mirror of
https://github.com/vanhoefm/fragattacks.git
synced 2024-11-26 09:18:24 -05:00
3402 lines
76 KiB
C
3402 lines
76 KiB
C
/*
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* Minimal code for RSA support from LibTomMath 0.41
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* http://libtom.org/
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* http://libtom.org/files/ltm-0.41.tar.bz2
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* This library was released in public domain by Tom St Denis.
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*
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* The combination in this file may not use all of the optimized algorithms
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* from LibTomMath and may be considerable slower than the LibTomMath with its
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* default settings. The main purpose of having this version here is to make it
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* easier to build bignum.c wrapper without having to install and build an
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* external library.
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*
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* If CONFIG_INTERNAL_LIBTOMMATH is defined, bignum.c includes this
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* libtommath.c file instead of using the external LibTomMath library.
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*/
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#ifndef CHAR_BIT
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#define CHAR_BIT 8
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#endif
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#define BN_MP_INVMOD_C
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#define BN_S_MP_EXPTMOD_C /* Note: #undef in tommath_superclass.h; this would
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* require BN_MP_EXPTMOD_FAST_C instead */
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#define BN_S_MP_MUL_DIGS_C
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#define BN_MP_INVMOD_SLOW_C
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#define BN_S_MP_SQR_C
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#define BN_S_MP_MUL_HIGH_DIGS_C /* Note: #undef in tommath_superclass.h; this
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* would require other than mp_reduce */
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#ifdef LTM_FAST
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/* Use faster div at the cost of about 1 kB */
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#define BN_MP_MUL_D_C
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/* Include faster exptmod (Montgomery) at the cost of about 2.5 kB in code */
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#define BN_MP_EXPTMOD_FAST_C
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#define BN_MP_MONTGOMERY_SETUP_C
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#define BN_FAST_MP_MONTGOMERY_REDUCE_C
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#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
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#define BN_MP_MUL_2_C
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/* Include faster sqr at the cost of about 0.5 kB in code */
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#define BN_FAST_S_MP_SQR_C
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/* About 0.25 kB of code, but ~1.7kB of stack space! */
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#define BN_FAST_S_MP_MUL_DIGS_C
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#else /* LTM_FAST */
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#define BN_MP_DIV_SMALL
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#define BN_MP_INIT_MULTI_C
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#define BN_MP_CLEAR_MULTI_C
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#define BN_MP_ABS_C
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#endif /* LTM_FAST */
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/* Current uses do not require support for negative exponent in exptmod, so we
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* can save about 1.5 kB in leaving out invmod. */
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#define LTM_NO_NEG_EXP
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/* from tommath.h */
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#ifndef MIN
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#define MIN(x,y) ((x)<(y)?(x):(y))
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#endif
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#ifndef MAX
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#define MAX(x,y) ((x)>(y)?(x):(y))
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#endif
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#define OPT_CAST(x)
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#ifdef __x86_64__
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typedef unsigned long mp_digit;
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typedef unsigned long mp_word __attribute__((mode(TI)));
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#define DIGIT_BIT 60
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#define MP_64BIT
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#else
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typedef unsigned long mp_digit;
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typedef u64 mp_word;
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#define DIGIT_BIT 28
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#define MP_28BIT
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#endif
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#define XMALLOC os_malloc
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#define XFREE os_free
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#define XREALLOC os_realloc
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#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
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#define MP_LT -1 /* less than */
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#define MP_EQ 0 /* equal to */
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#define MP_GT 1 /* greater than */
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#define MP_ZPOS 0 /* positive integer */
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#define MP_NEG 1 /* negative */
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#define MP_OKAY 0 /* ok result */
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#define MP_MEM -2 /* out of mem */
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#define MP_VAL -3 /* invalid input */
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#define MP_YES 1 /* yes response */
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#define MP_NO 0 /* no response */
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typedef int mp_err;
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/* define this to use lower memory usage routines (exptmods mostly) */
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#define MP_LOW_MEM
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/* default precision */
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#ifndef MP_PREC
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#ifndef MP_LOW_MEM
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#define MP_PREC 32 /* default digits of precision */
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#else
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#define MP_PREC 8 /* default digits of precision */
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#endif
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#endif
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/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
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#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
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/* the infamous mp_int structure */
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typedef struct {
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int used, alloc, sign;
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mp_digit *dp;
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} mp_int;
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/* ---> Basic Manipulations <--- */
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#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
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#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
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#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
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/* prototypes for copied functions */
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#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
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static int s_mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
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static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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static int s_mp_sqr(mp_int * a, mp_int * b);
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static int s_mp_mul_high_digs(mp_int * a, mp_int * b, mp_int * c, int digs);
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#ifdef BN_FAST_S_MP_MUL_DIGS_C
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static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs);
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#endif
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#ifdef BN_MP_INIT_MULTI_C
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static int mp_init_multi(mp_int *mp, ...);
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#endif
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#ifdef BN_MP_CLEAR_MULTI_C
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static void mp_clear_multi(mp_int *mp, ...);
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#endif
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static int mp_lshd(mp_int * a, int b);
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static void mp_set(mp_int * a, mp_digit b);
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static void mp_clamp(mp_int * a);
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static void mp_exch(mp_int * a, mp_int * b);
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static void mp_rshd(mp_int * a, int b);
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static void mp_zero(mp_int * a);
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static int mp_mod_2d(mp_int * a, int b, mp_int * c);
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static int mp_div_2d(mp_int * a, int b, mp_int * c, mp_int * d);
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static int mp_init_copy(mp_int * a, mp_int * b);
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static int mp_mul_2d(mp_int * a, int b, mp_int * c);
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#ifndef LTM_NO_NEG_EXP
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static int mp_div_2(mp_int * a, mp_int * b);
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static int mp_invmod(mp_int * a, mp_int * b, mp_int * c);
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static int mp_invmod_slow(mp_int * a, mp_int * b, mp_int * c);
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#endif /* LTM_NO_NEG_EXP */
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static int mp_copy(mp_int * a, mp_int * b);
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static int mp_count_bits(mp_int * a);
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static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d);
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static int mp_mod(mp_int * a, mp_int * b, mp_int * c);
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static int mp_grow(mp_int * a, int size);
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static int mp_cmp_mag(mp_int * a, mp_int * b);
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#ifdef BN_MP_ABS_C
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static int mp_abs(mp_int * a, mp_int * b);
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#endif
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static int mp_sqr(mp_int * a, mp_int * b);
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static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
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static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
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static int mp_2expt(mp_int * a, int b);
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static int mp_reduce_setup(mp_int * a, mp_int * b);
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static int mp_reduce(mp_int * x, mp_int * m, mp_int * mu);
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static int mp_init_size(mp_int * a, int size);
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#ifdef BN_MP_EXPTMOD_FAST_C
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static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
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#endif /* BN_MP_EXPTMOD_FAST_C */
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#ifdef BN_FAST_S_MP_SQR_C
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static int fast_s_mp_sqr (mp_int * a, mp_int * b);
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#endif /* BN_FAST_S_MP_SQR_C */
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#ifdef BN_MP_MUL_D_C
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static int mp_mul_d (mp_int * a, mp_digit b, mp_int * c);
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#endif /* BN_MP_MUL_D_C */
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/* functions from bn_<func name>.c */
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/* reverse an array, used for radix code */
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static void bn_reverse (unsigned char *s, int len)
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{
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int ix, iy;
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unsigned char t;
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ix = 0;
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iy = len - 1;
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while (ix < iy) {
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t = s[ix];
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s[ix] = s[iy];
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s[iy] = t;
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++ix;
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--iy;
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}
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}
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/* low level addition, based on HAC pp.594, Algorithm 14.7 */
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static int s_mp_add (mp_int * a, mp_int * b, mp_int * c)
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{
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mp_int *x;
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int olduse, res, min, max;
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/* find sizes, we let |a| <= |b| which means we have to sort
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* them. "x" will point to the input with the most digits
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*/
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if (a->used > b->used) {
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min = b->used;
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max = a->used;
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x = a;
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} else {
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min = a->used;
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max = b->used;
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x = b;
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}
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/* init result */
