1*1c9681d1Schristos /* $NetBSD: tommath.h,v 1.2 2017/01/28 21:31:47 christos Exp $ */ 2f59d82ffSelric 3f59d82ffSelric /* LibTomMath, multiple-precision integer library -- Tom St Denis 4f59d82ffSelric * 5f59d82ffSelric * LibTomMath is a library that provides multiple-precision 6f59d82ffSelric * integer arithmetic as well as number theoretic functionality. 7f59d82ffSelric * 8f59d82ffSelric * The library was designed directly after the MPI library by 9f59d82ffSelric * Michael Fromberger but has been written from scratch with 10f59d82ffSelric * additional optimizations in place. 11f59d82ffSelric * 12f59d82ffSelric * The library is free for all purposes without any express 13f59d82ffSelric * guarantee it works. 14f59d82ffSelric * 15f59d82ffSelric * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com 16f59d82ffSelric */ 17f59d82ffSelric #ifndef BN_H_ 18f59d82ffSelric #define BN_H_ 19f59d82ffSelric 20f59d82ffSelric #include <stdio.h> 21f59d82ffSelric #include <string.h> 22f59d82ffSelric #include <stdlib.h> 23f59d82ffSelric #include <ctype.h> 24f59d82ffSelric #include <limits.h> 25f59d82ffSelric 26f59d82ffSelric #include <tommath_class.h> 27f59d82ffSelric 28f59d82ffSelric #ifndef MIN 29f59d82ffSelric #define MIN(x,y) ((x)<(y)?(x):(y)) 30f59d82ffSelric #endif 31f59d82ffSelric 32f59d82ffSelric #ifndef MAX 33f59d82ffSelric #define MAX(x,y) ((x)>(y)?(x):(y)) 34f59d82ffSelric #endif 35f59d82ffSelric 36f59d82ffSelric #ifdef __cplusplus 37f59d82ffSelric extern "C" { 38f59d82ffSelric 39f59d82ffSelric /* C++ compilers don't like assigning void * to mp_digit * */ 40f59d82ffSelric #define OPT_CAST(x) (x *) 41f59d82ffSelric 42f59d82ffSelric #else 43f59d82ffSelric 44f59d82ffSelric /* C on the other hand doesn't care */ 45f59d82ffSelric #define OPT_CAST(x) 46f59d82ffSelric 47f59d82ffSelric #endif 48f59d82ffSelric 49f59d82ffSelric 50f59d82ffSelric /* detect 64-bit mode if possible */ 51e0895134Schristos #if defined(__x86_64__) && !defined(__ILP32__) 52f59d82ffSelric #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) 53f59d82ffSelric #define MP_64BIT 54f59d82ffSelric #endif 55f59d82ffSelric #endif 56f59d82ffSelric 57f59d82ffSelric /* some default configurations. 58f59d82ffSelric * 59f59d82ffSelric * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits 60f59d82ffSelric * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits 61f59d82ffSelric * 62f59d82ffSelric * At the very least a mp_digit must be able to hold 7 bits 63f59d82ffSelric * [any size beyond that is ok provided it doesn't overflow the data type] 64f59d82ffSelric */ 65f59d82ffSelric #ifdef MP_8BIT 66f59d82ffSelric typedef unsigned char mp_digit; 67f59d82ffSelric typedef unsigned short mp_word; 68f59d82ffSelric #elif defined(MP_16BIT) 69f59d82ffSelric typedef unsigned short mp_digit; 70f59d82ffSelric typedef unsigned long mp_word; 71f59d82ffSelric #elif defined(MP_64BIT) 72f59d82ffSelric /* for GCC only on supported platforms */ 73f59d82ffSelric #ifndef CRYPT 74f59d82ffSelric typedef unsigned long long ulong64; 75f59d82ffSelric typedef signed long long long64; 76f59d82ffSelric #endif 77f59d82ffSelric 78f59d82ffSelric typedef unsigned long mp_digit; 79f59d82ffSelric typedef unsigned long mp_word __attribute__ ((mode(TI))); 80f59d82ffSelric 81f59d82ffSelric #define DIGIT_BIT 60 82f59d82ffSelric #else 