.com/a51-pi.htm
<A HREF="http://jya.com/a51-pi.htm">A5/1 Pedagogical Implementation</A>
-----
10 May 1999.Thanks to Anonymous.
See related: http://jya.com/crack-a5.htm
------------------------------------------------------------------------
1. A Pedagogical Implementation of A5/1
2. A5/1 FAQ
------------------------------------------------------------------------
/*
* A pedagogical implementation of A5/1.
*
* Copyright (C) 1998-1999: Marc Briceno, Ian Goldberg, and David Wagner
*
* The source code below is optimized for instructional value and clarity.
* Performance will be terrible, but that's not the point.
* The algorithm is written in the C programming language to avoid ambiguities
* inherent to the English language. Complain to the 9th Circuit of Appeals
* if you have a problem with that.
*
* This software may be export-controlled by US law.
*
* This software is free for commercial and non-commercial use as long as
* the following conditions are aheared to.
* Copyright remains the authors' and as such any Copyright notices in
* the code are not to be removed.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The license and distribution terms for any publicly available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution license
* [including the GNU Public License.]
*
* Background: The Global System for Mobile communications is the most widely
* deployed cellular telephony system in the world. GSM makes use of
* four core cryptographic algorithms, neither of which has been published by
* the GSM MOU. This failure to subject the algorithms to public review is
all
* the more puzzling given that over 100 million GSM
* subscribers are expected to rely on the claimed security of the system.
*
* The four core GSM algorithms are:
* A3 authentication algorithm
* A5/1 "strong" over-the-air voice-privacy algorithm
* A5/2 "weak" over-the-air voice-privacy algorithm
* A8 voice-privacy key generation algorithm
*
* In April of 1998, our group showed that COMP128, the algorithm used by the
* overwhelming majority of GSM providers for both A3 and A8
* functionality was fatally flawed and allowed for cloning of GSM mobile
* phones.
* Furthermore, we demonstrated that all A8 implementations we could locate,
* including the few that did not use COMP128 for key generation, had been
* deliberately weakened by reducing the keyspace from 64 bits to 54 bits.
* The remaining 10 bits are simply set to zero!
*
* See http://www.scard.org/gsm for additional information.
*
* The question so far unanswered is if A5/1, the "stronger" of the two
* widely deployed voice-privacy algorithm is at least as strong as the
* key. Meaning: "Does A5/1 have a work factor of at least 54 bits"?
* Absent a publicly available A5/1 reference implementation, this question
* could not be answered. We hope that our reference implementation below,
* which has been verified against official A5/1 test vectors, will provide
* the cryptographic community with the base on which to construct the
* answer to this important question.
*
* Initial indications about the strength of A5/1 are not encouraging.
* A variant of A5, while not A5/1 itself, has been estimated to have a
* work factor of well below 54 bits. See http://jya.com/crack-a5.htm for
* background information and references.
*
* With COMP128 broken and A5/1 published below, we will now turn our
attention
* to A5/2. The latter has been acknowledged by the GSM community to have
* been specifically designed by intelligence agencies for lack of security.
*
* We hope to publish A5/2 later this year.
*
* -- Marc Briceno <[EMAIL PROTECTED]>
* Voice: +1 (925) 798-4042
*
*/
#include <stdio.h>
/* Masks for the three shift registers */
#define R1MASK 0x07FFFF /* 19 bits, numbered 0..18 */
#define R2MASK 0x3FFFFF /* 22 bits, numbered 0..21 */
#define R3MASK 0x7FFFFF /* 23 bits, numbered 0..22 */
/* Middle bit of each of the three shift registers, for clock control */
#define R1MID 0x000100 /* bit 8 */
#define R2MID 0x000400 /* bit 10 */
#define R3MID 0x000400 /* bit 10 */
/* Feedback taps, for clocking the shift registers.