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if (c->alloc < max + 1) {
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if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
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return res;
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}
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}
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/* get old used digit count and set new one */
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olduse = c->used;
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c->used = max + 1;
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{
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register mp_digit u, *tmpa, *tmpb, *tmpc;
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register int i;
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/* alias for digit pointers */
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/* first input */
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tmpa = a->dp;
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/* second input */
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tmpb = b->dp;
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/* destination */
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tmpc = c->dp;
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/* zero the carry */
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u = 0;
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for (i = 0; i < min; i++) {
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/* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
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*tmpc = *tmpa++ + *tmpb++ + u;
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/* U = carry bit of T[i] */
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u = *tmpc >> ((mp_digit)DIGIT_BIT);
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/* take away carry bit from T[i] */
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*tmpc++ &= MP_MASK;
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}
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/* now copy higher words if any, that is in A+B
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* if A or B has more digits add those in
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*/
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if (min != max) {
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for (; i < max; i++) {
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/* T[i] = X[i] + U */
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*tmpc = x->dp[i] + u;
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/* U = carry bit of T[i] */
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u = *tmpc >> ((mp_digit)DIGIT_BIT);
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/* take away carry bit from T[i] */
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*tmpc++ &= MP_MASK;
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}
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}
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/* add carry */
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*tmpc++ = u;
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/* clear digits above oldused */
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for (i = c->used; i < olduse; i++) {
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*tmpc++ = 0;
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}
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}
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mp_clamp (c);
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return MP_OKAY;
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}
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/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
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static int s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
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{
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int olduse, res, min, max;
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/* find sizes */
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min = b->used;
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max = a->used;
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/* init result */
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if (c->alloc < max) {
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if ((res = mp_grow (c, max)) != MP_OKAY) {
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return res;
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}
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}
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olduse = c->used;
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c->used = max;
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{
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register mp_digit u, *tmpa, *tmpb, *tmpc;
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register int i;
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/* alias for digit pointers */
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tmpa = a->dp;
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tmpb = b->dp;
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tmpc = c->dp;
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/* set carry to zero */
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u = 0;
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for (i = 0; i < min; i++) {
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/* T[i] = A[i] - B[i] - U */
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*tmpc = *tmpa++ - *tmpb++ - u;
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/* U = carry bit of T[i]
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* Note this saves performing an AND operation since
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* if a carry does occur it will propagate all the way to the
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* MSB. As a result a single shift is enough to get the carry
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*/
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u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
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/* Clear carry from T[i] */
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*tmpc++ &= MP_MASK;
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}
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/* now copy higher words if any, e.g. if A has more digits than B */
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for (; i < max; i++) {
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/* T[i] = A[i] - U */
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*tmpc = *tmpa++ - u;
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/* U = carry bit of T[i] */
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u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
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/* Clear carry from T[i] */
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*tmpc++ &= MP_MASK;
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}
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/* clear digits above used (since we may not have grown result above) */
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for (i = c->used; i < olduse; i++) {
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*tmpc++ = 0;
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}
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}
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mp_clamp (c);
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return MP_OKAY;
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}
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/* init a new mp_int */
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static int mp_init (mp_int * a)
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{
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int i;
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/* allocate memory required and clear it */
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a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
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if (a->dp == NULL) {
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return MP_MEM;
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}
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/* set the digits to zero */
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for (i = 0; i < MP_PREC; i++) {
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a->dp[i] = 0;
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}
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/* set the used to zero, allocated digits to the default precision
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* and sign to positive */
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a->used = 0;
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a->alloc = MP_PREC;
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a->sign = MP_ZPOS;
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return MP_OKAY;
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}
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/* clear one (frees) */
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static void mp_clear (mp_int * a)
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{
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int i;
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/* only do anything if a hasn't been freed previously */
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if (a->dp != NULL) {
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/* first zero the digits */
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for (i = 0; i < a->used; i++) {
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a->dp[i] = 0;
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}
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/* free ram */
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XFREE(a->dp);
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/* reset members to make debugging easier */
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a->dp = NULL;
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a->alloc = a->used = 0;
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a->sign = MP_ZPOS;
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}
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}
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/* high level addition (handles signs) */
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static int mp_add (mp_int * a, mp_int * b, mp_int * c)
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{
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int sa, sb, res;
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/* get sign of both inputs */
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sa = a->sign;
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sb = b->sign;
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/* handle two cases, not four */
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if (sa == sb) {
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/* both positive or both negative */
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/* add their magnitudes, copy the sign */
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c->sign = sa;
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res = s_mp_add (a, b, c);
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} else {
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/* one positive, the other negative */
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/* subtract the one with the greater magnitude from */
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/* the one of the lesser magnitude. The result gets */
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/* the sign of the one with the greater magnitude. */
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if (mp_cmp_mag (a, b) == MP_LT) {
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c->sign = sb;
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res = s_mp_sub (b, a, c);
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} else {
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c->sign = sa;
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res = s_mp_sub (a, b, c);
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}
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}
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return res;
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}
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/* high level subtraction (handles signs) */
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static int mp_sub (mp_int * a, mp_int * b, mp_int * c)
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{
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int sa, sb, res;
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sa = a->sign;
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sb = b->sign;
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if (sa != sb) {
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/* subtract a negative from a positive, OR */
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/* subtract a positive from a negative. */
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/* In either case, ADD their magnitudes, */
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/* and use the sign of the first number. */
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c->sign = sa;
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res = s_mp_add (a, b, c);
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} else {
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/* subtract a positive from a positive, OR */
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/* subtract a negative from a negative. */
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/* First, take the difference between their */
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/* magnitudes, then... */
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if (mp_cmp_mag (a, b) != MP_LT) {
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/* Copy the sign from the first */
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c->sign = sa;
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/* The first has a larger or equal magnitude */
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res = s_mp_sub (a, b, c);
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} else {
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/* The result has the *opposite* sign from */
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/* the first number. */
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c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
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/* The second has a larger magnitude */
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res = s_mp_sub (b, a, c);
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}
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}
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return res;
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}
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/* high level multiplication (handles sign) */
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static int mp_mul (mp_int * a, mp_int * b, mp_int * c)
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{
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int res, neg;
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neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
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|
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/* use Toom-Cook? */
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|
#ifdef BN_MP_TOOM_MUL_C
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|
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
|
|
res = mp_toom_mul(a, b, c);
|
|
} else
|
|
#endif
|
|
#ifdef BN_MP_KARATSUBA_MUL_C
|
|
/* use Karatsuba? */
|
|
if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
|
|
res = mp_karatsuba_mul (a, b, c);
|
|
} else
|
|
#endif
|
|
{
|
|
/* can we use the fast multiplier?