83f59d82ffSelric /* this is the default case, 28-bit digits */ 84f59d82ffSelric 85f59d82ffSelric /* this is to make porting into LibTomCrypt easier :-) */ 86f59d82ffSelric #ifndef CRYPT 87f59d82ffSelric #if defined(_MSC_VER) || defined(__BORLANDC__) 88f59d82ffSelric typedef unsigned __int64 ulong64; 89f59d82ffSelric typedef signed __int64 long64; 90f59d82ffSelric #else 91f59d82ffSelric typedef unsigned long long ulong64; 92f59d82ffSelric typedef signed long long long64; 93f59d82ffSelric #endif 94f59d82ffSelric #endif 95f59d82ffSelric 96f59d82ffSelric typedef unsigned long mp_digit; 97f59d82ffSelric typedef ulong64 mp_word; 98f59d82ffSelric 99f59d82ffSelric #ifdef MP_31BIT 100f59d82ffSelric /* this is an extension that uses 31-bit digits */ 101f59d82ffSelric #define DIGIT_BIT 31 102f59d82ffSelric #else 103f59d82ffSelric /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ 104f59d82ffSelric #define DIGIT_BIT 28 105f59d82ffSelric #define MP_28BIT 106f59d82ffSelric #endif 107f59d82ffSelric #endif 108f59d82ffSelric 109f59d82ffSelric /* define heap macros */ 110f59d82ffSelric #ifndef CRYPT 111f59d82ffSelric /* default to libc stuff */ 112f59d82ffSelric #ifndef XMALLOC 113f59d82ffSelric #define XMALLOC malloc 114f59d82ffSelric #define XFREE free 115f59d82ffSelric #define XREALLOC realloc 116f59d82ffSelric #define XCALLOC calloc 117f59d82ffSelric #else 118f59d82ffSelric /* prototypes for our heap functions */ 119f59d82ffSelric extern void *XMALLOC(size_t n); 120f59d82ffSelric extern void *XREALLOC(void *p, size_t n); 121f59d82ffSelric extern void *XCALLOC(size_t n, size_t s); 122f59d82ffSelric extern void XFREE(void *p); 123f59d82ffSelric #endif 124f59d82ffSelric #endif 125f59d82ffSelric 126f59d82ffSelric 127f59d82ffSelric /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ 128f59d82ffSelric #ifndef DIGIT_BIT 129f59d82ffSelric #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */ 130f59d82ffSelric #endif 131f59d82ffSelric 132f59d82ffSelric #define MP_DIGIT_BIT DIGIT_BIT 133f59d82ffSelric #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) 134f59d82ffSelric #define MP_DIGIT_MAX MP_MASK 135f59d82ffSelric 136f59d82ffSelric /* equalities */ 137f59d82ffSelric #define MP_LT -1 /* less than */ 138f59d82ffSelric #define MP_EQ 0 /* equal to */ 139f59d82ffSelric #define MP_GT 1 /* greater than */ 140f59d82ffSelric 141f59d82ffSelric #define MP_ZPOS 0 /* positive integer */ 142f59d82ffSelric #define MP_NEG 1 /* negative */ 143f59d82ffSelric 144f59d82ffSelric #define MP_OKAY 0 /* ok result */ 145f59d82ffSelric #define MP_MEM -2 /* out of mem */ 146f59d82ffSelric #define MP_VAL -3 /* invalid input */ 147f59d82ffSelric #define MP_RANGE MP_VAL 148f59d82ffSelric 149f59d82ffSelric #define MP_YES 1 /* yes response */ 150f59d82ffSelric #define MP_NO 0 /* no response */ 151f59d82ffSelric 152f59d82ffSelric /* Primality generation flags */ 153f59d82ffSelric #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ 154f59d82ffSelric #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ 155f59d82ffSelric #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ 156f59d82ffSelric 157f59d82ffSelric typedef int mp_err; 158f59d82ffSelric 159f59d82ffSelric /* you'll have to tune these... */ 160f59d82ffSelric extern int KARATSUBA_MUL_CUTOFF, 161f59d82ffSelric KARATSUBA_SQR_CUTOFF, 