* These correspond to the primitive polynomials
* x^19 + x^5 + x^2 + x + 1, x^22 + x + 1,
* and x^23 + x^15 + x^2 + x + 1. */
#define R1TAPS 0x072000 /* bits 18,17,16,13 */
#define R2TAPS 0x300000 /* bits 21,20 */
#define R3TAPS 0x700080 /* bits 22,21,20,7 */
/* Output taps, for output generation */
#define R1OUT 0x040000 /* bit 18 (the high bit) */
#define R2OUT 0x200000 /* bit 21 (the high bit) */
#define R3OUT 0x400000 /* bit 22 (the high bit) */
typedef unsigned char byte;
typedef unsigned long word;
typedef word bit;
/* Calculate the parity of a 32-bit word, i.e. the sum of its bits modulo 2 */
bit parity(word x) {
x ^= x>>16;
x ^= x>>8;
x ^= x>>4;
x ^= x>>2;
x ^= x>>1;
return x&1;
}
/* Clock one shift register */
word clockone(word reg, word mask, word taps) {
word t = reg & taps;
reg = (reg << 1) & mask;
reg |= parity(t);
return reg;
}
/* The three shift registers. They're in global variables to make the code
* easier to understand.
* A better implementation would not use global variables. */
word R1, R2, R3;
/* Look at the middle bits of R1,R2,R3, take a vote, and
* return the majority value of those 3 bits. */
bit majority() {
int sum;
sum = parity(R1&R1MID) + parity(R2&R2MID) + parity(R3&R3MID);
if (sum >= 2)
return 1;
else
return 0;
}
/* Clock two or three of R1,R2,R3, with clock control
* according to their middle bits.
* Specifically, we clock Ri whenever Ri's middle bit
* agrees with the majority value of the three middle bits.*/
void clock() {
bit maj = majority();
if (((R1&R1MID)!=0) == maj)
R1 = clockone(R1, R1MASK, R1TAPS);
if (((R2&R2MID)!=0) == maj)
R2 = clockone(R2, R2MASK, R2TAPS);
if (((R3&R3MID)!=0) == maj)
R3 = clockone(R3, R3MASK, R3TAPS);
}
/* Clock all three of R1,R2,R3, ignoring their middle bits.
* This is only used for key setup. */
void clockallthree() {
R1 = clockone(R1, R1MASK, R1TAPS);
R2 = clockone(R2, R2MASK, R2TAPS);
R3 = clockone(R3, R3MASK, R3TAPS);
}
/* Generate an output bit from the current state.
* You grab a bit from each register via the output generation taps;
* then you XOR the resulting three bits. */
bit getbit() {
return parity(R1&R1OUT)^parity(R2&R2OUT)^parity(R3&R3OUT);
}
/* Do the A5/1 key setup. This routine accepts a 64-bit key and
* a 22-bit frame number. */
void keysetup(byte key[8], word frame) {
int i;
bit keybit, framebit;
/* Zero out the shift registers. */
R1 = R2 = R3 = 0;
/* Load the key into the shift registers,
* LSB of first byte of key array first,
* clocking each register once for every
* key bit loaded. (The usual clock
* control rule is temporarily disabled.) */
for (i=0; i<64; i++) {
clockallthree(); /* always clock */
keybit = (key[i/8] >> (i&7)) & 1; /* The i-th bit of the key
*/
R1 ^= keybit; R2 ^= keybit; R3 ^= keybit;
}
/* Load the frame number into the shift
* registers, LSB first,
* clocking each register once for every
* key bit loaded. (The usual clock
* control rule is still disabled.) */
for (i=0; i<22; i++) {
clockallthree(); /* always clock */
framebit = (frame >> i) & 1; /* The i-th bit of the frame # */
R1 ^= framebit; R2 ^= framebit; R3 ^= framebit;
}
/* Run the shift registers for 100 clocks
* to mix the keying material and frame number
* together with output generation disabled,
* so that there is sufficient avalanche.