|
|
*
|
|
* The fast multiplier can be used if the output will
|
|
* have less than MP_WARRAY digits and the number of
|
|
* digits won't affect carry propagation
|
|
*/
|
|
#ifdef BN_FAST_S_MP_MUL_DIGS_C
|
|
int digs = a->used + b->used + 1;
|
|
|
|
if ((digs < MP_WARRAY) &&
|
|
MIN(a->used, b->used) <=
|
|
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
res = fast_s_mp_mul_digs (a, b, c, digs);
|
|
} else
|
|
#endif
|
|
#ifdef BN_S_MP_MUL_DIGS_C
|
|
res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
|
|
#else
|
|
#error mp_mul could fail
|
|
res = MP_VAL;
|
|
#endif
|
|
|
|
}
|
|
c->sign = (c->used > 0) ? neg : MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
|
|
/* d = a * b (mod c) */
|
|
static int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
int res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
res = mp_mod (&t, c, d);
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
|
|
/* c = a mod b, 0 <= c < b */
|
|
static int mp_mod (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int t;
|
|
int res;
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
if (t.sign != b->sign) {
|
|
res = mp_add (b, &t, c);
|
|
} else {
|
|
res = MP_OKAY;
|
|
mp_exch (&t, c);
|
|
}
|
|
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
|
|
/* this is a shell function that calls either the normal or Montgomery
|
|
* exptmod functions. Originally the call to the montgomery code was
|
|
* embedded in the normal function but that wasted a lot of stack space
|
|
* for nothing (since 99% of the time the Montgomery code would be called)
|
|
*/
|
|
static int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
|
|
{
|
|
int dr;
|
|
|
|
/* modulus P must be positive */
|
|
if (P->sign == MP_NEG) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if exponent X is negative we have to recurse */
|
|
if (X->sign == MP_NEG) {
|
|
#ifdef LTM_NO_NEG_EXP
|
|
return MP_VAL;
|
|
#else /* LTM_NO_NEG_EXP */
|
|
#ifdef BN_MP_INVMOD_C
|
|
mp_int tmpG, tmpX;
|
|
int err;
|
|
|
|
/* first compute 1/G mod P */
|
|
if ((err = mp_init(&tmpG)) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
|
|
/* now get |X| */
|
|
if ((err = mp_init(&tmpX)) != MP_OKAY) {
|
|
mp_clear(&tmpG);
|
|
return err;
|
|
}
|
|
if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
}
|
|
|
|
/* and now compute (1/G)**|X| instead of G**X [X < 0] */
|
|
err = mp_exptmod(&tmpG, &tmpX, P, Y);
|
|
mp_clear_multi(&tmpG, &tmpX, NULL);
|
|
return err;
|
|
#else
|
|
#error mp_exptmod would always fail
|
|
/* no invmod */
|
|
return MP_VAL;
|
|
#endif
|
|
#endif /* LTM_NO_NEG_EXP */
|
|
}
|
|
|
|
/* modified diminished radix reduction */
|
|
#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
|
|
if (mp_reduce_is_2k_l(P) == MP_YES) {
|
|
return s_mp_exptmod(G, X, P, Y, 1);
|
|
}
|
|
#endif
|
|
|
|
#ifdef BN_MP_DR_IS_MODULUS_C
|
|
/* is it a DR modulus? */
|
|
dr = mp_dr_is_modulus(P);
|
|
#else
|
|
/* default to no */
|
|
dr = 0;
|
|
#endif
|
|
|
|
#ifdef BN_MP_REDUCE_IS_2K_C
|
|
/* if not, is it a unrestricted DR modulus? */
|
|
if (dr == 0) {
|
|
dr = mp_reduce_is_2k(P) << 1;
|
|
}
|
|
#endif
|
|
|
|
/* if the modulus is odd or dr != 0 use the montgomery method */
|
|
#ifdef BN_MP_EXPTMOD_FAST_C
|
|
if (mp_isodd (P) == 1 || dr != 0) {
|
|
return mp_exptmod_fast (G, X, P, Y, dr);
|
|
} else {
|
|
#endif
|
|
#ifdef BN_S_MP_EXPTMOD_C
|
|
/* otherwise use the generic Barrett reduction technique */
|
|
return s_mp_exptmod (G, X, P, Y, 0);
|
|
#else
|
|
#error mp_exptmod could fail
|
|
/* no exptmod for evens */
|
|
return MP_VAL;
|
|
#endif
|
|
#ifdef BN_MP_EXPTMOD_FAST_C
|
|
}
|
|
#endif
|
|
if (dr == 0) {
|
|
/* avoid compiler warnings about possibly unused variable */
|
|
}
|
|
}
|
|
|
|
|
|
/* compare two ints (signed)*/
|
|
static int mp_cmp (mp_int * a, mp_int * b)
|
|
{
|
|
/* compare based on sign */
|
|
if (a->sign != b->sign) {
|
|
if (a->sign == MP_NEG) {
|
|
return MP_LT;
|
|
} else {
|
|
return MP_GT;
|
|
}
|
|
}
|
|
|
|
/* compare digits */
|
|
if (a->sign == MP_NEG) {
|
|
/* if negative compare opposite direction */
|
|
return mp_cmp_mag(b, a);
|
|
} else {
|
|
return mp_cmp_mag(a, b);
|
|
}
|
|
}
|
|
|
|
|
|
/* compare a digit */
|
|
static int mp_cmp_d(mp_int * a, mp_digit b)
|
|
{
|
|
/* compare based on sign */
|
|
if (a->sign == MP_NEG) {
|
|
return MP_LT;
|
|
}
|
|
|
|
/* compare based on magnitude */
|
|
if (a->used > 1) {
|
|
return MP_GT;
|
|
}
|
|
|
|
/* compare the only digit of a to b */
|
|
if (a->dp[0] > b) {
|
|
return MP_GT;
|
|
} else if (a->dp[0] < b) {
|
|
return MP_LT;
|
|
} else {
|
|
return MP_EQ;
|
|
}
|
|
}
|
|
|
|
|
|
#ifndef LTM_NO_NEG_EXP
|
|
/* hac 14.61, pp608 */
|
|
static int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
/* b cannot be negative */
|
|
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
#ifdef BN_FAST_MP_INVMOD_C
|
|
/* if the modulus is odd we can use a faster routine instead */
|
|
if (mp_isodd (b) == 1) {
|
|
return fast_mp_invmod (a, b, c);
|
|
}
|
|
#endif
|
|
|
|
#ifdef BN_MP_INVMOD_SLOW_C