162f59d82ffSelric TOOM_MUL_CUTOFF, 163f59d82ffSelric TOOM_SQR_CUTOFF; 164f59d82ffSelric 165f59d82ffSelric /* define this to use lower memory usage routines (exptmods mostly) */ 166f59d82ffSelric /* #define MP_LOW_MEM */ 167f59d82ffSelric 168f59d82ffSelric /* default precision */ 169f59d82ffSelric #ifndef MP_PREC 170f59d82ffSelric #ifndef MP_LOW_MEM 171f59d82ffSelric #define MP_PREC 32 /* default digits of precision */ 172f59d82ffSelric #else 173f59d82ffSelric #define MP_PREC 8 /* default digits of precision */ 174f59d82ffSelric #endif 175f59d82ffSelric #endif 176f59d82ffSelric 177f59d82ffSelric /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ 178f59d82ffSelric #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) 179f59d82ffSelric 180f59d82ffSelric /* the infamous mp_int structure */ 181f59d82ffSelric typedef struct { 182f59d82ffSelric int used, alloc, sign; 183f59d82ffSelric mp_digit *dp; 184f59d82ffSelric } mp_int; 185f59d82ffSelric 186f59d82ffSelric /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ 187f59d82ffSelric typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); 188f59d82ffSelric 189f59d82ffSelric 190f59d82ffSelric #define USED(m) ((m)->used) 191f59d82ffSelric #define DIGIT(m,k) ((m)->dp[(k)]) 192f59d82ffSelric #define SIGN(m) ((m)->sign) 193f59d82ffSelric 194e0895134Schristos /* error code to const char* string */ 195e0895134Schristos const char *mp_error_to_string(int code); 196f59d82ffSelric 197f59d82ffSelric /* ---> init and deinit bignum functions <--- */ 198f59d82ffSelric /* init a bignum */ 199f59d82ffSelric int mp_init(mp_int *a); 200f59d82ffSelric 201f59d82ffSelric /* free a bignum */ 202f59d82ffSelric void mp_clear(mp_int *a); 203f59d82ffSelric 204f59d82ffSelric /* init a null terminated series of arguments */ 205f59d82ffSelric int mp_init_multi(mp_int *mp, ...); 206f59d82ffSelric 207f59d82ffSelric /* clear a null terminated series of arguments */ 208f59d82ffSelric void mp_clear_multi(mp_int *mp, ...); 209f59d82ffSelric 210f59d82ffSelric /* exchange two ints */ 211f59d82ffSelric void mp_exch(mp_int *a, mp_int *b); 212f59d82ffSelric 213f59d82ffSelric /* shrink ram required for a bignum */ 214f59d82ffSelric int mp_shrink(mp_int *a); 215f59d82ffSelric 216f59d82ffSelric /* grow an int to a given size */ 217f59d82ffSelric int mp_grow(mp_int *a, int size); 218f59d82ffSelric 219f59d82ffSelric /* init to a given number of digits */ 220f59d82ffSelric int mp_init_size(mp_int *a, int size); 221f59d82ffSelric 222f59d82ffSelric /* ---> Basic Manipulations <--- */ 223f59d82ffSelric #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) 224f59d82ffSelric #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) 225f59d82ffSelric #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) 226f59d82ffSelric #define mp_isneg(a) (((a)->sign) ? MP_YES : MP_NO) 227f59d82ffSelric 228f59d82ffSelric /* set to zero */ 229f59d82ffSelric void mp_zero(mp_int *a); 230f59d82ffSelric 231f59d82ffSelric /* set to zero, multi */ 232f59d82ffSelric void mp_zero_multi(mp_int *a, ...); 233f59d82ffSelric 234f59d82ffSelric /* set to a digit */ 235f59d82ffSelric void mp_set(mp_int *a, mp_digit b); 236f59d82ffSelric 237f59d82ffSelric /* set a 32-bit const */ 238f59d82ffSelric int mp_set_int(mp_int *a, unsigned long b); 239f59d82ffSelric 240f59d82ffSelric /* get a 32-bit value */ 241f59d82ffSelric unsigned long mp_get_int(mp_int * a); 242f59d82ffSelric 243f59d82ffSelric /* initialize and set a digit */ 244f59d82ffSelric int mp_init_set (mp_int * a, mp_digit b); 245f59d82ffSelric 246f59d82ffSelric /* initialize and set 32-bit value */ 247f59d82ffSelric int mp_init_set_int (mp_int * a, unsigned long b); 248f59d82ffSelric 249f59d82ffSelric /* copy, b = a */ 250f59d82ffSelric int mp_copy(mp_int *a, mp_int *b); 251f59d82ffSelric 252f59d82ffSelric /* inits and copies, a = b */ 253f59d82ffSelric int mp_init_copy(mp_int *a, mp_int *b); 254f59d82ffSelric 255f59d82ffSelric /* trim unused digits */ 256f59d82ffSelric void mp_clamp(mp_int *a); 257f59d82ffSelric 258f59d82ffSelric /* ---> digit manipulation <--- */ 259f59d82ffSelric 260f59d82ffSelric /* right shift by "b" digits */ 261f59d82ffSelric void mp_rshd(mp_int *a, int b); 262f59d82ffSelric 263f59d82ffSelric /* left shift by "b" digits */ 264f59d82ffSelric int mp_lshd(mp_int *a, int b); 265f59d82ffSelric 266f59d82ffSelric /* c = a / 2**b */ 267f59d82ffSelric int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); 268f59d82ffSelric 269f59d82ffSelric /* b = a/2 */ 270f59d82ffSelric int mp_div_2(mp_int *a, mp_int *b); 271f59d82ffSelric 272f59d82ffSelric /* c = a * 2**b */ 273f59d82ffSelric int mp_mul_2d(mp_int *a, int b, mp_int *c); 274f59d82ffSelric 275f59d82ffSelric /* b = a*2 */ 276f59d82ffSelric int mp_mul_2(mp_int *a, mp_int *b); 277f59d82ffSelric 278f59d82ffSelric /* c = a mod 2**d */ 279f59d82ffSelric int mp_mod_2d(mp_int *a, int b, mp_int *c); 280f59d82ffSelric 281f59d82ffSelric /* computes a = 2**b */ 282f59d82ffSelric int mp_2expt(mp_int *a, int b); 283f59d82ffSelric 284f59d82ffSelric /* Counts the number of lsbs which are zero before the first zero bit */ 285f59d82ffSelric int mp_cnt_lsb(mp_int *a); 286f59d82ffSelric 287f59d82ffSelric /* I Love Earth! */ 288f59d82ffSelric 289f59d82ffSelric /* makes a pseudo-random int of a given size */ 290f59d82ffSelric int mp_rand(mp_int *a, int digits); 291f59d82ffSelric 292f59d82ffSelric /* ---> binary operations <--- */ 293f59d82ffSelric /* c = a XOR b */ 294f59d82ffSelric int mp_xor(mp_int *a, mp_int *b, mp_int *c); 295f59d82ffSelric 296f59d82ffSelric /* c = a OR b */ 297f59d82ffSelric int mp_or(mp_int *a, mp_int *b, mp_int *c); 298f59d82ffSelric 299f59d82ffSelric /* c = a AND b */ 300f59d82ffSelric int mp_and(mp_int *a, mp_int *b, mp_int *c); 301f59d82ffSelric 302f59d82ffSelric /* ---> Basic arithmetic <--- */ 303f59d82ffSelric 304f59d82ffSelric /* b = -a */ 305f59d82ffSelric int mp_neg(mp_int *a, mp_int *b); 306f59d82ffSelric 307f59d82ffSelric /* b = |a| */ 308f59d82ffSelric int mp_abs(mp_int *a, mp_int *b); 309f59d82ffSelric 310f59d82ffSelric /* compare a to b */ 311f59d82ffSelric int mp_cmp(mp_int *a, mp_int *b); 312f59d82ffSelric 313f59d82ffSelric /* compare |a| to |b| */ 314f59d82ffSelric int mp_cmp_mag(mp_int *a, mp_int *b); 315f59d82ffSelric 316f59d82ffSelric /* c = a + b */ 317f59d82ffSelric int mp_add(mp_int *a, mp_int *b, mp_int *c); 318f59d82ffSelric 319f59d82ffSelric /* c = a - b */ 320f59d82ffSelric int mp_sub(mp_int *a, mp_int *b, mp_int *c); 321f59d82ffSelric 322f59d82ffSelric /* c = a * b */ 323f59d82ffSelric int mp_mul(mp_int *a, mp_int *b, mp_int *c); 324f59d82ffSelric 