* We re-enable the majority-based clock control
* rule from now on. */
for (i=0; i<100; i++) {
clock();
}
/* Now the key is properly set up. */
}
/* Generate output. We generate 228 bits of
* keystream output. The first 114 bits is for
* the A->B frame; the next 114 bits is for the
* B->A frame. You allocate a 15-byte buffer
* for each direction, and this function fills
* it in. */
void run(byte AtoBkeystream[], byte BtoAkeystream[]) {
int i;
/* Zero out the output buffers. */
for (i=0; i<=113/8; i++)
AtoBkeystream[i] = BtoAkeystream[i] = 0;
/* Generate 114 bits of keystream for the
* A->B direction. Store it, MSB first. */
for (i=0; i<114; i++) {
clock();
AtoBkeystream[i/8] |= getbit() << (7-(i&7));
}
/* Generate 114 bits of keystream for the
* B->A direction. Store it, MSB first. */
for (i=0; i<114; i++) {
clock();
BtoAkeystream[i/8] |= getbit() << (7-(i&7));
}
}
/* Test the code by comparing it against
* a known-good test vector. */
void test() {
byte key[8] = {0x12, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF};
word frame = 0x134;
byte goodAtoB[15] = { 0x53, 0x4E, 0xAA, 0x58, 0x2F, 0xE8, 0x15,
0x1A, 0xB6, 0xE1, 0x85, 0x5A, 0x72, 0x8C, 0x00
};
byte goodBtoA[15] = { 0x24, 0xFD, 0x35, 0xA3, 0x5D, 0x5F, 0xB6,
0x52, 0x6D, 0x32, 0xF9, 0x06, 0xDF, 0x1A, 0xC0
};
byte AtoB[15], BtoA[15];
int i, failed=0;
keysetup(key, frame);
run(AtoB, BtoA);
/* Compare against the test vector. */
for (i=0; i<15; i++)
if (AtoB[i] != goodAtoB[i])
failed = 1;
for (i=0; i<15; i++)
if (BtoA[i] != goodBtoA[i])
failed = 1;
/* Print some debugging output. */
printf("key: 0x");
for (i=0; i<8; i++)
printf("%02X", key[i]);
printf("\n");
printf("frame number: 0x%06X\n", (unsigned int)frame);
printf("known good output:\n");
printf(" A->B: 0x");
for (i=0; i<15; i++)
printf("%02X", goodAtoB[i]);
printf(" B->A: 0x");
for (i=0; i<15; i++)
printf("%02X", goodBtoA[i]);
printf("\n");
printf("observed output:\n");
printf(" A->B: 0x");
for (i=0; i<15; i++)
printf("%02X", AtoB[i]);
printf(" B->A: 0x");
for (i=0; i<15; i++)
printf("%02X", BtoA[i]);
printf("\n");
if (!failed) {
printf("Self-check succeeded: everything looks ok.\n");
return;
} else {
/* Problems! The test vectors didn't compare*/
printf("\nI don't know why this broke; contact the
authors.\n");
exit(1);
}
}
int main(void) {
test();
return 0;
}
------------------------------------------------------------------------
Date: Mon, 10 May 1999 10:58:43 +0200 (CEST)
From: Lucky Green <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Subject: A5/1 FAQ
The A5/1 release at this month's Cypherpunks meeting brought up a few
questions from the attendees. Since I suspect others might have the same
questions, I'll answer them below.
o A5 is an LFSR-based stream cipher. It takes a 64 bit key and a 22 bit
frame number. Ross Anderson's variant was mostly correct.
o All GSM keygen implementations we looked at set the last 10 bits of the
key to zero. That doesn't mean there may not be GSM providers that use the
full 64 bit keyspace. It simply means we have yet to find one that does.
As a first approximation, the attacker knows 10 bits of the key.
o During about the first 1/10th of a call the vocoder will encode silence.
A very rough estimate is 13000 bps * 0.1 s = 1300 bits of known plaintext.
Clearly, the cryptanalyst has a lot to work with here.
o I would love to read some well-founded estimates on how fast this
algorithm could be made to run on a Pentium class CPU and a low-cost FPGA.
Just so we all know what the upper bounds for a brute force attack are.
Not that I believe brute force to be the most efficient means of attack.
o I am pretty sure we know how to find A5/2. It mostly requires some
simple hardware work that we have not had time to implement. Stay tuned.
(I don't make a dime of exposing the incompetence of the GSM designers or
how intelligence agencies have subverted GSM's security to the detriment
of over 100 million users worldwide. This project only gets cycles when I
have some spare time. Claims by members of the GSM MOU that our work is
funded by suitcases full of cash from GSM's competition notwithstanding.
My apologies if things have been a bit slow in progressing for a while.
o offers from websites with export controls in place to host the code are
appreciated. I will email the algorithm to anybody I personally know to be
an US citizen. The rest has to wait until nature takes it course. Which,
if history is any guide, won't be very long.
Have fun,
-- Lucky Green <[EMAIL PROTECTED]> PGP v5 encrypted email preferred.
------------------------------------------------------------------------
-----
Aloha, He'Ping,
Om, Shalom, Salaam.
Em Hotep, Peace Be,
Omnia Bona Bonis,
All My Relations.
Adieu, Adios, Aloha.
Amen.
Roads End
Kris
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