|
|
return mp_invmod_slow(a, b, c);
|
|
#endif
|
|
|
|
#ifndef BN_FAST_MP_INVMOD_C
|
|
#ifndef BN_MP_INVMOD_SLOW_C
|
|
#error mp_invmod would always fail
|
|
#endif
|
|
#endif
|
|
return MP_VAL;
|
|
}
|
|
#endif /* LTM_NO_NEG_EXP */
|
|
|
|
|
|
/* get the size for an unsigned equivalent */
|
|
static int mp_unsigned_bin_size (mp_int * a)
|
|
{
|
|
int size = mp_count_bits (a);
|
|
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
|
|
}
|
|
|
|
|
|
#ifndef LTM_NO_NEG_EXP
|
|
/* hac 14.61, pp608 */
|
|
static int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
|
|
{
|
|
mp_int x, y, u, v, A, B, C, D;
|
|
int res;
|
|
|
|
/* b cannot be negative */
|
|
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* init temps */
|
|
if ((res = mp_init_multi(&x, &y, &u, &v,
|
|
&A, &B, &C, &D, NULL)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* x = a, y = b */
|
|
if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_copy (b, &y)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 2. [modified] if x,y are both even then return an error! */
|
|
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
|
|
res = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
|
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_copy (&y, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
mp_set (&A, 1);
|
|
mp_set (&D, 1);
|
|
|
|
top:
|
|
/* 4. while u is even do */
|
|
while (mp_iseven (&u) == 1) {
|
|
/* 4.1 u = u/2 */
|
|
if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 4.2 if A or B is odd then */
|
|
if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
|
|
/* A = (A+y)/2, B = (B-x)/2 */
|
|
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* A = A/2, B = B/2 */
|
|
if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 5. while v is even do */
|
|
while (mp_iseven (&v) == 1) {
|
|
/* 5.1 v = v/2 */
|
|
if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
/* 5.2 if C or D is odd then */
|
|
if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
|
|
/* C = (C+y)/2, D = (D-x)/2 */
|
|
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
/* C = C/2, D = D/2 */
|
|
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* 6. if u >= v then */
|
|
if (mp_cmp (&u, &v) != MP_LT) {
|
|
/* u = u - v, A = A - C, B = B - D */
|
|
if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
} else {
|
|
/* v - v - u, C = C - A, D = D - B */
|
|
if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* if not zero goto step 4 */
|
|
if (mp_iszero (&u) == 0)
|
|
goto top;
|
|
|
|
/* now a = C, b = D, gcd == g*v */
|
|
|
|
/* if v != 1 then there is no inverse */
|
|
if (mp_cmp_d (&v, 1) != MP_EQ) {
|
|
res = MP_VAL;
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
/* if its too low */
|
|
while (mp_cmp_d(&C, 0) == MP_LT) {
|
|
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* too big */
|
|
while (mp_cmp_mag(&C, b) != MP_LT) {
|
|
if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* C is now the inverse */
|
|
mp_exch (&C, c);
|
|
res = MP_OKAY;
|
|
LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
|
|
return res;
|
|
}
|
|
#endif /* LTM_NO_NEG_EXP */
|
|
|
|
|
|
/* compare maginitude of two ints (unsigned) */
|
|
static int mp_cmp_mag (mp_int * a, mp_int * b)
|
|
{
|
|
int n;
|
|
mp_digit *tmpa, *tmpb;
|
|
|
|
/* compare based on # of non-zero digits */
|
|
if (a->used > b->used) {
|
|
return MP_GT;
|
|
}
|
|
|
|
if (a->used < b->used) {
|
|
return MP_LT;
|
|
}
|
|
|
|
/* alias for a */
|
|
tmpa = a->dp + (a->used - 1);
|
|
|
|
/* alias for b */
|
|
tmpb = b->dp + (a->used - 1);
|
|
|
|
/* compare based on digits */
|
|
for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
|
|
if (*tmpa > *tmpb) {
|
|
return MP_GT;
|
|
}
|
|
|
|
if (*tmpa < *tmpb) {
|
|
return MP_LT;
|
|
}
|
|
}
|
|
return MP_EQ;
|
|
}
|
|
|
|
|
|
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
|
|
static int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
|
|
{
|
|
int res;
|
|
|
|
/* make sure there are at least two digits */
|
|
if (a->alloc < 2) {
|
|
if ((res = mp_grow(a, 2)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* zero the int */
|
|
mp_zero (a);
|
|
|
|
/* read the bytes in */
|
|
while (c-- > 0) {
|
|
if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
#ifndef MP_8BIT
|
|
a->dp[0] |= *b++;
|
|
a->used += 1;
|
|
#else
|
|
a->dp[0] = (*b & MP_MASK);
|
|
a->dp[1] |= ((*b++ >> 7U) & 1);
|
|
a->used += 2;
|
|
#endif
|
|
}
|
|
mp_clamp (a);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* store in unsigned [big endian] format */
|
|
static int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
|
|
{
|
|
int x, res;
|
|
mp_int t;
|
|
|
|
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
x = 0;
|
|
while (mp_iszero (&t) == 0) {
|
|
#ifndef MP_8BIT
|
|
b[x++] = (unsigned char) (t.dp[0] & 255);
|
|
#else
|
|
b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
|
|
#endif
|
|
if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
}
|
|
bn_reverse (b, x);
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