325f59d82ffSelric /* b = a*a */ 326f59d82ffSelric int mp_sqr(mp_int *a, mp_int *b); 327f59d82ffSelric 328f59d82ffSelric /* a/b => cb + d == a */ 329f59d82ffSelric int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 330f59d82ffSelric 331f59d82ffSelric /* c = a mod b, 0 <= c < b */ 332f59d82ffSelric int mp_mod(mp_int *a, mp_int *b, mp_int *c); 333f59d82ffSelric 334f59d82ffSelric /* ---> single digit functions <--- */ 335f59d82ffSelric 336f59d82ffSelric /* compare against a single digit */ 337f59d82ffSelric int mp_cmp_d(mp_int *a, mp_digit b); 338f59d82ffSelric 339f59d82ffSelric /* c = a + b */ 340f59d82ffSelric int mp_add_d(mp_int *a, mp_digit b, mp_int *c); 341f59d82ffSelric 342f59d82ffSelric /* c = a - b */ 343f59d82ffSelric int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); 344f59d82ffSelric 345f59d82ffSelric /* c = a * b */ 346f59d82ffSelric int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); 347f59d82ffSelric 348f59d82ffSelric /* a/b => cb + d == a */ 349f59d82ffSelric int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); 350f59d82ffSelric 351f59d82ffSelric /* a/3 => 3c + d == a */ 352f59d82ffSelric int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); 353f59d82ffSelric 354f59d82ffSelric /* c = a**b */ 355f59d82ffSelric int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); 356f59d82ffSelric 357f59d82ffSelric /* c = a mod b, 0 <= c < b */ 358f59d82ffSelric int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); 359f59d82ffSelric 360f59d82ffSelric /* ---> number theory <--- */ 361f59d82ffSelric 362f59d82ffSelric /* d = a + b (mod c) */ 363f59d82ffSelric int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 364f59d82ffSelric 365f59d82ffSelric /* d = a - b (mod c) */ 366f59d82ffSelric int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 367f59d82ffSelric 368f59d82ffSelric /* d = a * b (mod c) */ 369f59d82ffSelric int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 370f59d82ffSelric 371f59d82ffSelric /* c = a * a (mod b) */ 372f59d82ffSelric int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); 373f59d82ffSelric 374f59d82ffSelric /* c = 1/a (mod b) */ 375f59d82ffSelric int mp_invmod(mp_int *a, mp_int *b, mp_int *c); 376f59d82ffSelric 377f59d82ffSelric /* c = (a, b) */ 378f59d82ffSelric int mp_gcd(mp_int *a, mp_int *b, mp_int *c); 379f59d82ffSelric 380f59d82ffSelric /* produces value such that U1*a + U2*b = U3 */ 381f59d82ffSelric int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); 382f59d82ffSelric 383f59d82ffSelric /* c = [a, b] or (a*b)/(a, b) */ 384f59d82ffSelric int mp_lcm(mp_int *a, mp_int *b, mp_int *c); 385f59d82ffSelric 386f59d82ffSelric /* finds one of the b'th root of a, such that |c|**b <= |a| 387f59d82ffSelric * 388f59d82ffSelric * returns error if a < 0 and b is even 389f59d82ffSelric */ 390f59d82ffSelric int mp_n_root(mp_int *a, mp_digit b, mp_int *c); 391f59d82ffSelric 392f59d82ffSelric /* special sqrt algo */ 393f59d82ffSelric int mp_sqrt(mp_int *arg, mp_int *ret); 394f59d82ffSelric 395f59d82ffSelric /* is number a square? */ 396f59d82ffSelric int mp_is_square(mp_int *arg, int *ret); 397f59d82ffSelric 398f59d82ffSelric /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ 399f59d82ffSelric int mp_jacobi(mp_int *a, mp_int *n, int *c); 400f59d82ffSelric 401f59d82ffSelric /* used to setup the Barrett reduction for a given modulus b */ 402f59d82ffSelric int mp_reduce_setup(mp_int *a, mp_int *b); 403f59d82ffSelric 404f59d82ffSelric /* Barrett Reduction, computes a (mod b) with a precomputed value c 405f59d82ffSelric * 406f59d82ffSelric * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely 407f59d82ffSelric * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. 