A5/2

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A5/2 is a stream cipher used to provide voice privacy in the GSM cellular telephone protocol.

The A5 algorithm is used in the GSM ciphering process between a MS (Mobile Station) and the GSM network.

A5-GSM.jpg

This algorithm is simpler than A5/1 and was developed by ETSI (European Telecommunications Standards Institute) for use in Eastern European states that had restrictions to certain Western technologies.

The cipher is based around a combination of four linear feedback shift registers with irregular clocking and a non-linear combiner.

In 1999, Ian Goldberg and David Wagner cryptanalyzed A5/2 in the same month it was published, and showed that it was extremely weak — so much so that low end equipment can probably break it in real time.

According with the GSMA (GSM Association) since July 01st 2006, Mobile Phones will not support anymore Ciphering A5/2, developed mainly for Asia countries, since the code was cracked in 1999, anyway A5/1 is stronger than A5/2, and is supported as mandatory, by the 3GPP association.

Contents

Source Code

Given below is the pedagogical implementation of the A5/1 algorithm<ref>A pedagogical implementation of the GSM A5/1 and A5/2 "voice privacy" encryption algorithms</ref>

/*

* A pedagogical implementation of the GSM A5/1 and A5/2 "voice privacy"
* encryption algorithms.
*
* 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.
*
* 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 adhered 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 digital cellular telephony system in the world. GSM
* makes use of four core cryptographic algorithms, none 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
* 215 million GSM subscribers are expected to rely on the claimed
* security of the system.
*
* The four core GSM cryptographic algorithms are:
* A3              authentication algorithm
* A5/1 "stronger" over-the-air voice-privacy algorithm
* A5/2  "weaker"  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
* is fatally flawed and allows 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.
*
* [May 1999]
* One 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.
*
* [August 1999]
* 19th Annual International Cryptology Conference - Crypto'99
* Santa Barbara, California
*
* A5/2 has been added to the previously published A5/1 source. Our
* implementation has been verified against official test vectors.
*
* This means that our group has now reverse engineered the entire set
* of cryptographic algorithms used in the overwhelming majority of GSM
* installations, including all the over-the-air "voice privacy" algorithms.
*
* The "voice privacy" algorithm A5/2 proved especially weak. Which perhaps
* should come as no surprise, since even GSM MOU members have admitted that
* A5/2 was designed with heavy input by intelligence agencies to ensure
* breakability. Just how insecure is A5/2?  It can be broken in real time
* with a work factor of a mere 16 bits. GSM might just as well use no "voice
* privacy" algorithm at all.
*
* We announced the break of A5/2 at the Crypto'99 Rump Session.
* Details will be published in a scientific paper following soon.
*
*
* -- Marc Briceno      <marc@scard.org>
*    Voice:            +1 (925) 798-4042
*
*/


  1. include <stdio.h>


/* Masks for the shift registers */

  1. define R1MASK 0x07FFFF /* 19 bits, numbered 0..18 */
  2. define R2MASK 0x3FFFFF /* 22 bits, numbered 0..21 */
  3. define R3MASK 0x7FFFFF /* 23 bits, numbered 0..22 */
  4. ifdef A5_2
  5. define R4MASK 0x01FFFF /* 17 bits, numbered 0..16 */
  6. endif /* A5_2 */


  1. ifndef A5_2

/* Middle bit of each of the three shift registers, for clock control */

  1. define R1MID 0x000100 /* bit 8 */
  2. define R2MID 0x000400 /* bit 10 */
  3. define R3MID 0x000400 /* bit 10 */
  4. else /* A5_2 */

/* A bit of R4 that controls each of the shift registers */

  1. define R4TAP1 0x000400 /* bit 10 */
  2. define R4TAP2 0x000008 /* bit 3 */
  3. define R4TAP3 0x000080 /* bit 7 */
  4. endif /* A5_2 */


/* 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,
* x^23 + x^15 + x^2 + x + 1, and x^17 + x^5 + 1. */


  1. define R1TAPS 0x072000 /* bits 18,17,16,13 */
  2. define R2TAPS 0x300000 /* bits 21,20 */
  3. define R3TAPS 0x700080 /* bits 22,21,20,7 */
  4. ifdef A5_2
  5. define R4TAPS 0x010800 /* bits 16,11 */
  6. endif /* A5_2 */


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. For A5/2, when the last bit of the frame

* is loaded in, one particular bit of each register is forced to '1';
* that bit is passed in as the last argument. */
  1. ifndef A5_2

word clockone(word reg, word mask, word taps) {

  1. else /* A5_2 */

word clockone(word reg, word mask, word taps, word loaded_bit) {

  1. endif /* A5_2 */
       word t = reg & taps;
       reg = (reg << 1) & mask;
       reg |= parity(t);
  1. ifdef A5_2
       reg |= loaded_bit;
  1. endif /* A5_2 */
       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;

  1. ifdef A5_2

word R4;