|
|
static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_digit D, r, rr;
|
|
int x, res;
|
|
mp_int t;
|
|
|
|
|
|
/* if the shift count is <= 0 then we do no work */
|
|
if (b <= 0) {
|
|
res = mp_copy (a, c);
|
|
if (d != NULL) {
|
|
mp_zero (d);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init (&t)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* get the remainder */
|
|
if (d != NULL) {
|
|
if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* copy */
|
|
if ((res = mp_copy (a, c)) != MP_OKAY) {
|
|
mp_clear (&t);
|
|
return res;
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= (int)DIGIT_BIT) {
|
|
mp_rshd (c, b / DIGIT_BIT);
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
D = (mp_digit) (b % DIGIT_BIT);
|
|
if (D != 0) {
|
|
register mp_digit *tmpc, mask, shift;
|
|
|
|
/* mask */
|
|
mask = (((mp_digit)1) << D) - 1;
|
|
|
|
/* shift for lsb */
|
|
shift = DIGIT_BIT - D;
|
|
|
|
/* alias */
|
|
tmpc = c->dp + (c->used - 1);
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = c->used - 1; x >= 0; x--) {
|
|
/* get the lower bits of this word in a temp */
|
|
rr = *tmpc & mask;
|
|
|
|
/* shift the current word and mix in the carry bits from the previous word */
|
|
*tmpc = (*tmpc >> D) | (r << shift);
|
|
--tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word found above */
|
|
r = rr;
|
|
}
|
|
}
|
|
mp_clamp (c);
|
|
if (d != NULL) {
|
|
mp_exch (&t, d);
|
|
}
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
static int mp_init_copy (mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_init (a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return mp_copy (b, a);
|
|
}
|
|
|
|
|
|
/* set to zero */
|
|
static void mp_zero (mp_int * a)
|
|
{
|
|
int n;
|
|
mp_digit *tmp;
|
|
|
|
a->sign = MP_ZPOS;
|
|
a->used = 0;
|
|
|
|
tmp = a->dp;
|
|
for (n = 0; n < a->alloc; n++) {
|
|
*tmp++ = 0;
|
|
}
|
|
}
|
|
|
|
|
|
/* copy, b = a */
|
|
static int mp_copy (mp_int * a, mp_int * b)
|
|
{
|
|
int res, n;
|
|
|
|
/* if dst == src do nothing */
|
|
if (a == b) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* grow dest */
|
|
if (b->alloc < a->used) {
|
|
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* zero b and copy the parameters over */
|
|
{
|
|
register mp_digit *tmpa, *tmpb;
|
|
|
|
/* pointer aliases */
|
|
|
|
/* source */
|
|
tmpa = a->dp;
|
|
|
|
/* destination */
|
|
tmpb = b->dp;
|
|
|
|
/* copy all the digits */
|
|
for (n = 0; n < a->used; n++) {
|
|
*tmpb++ = *tmpa++;
|
|
}
|
|
|
|
/* clear high digits */
|
|
for (; n < b->used; n++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
|
|
/* copy used count and sign */
|
|
b->used = a->used;
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* shift right a certain amount of digits */
|
|
static void mp_rshd (mp_int * a, int b)
|
|
{
|
|
int x;
|
|
|
|
/* if b <= 0 then ignore it */
|
|
if (b <= 0) {
|
|
return;
|
|
}
|
|
|
|
/* if b > used then simply zero it and return */
|
|
if (a->used <= b) {
|
|
mp_zero (a);
|
|
return;
|
|
}
|
|
|
|
{
|
|
register mp_digit *bottom, *top;
|
|
|
|
/* shift the digits down */
|
|
|
|
/* bottom */
|
|
bottom = a->dp;
|
|
|
|
/* top [offset into digits] */
|
|
top = a->dp + b;
|
|
|
|
/* this is implemented as a sliding window where
|
|
* the window is b-digits long and digits from
|
|
* the top of the window are copied to the bottom
|
|
*
|
|
* e.g.
|
|
|
|
b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
|
|
/\ | ---->
|
|
\-------------------/ ---->
|
|
*/
|
|
for (x = 0; x < (a->used - b); x++) {
|
|
*bottom++ = *top++;
|
|
}
|
|
|
|
/* zero the top digits */
|
|
for (; x < a->used; x++) {
|
|
*bottom++ = 0;
|
|
}
|
|
}
|
|
|
|
/* remove excess digits */
|
|
a->used -= b;
|
|
}
|
|
|
|
|
|
/* swap the elements of two integers, for cases where you can't simply swap the
|
|
* mp_int pointers around
|
|
*/
|
|
static void mp_exch (mp_int * a, mp_int * b)
|
|
{
|
|
mp_int t;
|
|
|
|
t = *a;
|
|
*a = *b;
|
|
*b = t;
|
|
}
|
|
|
|
|
|
/* trim unused digits
|
|
*
|
|
* This is used to ensure that leading zero digits are
|
|
* trimed and the leading "used" digit will be non-zero
|
|
* Typically very fast. Also fixes the sign if there
|
|
* are no more leading digits
|
|
*/
|
|
static void mp_clamp (mp_int * a)
|
|
{
|
|
/* decrease used while the most significant digit is
|
|
* zero.
|
|
*/
|
|
while (a->used > 0 && a->dp[a->used - 1] == 0) {
|
|
--(a->used);
|
|
}
|
|
|
|
/* reset the sign flag if used == 0 */
|
|
if (a->used == 0) {
|
|
a->sign = MP_ZPOS;
|
|
}
|
|
}
|
|
|
|
|
|
/* grow as required */
|
|
static int mp_grow (mp_int * a, int size)
|
|
{
|
|
int i;
|
|
mp_digit *tmp;
|
|
|
|
/* if the alloc size is smaller alloc more ram */
|
|
if (a->alloc < size) {
|
|
/* ensure there are always at least MP_PREC digits extra on top */
|
|
size += (MP_PREC * 2) - (size % MP_PREC);
|
|
|
|
/* reallocate the array a->dp
|
|
*
|
|
* We store the return in a temporary variable
|
|
* in case the operation failed we don't want
|
|
* to overwrite the dp member of a.