408f59d82ffSelric */ 409f59d82ffSelric int mp_reduce(mp_int *a, mp_int *b, mp_int *c); 410f59d82ffSelric 411f59d82ffSelric /* setups the montgomery reduction */ 412f59d82ffSelric int mp_montgomery_setup(mp_int *a, mp_digit *mp); 413f59d82ffSelric 414f59d82ffSelric /* computes a = B**n mod b without division or multiplication useful for 415f59d82ffSelric * normalizing numbers in a Montgomery system. 416f59d82ffSelric */ 417f59d82ffSelric int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); 418f59d82ffSelric 419f59d82ffSelric /* computes x/R == x (mod N) via Montgomery Reduction */ 420f59d82ffSelric int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 421f59d82ffSelric 422f59d82ffSelric /* returns 1 if a is a valid DR modulus */ 423f59d82ffSelric int mp_dr_is_modulus(mp_int *a); 424f59d82ffSelric 425f59d82ffSelric /* sets the value of "d" required for mp_dr_reduce */ 426f59d82ffSelric void mp_dr_setup(mp_int *a, mp_digit *d); 427f59d82ffSelric 428f59d82ffSelric /* reduces a modulo b using the Diminished Radix method */ 429f59d82ffSelric int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); 430f59d82ffSelric 431f59d82ffSelric /* returns true if a can be reduced with mp_reduce_2k */ 432f59d82ffSelric int mp_reduce_is_2k(mp_int *a); 433f59d82ffSelric 434f59d82ffSelric /* determines k value for 2k reduction */ 435f59d82ffSelric int mp_reduce_2k_setup(mp_int *a, mp_digit *d); 436f59d82ffSelric 437f59d82ffSelric /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ 438f59d82ffSelric int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); 439f59d82ffSelric 440f59d82ffSelric /* returns true if a can be reduced with mp_reduce_2k_l */ 441f59d82ffSelric int mp_reduce_is_2k_l(mp_int *a); 442f59d82ffSelric 443f59d82ffSelric /* determines k value for 2k reduction */ 444f59d82ffSelric int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); 445f59d82ffSelric 446f59d82ffSelric /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ 447f59d82ffSelric int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); 448f59d82ffSelric 449f59d82ffSelric /* d = a**b (mod c) */ 450f59d82ffSelric int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 451f59d82ffSelric 452f59d82ffSelric /* ---> Primes <--- */ 453f59d82ffSelric 454f59d82ffSelric /* number of primes */ 455f59d82ffSelric #ifdef MP_8BIT 456f59d82ffSelric #define PRIME_SIZE 31 457f59d82ffSelric #else 458f59d82ffSelric #define PRIME_SIZE 256 459f59d82ffSelric #endif 460f59d82ffSelric 461f59d82ffSelric /* table of first PRIME_SIZE primes */ 462f59d82ffSelric extern const mp_digit ltm_prime_tab[]; 463f59d82ffSelric 464f59d82ffSelric /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ 465f59d82ffSelric int mp_prime_is_divisible(mp_int *a, int *result); 466f59d82ffSelric 467f59d82ffSelric /* performs one Fermat test of "a" using base "b". 