  1. endif /* A5_2 */


/* Return 1 iff at least two of the parameter words are non-zero. */ bit majority(word w1, word w2, word w3) {

       int sum = (w1 != 0) + (w2 != 0) + (w3 != 0);
       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.  For A5/2,
* use particular bits of R4 instead of the middle bits.  Also, for A5/2,
* always clock R4.
* If allP == 1, clock all three of R1,R2,R3, ignoring their middle bits.
* This is only used for key setup.  If loaded == 1, then this is the last
* bit of the frame number, and if we're doing A5/2, we have to set a
* particular bit in each of the four registers. */

void clock(int allP, int loaded) {

  1. ifndef A5_2
       bit maj = majority(R1&R1MID, R2&R2MID, R3&R3MID);
       if (allP || (((R1&R1MID)!=0) == maj))
               R1 = clockone(R1, R1MASK, R1TAPS);
       if (allP || (((R2&R2MID)!=0) == maj))
               R2 = clockone(R2, R2MASK, R2TAPS);
       if (allP || (((R3&R3MID)!=0) == maj))
               R3 = clockone(R3, R3MASK, R3TAPS);
  1. else /* A5_2 */
       bit maj = majority(R4&R4TAP1, R4&R4TAP2, R4&R4TAP3);
       if (allP || (((R4&R4TAP1)!=0) == maj))
               R1 = clockone(R1, R1MASK, R1TAPS, loaded<<15);
       if (allP || (((R4&R4TAP2)!=0) == maj))
               R2 = clockone(R2, R2MASK, R2TAPS, loaded<<16);
       if (allP || (((R4&R4TAP3)!=0) == maj))
               R3 = clockone(R3, R3MASK, R3TAPS, loaded<<18);
       R4 = clockone(R4, R4MASK, R4TAPS, loaded<<10);
  1. endif /* A5_2 */

}


/* 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.  For A5/2, in addition to
* the top bit of each of R1,R2,R3, also XOR in a majority function
* of three particular bits of the register (one of them complemented)
* to make it non-linear.  Also, for A5/2, delay the output by one
* clock cycle for some reason. */

bit getbit() {

       bit topbits = (((R1 >> 18) ^ (R2 >> 21) ^ (R3 >> 22)) & 0x01);
  1. ifndef A5_2
       return topbits;
  1. else /* A5_2 */
       static bit delaybit = 0;
       bit nowbit = delaybit;
       delaybit = (
           topbits
           ^ majority(R1&0x8000, (~R1)&0x4000, R1&0x1000)
           ^ majority((~R2)&0x10000, R2&0x2000, R2&0x200)
           ^ majority(R3&0x40000, R3&0x10000, (~R3)&0x2000)
           );
       return nowbit;
  1. endif /* A5_2 */

}


/* Do the A5 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;
  1. ifdef A5_2
       R4 = 0;
  1. endif /* A5_2 */


       /* 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++) {
               clock(1,0); /* always clock */
               keybit = (key[i/8] >> (i&7)) & 1; /* The i-th bit of the key */
               R1 ^= keybit; R2 ^= keybit; R3 ^= keybit;
  1. ifdef A5_2
               R4 ^= keybit;
  1. endif /* A5_2 */
       }


       /* 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 A5/2, signal when the last bit is being clocked in. */
       for (i=0; i<22; i++) {
               clock(1,i==21); /* always clock */
               framebit = (frame >> i) & 1; /* The i-th bit of the frame # */
               R1 ^= framebit; R2 ^= framebit; R3 ^= framebit;
  1. ifdef A5_2
               R4 ^= framebit;
  1. endif /* A5_2 */
       }


       /* 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(0,0);
       }
       /* For A5/2, we have to load the delayed output bit.  This does _not_
        * change the state of the registers.  For A5/1, this is a no-op. */
       getbit();


       /* 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(0,0);
               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(0,0);
               BtoAkeystream[i/8] |= getbit() << (7-(i&7));
       }

}


/* Test the code by comparing it against

* a known-good test vector. */

void test() {

  1. ifndef A5_2
       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 };
  1. else /* A5_2 */
       byte key[8] = {0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff};
       word frame = 0x21;
       byte goodAtoB[15] = { 0xf4, 0x51, 0x2c, 0xac, 0x13, 0x59, 0x37,
                             0x64, 0x46, 0x0b, 0x72, 0x2d, 0xad, 0xd5, 0x00 };
       byte goodBtoA[15] = { 0x48, 0x00, 0xd4, 0x32, 0x8e, 0x16, 0xa1,
                             0x4d, 0xcd, 0x7b, 0x97, 0x22, 0x26, 0x51, 0x00 };
  1. endif /* A5_2 */
       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");
               exit(0);
       } else {
               /* Problems!  The test vectors didn't compare*/
               printf("\nI don't know why this broke; contact the authors.\n");
       }

}


int main(void) {

       test();
       return 0;

}

References

<references/>

See Also

  • A5/0: Dummy cipher, no encryption
  • A5/1: The original A5 algorithm used in Europe.
  • A5/3: 3G algorithm

External Links

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