|
|
*/
|
|
tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
|
|
if (tmp == NULL) {
|
|
/* reallocation failed but "a" is still valid [can be freed] */
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* reallocation succeeded so set a->dp */
|
|
a->dp = tmp;
|
|
|
|
/* zero excess digits */
|
|
i = a->alloc;
|
|
a->alloc = size;
|
|
for (; i < a->alloc; i++) {
|
|
a->dp[i] = 0;
|
|
}
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef BN_MP_ABS_C
|
|
/* b = |a|
|
|
*
|
|
* Simple function copies the input and fixes the sign to positive
|
|
*/
|
|
static int mp_abs (mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
/* copy a to b */
|
|
if (a != b) {
|
|
if ((res = mp_copy (a, b)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* force the sign of b to positive */
|
|
b->sign = MP_ZPOS;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
/* set to a digit */
|
|
static void mp_set (mp_int * a, mp_digit b)
|
|
{
|
|
mp_zero (a);
|
|
a->dp[0] = b & MP_MASK;
|
|
a->used = (a->dp[0] != 0) ? 1 : 0;
|
|
}
|
|
|
|
|
|
#ifndef LTM_NO_NEG_EXP
|
|
/* b = a/2 */
|
|
static int mp_div_2(mp_int * a, mp_int * b)
|
|
{
|
|
int x, res, oldused;
|
|
|
|
/* copy */
|
|
if (b->alloc < a->used) {
|
|
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
{
|
|
register mp_digit r, rr, *tmpa, *tmpb;
|
|
|
|
/* source alias */
|
|
tmpa = a->dp + b->used - 1;
|
|
|
|
/* dest alias */
|
|
tmpb = b->dp + b->used - 1;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = b->used - 1; x >= 0; x--) {
|
|
/* get the carry for the next iteration */
|
|
rr = *tmpa & 1;
|
|
|
|
/* shift the current digit, add in carry and store */
|
|
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
|
|
|
|
/* forward carry to next iteration */
|
|
r = rr;
|
|
}
|
|
|
|
/* zero excess digits */
|
|
tmpb = b->dp + b->used;
|
|
for (x = b->used; x < oldused; x++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
b->sign = a->sign;
|
|
mp_clamp (b);
|
|
return MP_OKAY;
|
|
}
|
|
#endif /* LTM_NO_NEG_EXP */
|
|
|
|
|
|
/* shift left by a certain bit count */
|
|
static int mp_mul_2d (mp_int * a, int b, mp_int * c)
|
|
{
|
|
mp_digit d;
|
|
int res;
|
|
|
|
/* copy */
|
|
if (a != c) {
|
|
if ((res = mp_copy (a, c)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
|
|
if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* shift by as many digits in the bit count */
|
|
if (b >= (int)DIGIT_BIT) {
|
|
if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* shift any bit count < DIGIT_BIT */
|
|
d = (mp_digit) (b % DIGIT_BIT);
|
|
if (d != 0) {
|
|
register mp_digit *tmpc, shift, mask, r, rr;
|
|
register int x;
|
|
|
|
/* bitmask for carries */
|
|
mask = (((mp_digit)1) << d) - 1;
|
|
|
|
/* shift for msbs */
|
|
shift = DIGIT_BIT - d;
|
|
|
|
/* alias */
|
|
tmpc = c->dp;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < c->used; x++) {
|
|
/* get the higher bits of the current word */
|
|
rr = (*tmpc >> shift) & mask;
|
|
|
|
/* shift the current word and OR in the carry */
|
|
*tmpc = ((*tmpc << d) | r) & MP_MASK;
|
|
++tmpc;
|
|
|
|
/* set the carry to the carry bits of the current word */
|
|
r = rr;
|
|
}
|
|
|
|
/* set final carry */
|
|
if (r != 0) {
|
|
c->dp[(c->used)++] = r;
|
|
}
|
|
}
|
|
mp_clamp (c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef BN_MP_INIT_MULTI_C
|
|
static int mp_init_multi(mp_int *mp, ...)
|
|
{
|
|
mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
|
|
int n = 0; /* Number of ok inits */
|
|
mp_int* cur_arg = mp;
|
|
va_list args;
|
|
|
|
va_start(args, mp); /* init args to next argument from caller */
|
|
while (cur_arg != NULL) {
|
|
if (mp_init(cur_arg) != MP_OKAY) {
|
|
/* Oops - error! Back-track and mp_clear what we already
|
|
succeeded in init-ing, then return error.
|
|
*/
|
|
va_list clean_args;
|
|
|
|
/* end the current list */
|
|
va_end(args);
|
|
|
|
/* now start cleaning up */
|
|
cur_arg = mp;
|
|
va_start(clean_args, mp);
|
|
while (n--) {
|
|
mp_clear(cur_arg);
|
|
cur_arg = va_arg(clean_args, mp_int*);
|
|
}
|
|
va_end(clean_args);
|
|
res = MP_MEM;
|
|
break;
|
|
}
|
|
n++;
|
|
cur_arg = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
return res; /* Assumed ok, if error flagged above. */
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_MP_CLEAR_MULTI_C
|
|
static void mp_clear_multi(mp_int *mp, ...)
|
|
{
|
|
mp_int* next_mp = mp;
|
|
va_list args;
|
|
va_start(args, mp);
|
|
while (next_mp != NULL) {
|
|
mp_clear(next_mp);
|
|
next_mp = va_arg(args, mp_int*);
|
|
}
|
|
va_end(args);
|
|
}
|
|
#endif
|
|
|
|
|
|
/* shift left a certain amount of digits */
|
|
static int mp_lshd (mp_int * a, int b)
|
|
{
|
|
int x, res;
|
|
|
|
/* if its less than zero return */
|
|
if (b <= 0) {
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* grow to fit the new digits */
|
|
if (a->alloc < a->used + b) {
|
|
if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
{
|
|
register mp_digit *top, *bottom;
|
|
|
|
/* increment the used by the shift amount then copy upwards */
|
|
a->used += b;
|
|
|
|
/* top */
|
|
top = a->dp + a->used - 1;
|
|
|
|
/* base */
|
|
bottom = a->dp + a->used - 1 - b;
|
|
|
|
/* much like mp_rshd this is implemented using a sliding window
|
|
* except the window goes the otherway around. Copying from
|
|
* the bottom to the top. see bn_mp_rshd.c for more info.