468f59d82ffSelric * Sets result to 0 if composite or 1 if probable prime 469f59d82ffSelric */ 470f59d82ffSelric int mp_prime_fermat(mp_int *a, mp_int *b, int *result); 471f59d82ffSelric 472f59d82ffSelric /* performs one Miller-Rabin test of "a" using base "b". 473f59d82ffSelric * Sets result to 0 if composite or 1 if probable prime 474f59d82ffSelric */ 475f59d82ffSelric int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result); 476f59d82ffSelric 477f59d82ffSelric /* This gives [for a given bit size] the number of trials required 478f59d82ffSelric * such that Miller-Rabin gives a prob of failure lower than 2^-96 479f59d82ffSelric */ 480f59d82ffSelric int mp_prime_rabin_miller_trials(int size); 481f59d82ffSelric 482f59d82ffSelric /* performs t rounds of Miller-Rabin on "a" using the first 483f59d82ffSelric * t prime bases. Also performs an initial sieve of trial 484f59d82ffSelric * division. Determines if "a" is prime with probability 485f59d82ffSelric * of error no more than (1/4)**t. 486f59d82ffSelric * 487f59d82ffSelric * Sets result to 1 if probably prime, 0 otherwise 488f59d82ffSelric */ 489f59d82ffSelric int mp_prime_is_prime(mp_int *a, int t, int *result); 490f59d82ffSelric 491f59d82ffSelric /* finds the next prime after the number "a" using "t" trials 492f59d82ffSelric * of Miller-Rabin. 493f59d82ffSelric * 494f59d82ffSelric * bbs_style = 1 means the prime must be congruent to 3 mod 4 495f59d82ffSelric */ 496f59d82ffSelric int mp_prime_next_prime(mp_int *a, int t, int bbs_style); 497f59d82ffSelric 498f59d82ffSelric /* makes a truly random prime of a given size (bytes), 499f59d82ffSelric * call with bbs = 1 if you want it to be congruent to 3 mod 4 500f59d82ffSelric * 501f59d82ffSelric * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can 502f59d82ffSelric * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself 503f59d82ffSelric * so it can be NULL 504f59d82ffSelric * 505f59d82ffSelric * The prime generated will be larger than 2^(8*size). 506f59d82ffSelric */ 507f59d82ffSelric #define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat) 508f59d82ffSelric 509f59d82ffSelric /* makes a truly random prime of a given size (bits), 510f59d82ffSelric * 511f59d82ffSelric * Flags are as follows: 512f59d82ffSelric * 513f59d82ffSelric * LTM_PRIME_BBS - make prime congruent to 3 mod 4 514f59d82ffSelric * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) 515f59d82ffSelric * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero 516f59d82ffSelric * LTM_PRIME_2MSB_ON - make the 2nd highest bit one 517f59d82ffSelric * 518f59d82ffSelric * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can 519f59d82ffSelric * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself 520f59d82ffSelric * so it can be NULL 521f59d82ffSelric * 522f59d82ffSelric */ 523f59d82ffSelric int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); 524f59d82ffSelric 525e0895134Schristos int mp_find_prime(mp_int *a, int t); 526f59d82ffSelric 527f59d82ffSelric /* ---> radix conversion <--- */ 528f59d82ffSelric int mp_count_bits(mp_int *a); 529f59d82ffSelric 530f59d82ffSelric int mp_unsigned_bin_size(mp_int *a); 531f59d82ffSelric int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); 532f59d82ffSelric int mp_to_unsigned_bin(mp_int *a, unsigned char *b); 533f59d82ffSelric int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 534f59d82ffSelric 