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+/*
+ * 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
+ *
+ */
+
+
+#include <stdio.h>
+
+
+/* Masks for the 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 */
+#ifdef A5_2
+#define R4MASK  0x01FFFF /* 17 bits, numbered 0..16 */
+#endif /* A5_2 */
+
+
+#ifndef A5_2
+/* 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 */
+#else /* A5_2 */
+/* A bit of R4 that controls each of the shift registers */
+#define R4TAP1  0x000400 /* bit 10 */
+#define R4TAP2  0x000008 /* bit 3 */
+#define R4TAP3  0x000080 /* bit 7 */
+#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. */
+
+
+#define R1TAPS  0x072000 /* bits 18,17,16,13 */
+#define R2TAPS  0x300000 /* bits 21,20 */
+#define R3TAPS  0x700080 /* bits 22,21,20,7 */
+#ifdef A5_2
+#define R4TAPS  0x010800 /* bits 16,11 */
+#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. */
+#ifndef A5_2
+word clockone(word reg, word mask, word taps)
+{
+#else /* A5_2 */
+word clockone(word reg, word mask, word taps, word loaded_bit) {
+#endif /* A5_2 */
+  word t = reg & taps;
+  reg = (reg << 1) & mask;
+  reg |= parity(t);
+#ifdef A5_2
+  reg |= loaded_bit;
+#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;
+#ifdef A5_2
+word R4;
+#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) {
+#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);
+#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);
+#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);
+#ifndef A5_2
+  return topbits;
+#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;
+#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_reversed[8], word frame) {
+  int i;
+  bit keybit, framebit;
+
+  byte key[8];
+  for(i=0; i<8; i++){
+    key[i] = key_reversed[7-i];
+  }
+  /* Zero out the shift registers. */
+  R1 = R2 = R3 = 0;
+#ifdef A5_2
+  R4 = 0;
+#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;
+#ifdef A5_2
+    R4 ^= keybit;
+#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;
+#ifdef A5_2
+    R4 ^= framebit;
+#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));
+  }
+}
+
+void runA51(unsigned char AtoBkeystream[]) {
+  int i;
+
+  /* Zero out the output buffers. */
+  for (i = 0; i < 114; i++)
+    AtoBkeystream[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] = getbit();
+  }
+}
+
+
+/* Test the code by comparing it against
+ * a known-good test vector. */
+void test() {
+#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
+                      };
+#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
+                      };
+#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");
+  }
+}
+