|
|
*/
|
|
for (x = a->used - 1; x >= b; x--) {
|
|
*top-- = *bottom--;
|
|
}
|
|
|
|
/* zero the lower digits */
|
|
top = a->dp;
|
|
for (x = 0; x < b; x++) {
|
|
*top++ = 0;
|
|
}
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* returns the number of bits in an int */
|
|
static int mp_count_bits (mp_int * a)
|
|
{
|
|
int r;
|
|
mp_digit q;
|
|
|
|
/* shortcut */
|
|
if (a->used == 0) {
|
|
return 0;
|
|
}
|
|
|
|
/* get number of digits and add that */
|
|
r = (a->used - 1) * DIGIT_BIT;
|
|
|
|
/* take the last digit and count the bits in it */
|
|
q = a->dp[a->used - 1];
|
|
while (q > ((mp_digit) 0)) {
|
|
++r;
|
|
q >>= ((mp_digit) 1);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
|
|
/* calc a value mod 2**b */
|
|
static int mp_mod_2d (mp_int * a, int b, mp_int * c)
|
|
{
|
|
int x, res;
|
|
|
|
/* if b is <= 0 then zero the int */
|
|
if (b <= 0) {
|
|
mp_zero (c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
/* if the modulus is larger than the value than return */
|
|
if (b >= (int) (a->used * DIGIT_BIT)) {
|
|
res = mp_copy (a, c);
|
|
return res;
|
|
}
|
|
|
|
/* copy */
|
|
if ((res = mp_copy (a, c)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* zero digits above the last digit of the modulus */
|
|
for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
|
|
c->dp[x] = 0;
|
|
}
|
|
/* clear the digit that is not completely outside/inside the modulus */
|
|
c->dp[b / DIGIT_BIT] &=
|
|
(mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
|
|
mp_clamp (c);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef BN_MP_DIV_SMALL
|
|
|
|
/* slower bit-bang division... also smaller */
|
|
static int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_int ta, tb, tq, q;
|
|
int res, n, n2;
|
|
|
|
/* is divisor zero ? */
|
|
if (mp_iszero (b) == 1) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if a < b then q=0, r = a */
|
|
if (mp_cmp_mag (a, b) == MP_LT) {
|
|
if (d != NULL) {
|
|
res = mp_copy (a, d);
|
|
} else {
|
|
res = MP_OKAY;
|
|
}
|
|
if (c != NULL) {
|
|
mp_zero (c);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
/* init our temps */
|
|
if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
|
|
return res;
|
|
}
|
|
|
|
|
|
mp_set(&tq, 1);
|
|
n = mp_count_bits(a) - mp_count_bits(b);
|
|
if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
|
|
((res = mp_abs(b, &tb)) != MP_OKAY) ||
|
|
((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
|
|
((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
|
|
goto LBL_ERR;
|
|
}
|
|
|
|
while (n-- >= 0) {
|
|
if (mp_cmp(&tb, &ta) != MP_GT) {
|
|
if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
|
|
((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
|
|
((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
|
|
goto LBL_ERR;
|
|
}
|
|
}
|
|
|
|
/* now q == quotient and ta == remainder */
|
|
n = a->sign;
|
|
n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
|
|
if (c != NULL) {
|
|
mp_exch(c, &q);
|
|
c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
|
|
}
|
|
if (d != NULL) {
|
|
mp_exch(d, &ta);
|
|
d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
|
|
}
|
|
LBL_ERR:
|
|
mp_clear_multi(&ta, &tb, &tq, &q, NULL);
|
|
return res;
|
|
}
|
|
|
|
#else
|
|
|
|
/* integer signed division.
|
|
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
|
|
* HAC pp.598 Algorithm 14.20
|
|
*
|
|
* Note that the description in HAC is horribly
|
|
* incomplete. For example, it doesn't consider
|
|
* the case where digits are removed from 'x' in
|
|
* the inner loop. It also doesn't consider the
|
|
* case that y has fewer than three digits, etc..
|
|
*
|
|
* The overall algorithm is as described as
|
|
* 14.20 from HAC but fixed to treat these cases.
|
|
*/
|
|
static int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
|
|
{
|
|
mp_int q, x, y, t1, t2;
|
|
int res, n, t, i, norm, neg;
|
|
|
|
/* is divisor zero ? */
|
|
if (mp_iszero (b) == 1) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
/* if a < b then q=0, r = a */
|
|
if (mp_cmp_mag (a, b) == MP_LT) {
|
|
if (d != NULL) {
|
|
res = mp_copy (a, d);
|
|
} else {
|
|
res = MP_OKAY;
|
|
}
|
|
if (c != NULL) {
|
|
mp_zero (c);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
q.used = a->used + 2;
|
|
|
|
if ((res = mp_init (&t1)) != MP_OKAY) {
|
|
goto LBL_Q;
|
|
}
|
|
|
|
if ((res = mp_init (&t2)) != MP_OKAY) {
|
|
goto LBL_T1;
|
|
}
|
|
|
|
if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
|
|
goto LBL_T2;
|
|
}
|
|
|
|
if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
|
|
goto LBL_X;
|
|
}
|
|
|
|
/* fix the sign */
|
|
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
|
|
x.sign = y.sign = MP_ZPOS;
|
|
|
|
/* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
|
|
norm = mp_count_bits(&y) % DIGIT_BIT;
|
|
if (norm < (int)(DIGIT_BIT-1)) {
|
|
norm = (DIGIT_BIT-1) - norm;
|
|
if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
} else {
|
|
norm = 0;
|
|
}
|
|
|
|
/* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
|
|
n = x.used - 1;
|
|
t = y.used - 1;
|
|
|
|
/* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
|
|
if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
|
|
goto LBL_Y;
|
|
}
|
|
|
|
while (mp_cmp (&x, &y) != MP_LT) {
|
|
++(q.dp[n - t]);
|
|
if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
}
|
|
|
|
/* reset y by shifting it back down */
|
|
mp_rshd (&y, n - t);
|
|
|
|
/* step 3. for i from n down to (t + 1) */
|
|
for (i = n; i >= (t + 1); i--) {
|
|
if (i > x.used) {
|
|
continue;
|
|
}
|
|
|
|
/* step 3.1 if xi == yt then set q{i-t-1} to b-1,
|
|
* otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
|
|
if (x.dp[i] == y.dp[t]) {
|
|
q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
|
|
} else {
|
|
mp_word tmp;
|
|
tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
|
|
tmp |= ((mp_word) x.dp[i - 1]);
|
|
tmp /= ((mp_word) y.dp[t]);
|
|
if (tmp > (mp_word) MP_MASK)
|
|
tmp = MP_MASK;
|
|
q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
|
|
}
|
|
|
|
/* while (q{i-t-1} * (yt * b + y{t-1})) >
|
|
xi * b**2 + xi-1 * b + xi-2
|
|
|
|
do q{i-t-1} -= 1;
|
|
*/
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
|
|
do {