535f59d82ffSelric int mp_signed_bin_size(mp_int *a); 536f59d82ffSelric int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); 537f59d82ffSelric int mp_to_signed_bin(mp_int *a, unsigned char *b); 538f59d82ffSelric int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 539f59d82ffSelric 540f59d82ffSelric int mp_read_radix(mp_int *a, const char *str, int radix); 541f59d82ffSelric int mp_toradix(mp_int *a, char *str, int radix); 542f59d82ffSelric int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); 543f59d82ffSelric int mp_radix_size(mp_int *a, int radix, int *size); 544f59d82ffSelric 545f59d82ffSelric int mp_fread(mp_int *a, int radix, FILE *stream); 546f59d82ffSelric int mp_fwrite(mp_int *a, int radix, FILE *stream); 547f59d82ffSelric 548f59d82ffSelric #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) 549f59d82ffSelric #define mp_raw_size(mp) mp_signed_bin_size(mp) 550f59d82ffSelric #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) 551f59d82ffSelric #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) 552f59d82ffSelric #define mp_mag_size(mp) mp_unsigned_bin_size(mp) 553f59d82ffSelric #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) 554f59d82ffSelric 555f59d82ffSelric #define mp_tobinary(M, S) mp_toradix((M), (S), 2) 556f59d82ffSelric #define mp_tooctal(M, S) mp_toradix((M), (S), 8) 557f59d82ffSelric #define mp_todecimal(M, S) mp_toradix((M), (S), 10) 558f59d82ffSelric #define mp_tohex(M, S) mp_toradix((M), (S), 16) 559f59d82ffSelric 560f59d82ffSelric /* lowlevel functions, do not call! */ 561f59d82ffSelric int s_mp_add(mp_int *a, mp_int *b, mp_int *c); 562f59d82ffSelric int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); 563f59d82ffSelric #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) 564f59d82ffSelric int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 565f59d82ffSelric int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 566f59d82ffSelric int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 567f59d82ffSelric int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 568f59d82ffSelric int fast_s_mp_sqr(mp_int *a, mp_int *b); 569f59d82ffSelric int s_mp_sqr(mp_int *a, mp_int *b); 570f59d82ffSelric int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); 571f59d82ffSelric int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); 572f59d82ffSelric int mp_karatsuba_sqr(mp_int *a, mp_int *b); 573f59d82ffSelric int mp_toom_sqr(mp_int *a, mp_int *b); 574f59d82ffSelric int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); 575f59d82ffSelric int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); 576f59d82ffSelric int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 577f59d82ffSelric int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); 578f59d82ffSelric int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); 579f59d82ffSelric void bn_reverse(unsigned char *s, int len); 580f59d82ffSelric 581f59d82ffSelric extern const char *mp_s_rmap; 582f59d82ffSelric 583f59d82ffSelric #ifdef __cplusplus 584f59d82ffSelric } 585f59d82ffSelric #endif 586f59d82ffSelric 587f59d82ffSelric #endif 588f59d82ffSelric 589f59d82ffSelric 590f59d82ffSelric /* Source: /cvs/libtom/libtommath/tommath.h,v */ 591f59d82ffSelric /* Revision: 1.8 */ 592f59d82ffSelric /* Date: 2006/03/31 14:18:44 */ 593