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
|
|
|
|
/* find left hand */
|
|
mp_zero (&t1);
|
|
t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
|
|
t1.dp[1] = y.dp[t];
|
|
t1.used = 2;
|
|
if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* find right hand */
|
|
t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
|
|
t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
|
|
t2.dp[2] = x.dp[i];
|
|
t2.used = 3;
|
|
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
|
|
|
|
/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
|
|
if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
/* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
|
|
if (x.sign == MP_NEG) {
|
|
if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
|
|
goto LBL_Y;
|
|
}
|
|
|
|
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
|
|
}
|
|
}
|
|
|
|
/* now q is the quotient and x is the remainder
|
|
* [which we have to normalize]
|
|
*/
|
|
|
|
/* get sign before writing to c */
|
|
x.sign = x.used == 0 ? MP_ZPOS : a->sign;
|
|
|
|
if (c != NULL) {
|
|
mp_clamp (&q);
|
|
mp_exch (&q, c);
|
|
c->sign = neg;
|
|
}
|
|
|
|
if (d != NULL) {
|
|
mp_div_2d (&x, norm, &x, NULL);
|
|
mp_exch (&x, d);
|
|
}
|
|
|
|
res = MP_OKAY;
|
|
|
|
LBL_Y:mp_clear (&y);
|
|
LBL_X:mp_clear (&x);
|
|
LBL_T2:mp_clear (&t2);
|
|
LBL_T1:mp_clear (&t1);
|
|
LBL_Q:mp_clear (&q);
|
|
return res;
|
|
}
|
|
|
|
#endif
|
|
|
|
|
|
#ifdef MP_LOW_MEM
|
|
#define TAB_SIZE 32
|
|
#else
|
|
#define TAB_SIZE 256
|
|
#endif
|
|
|
|
static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res, mu;
|
|
mp_digit buf;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
int (*redux)(mp_int*,mp_int*,mp_int*);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits (X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
#ifdef MP_LOW_MEM
|
|
if (winsize > 5) {
|
|
winsize = 5;
|
|
}
|
|
#endif
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&M[1])) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear (&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* create mu, used for Barrett reduction */
|
|
if ((err = mp_init (&mu)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
redux = mp_reduce;
|
|
} else {
|
|
if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
redux = mp_reduce_2k_l;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
* The M table contains powers of the base,
|
|
* e.g. M[x] = G**x mod P
|
|
*
|
|
* The first half of the table is not
|
|
* computed though accept for M[0] and M[1]
|
|
*/
|
|
if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring
|
|
* M[1] (winsize-1) times
|
|
*/
|
|
if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
/* square it */
|
|
if ((err = mp_sqr (&M[1 << (winsize - 1)],
|
|
&M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
/* reduce modulo P */
|
|
if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
}
|
|
|
|
/* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
|
|
* for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
|
|
*/
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init (&res)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
mp_set (&res, 1);
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset the bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int) DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
|
|
buf <<= (mp_digit)1;
|
|
|
|
/* if the bit is zero and mode == 0 then we ignore it
|
|
* These represent the leading zero bits before the first 1 bit
|
|
* in the exponent. Technically this opt is not required but it
|
|
* does lower the # of trivial squaring/reductions used
|
|
*/
|
|
if (mode == 0 && y == 0) {
|
|
continue;
|
|
}
|
|
|
|
/* if the bit is zero and mode == 1 then we square */
|
|
if (mode == 1 && y == 0) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
continue;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* empty window and reset */
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
mode = 1;
|
|
}
|
|
}
|
|
|
|
/* if bits remain then square/multiply */
|
|
if (mode == 2 && bitcpy > 0) {
|
|
/* square then multiply if the bit is set */
|
|
for (x = 0; x < bitcpy; x++) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, &mu)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
mp_exch (&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:mp_clear (&res);
|
|
LBL_MU:mp_clear (&mu);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear (&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
|
|
|
|
/* computes b = a*a */
|
|
static int mp_sqr (mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
#ifdef BN_MP_TOOM_SQR_C
|
|
/* use Toom-Cook? */
|
|
if (a->used >= TOOM_SQR_CUTOFF) {
|
|
res = mp_toom_sqr(a, b);
|
|
/* Karatsuba? */
|
|
} else
|
|
#endif
|
|
#ifdef BN_MP_KARATSUBA_SQR_C
|
|
if (a->used >= KARATSUBA_SQR_CUTOFF) {
|
|
res = mp_karatsuba_sqr (a, b);
|
|
} else
|
|
#endif
|
|
{
|
|
#ifdef BN_FAST_S_MP_SQR_C
|
|
/* can we use the fast comba multiplier? */
|
|
if ((a->used * 2 + 1) < MP_WARRAY &&
|
|
a->used <
|
|
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
|
|
res = fast_s_mp_sqr (a, b);
|
|
} else
|
|
#endif
|
|
#ifdef BN_S_MP_SQR_C
|
|
res = s_mp_sqr (a, b);
|
|
#else
|
|
#error mp_sqr could fail
|
|
res = MP_VAL;
|
|
#endif
|
|
}
|
|
b->sign = MP_ZPOS;
|
|
return res;
|
|
}
|
|
|
|
|
|
/* reduces a modulo n where n is of the form 2**p - d
|
|
This differs from reduce_2k since "d" can be larger
|
|
than a single digit.
|
|
*/
|
|
static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
|
|
{
|
|
mp_int q;
|
|
int p, res;
|
|
|
|
if ((res = mp_init(&q)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
p = mp_count_bits(n);
|
|
top:
|
|
/* q = a/2**p, a = a mod 2**p */
|
|
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* q = q * d */
|
|
if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
/* a = a + q */
|
|
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if (mp_cmp_mag(a, n) != MP_LT) {
|
|
s_mp_sub(a, n, a);
|
|
goto top;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&q);
|
|
return res;
|
|
}
|
|
|
|
|
|
/* determines the setup value */
|
|
static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
|
|
{
|
|
int res;
|
|
mp_int tmp;
|
|
|
|
if ((res = mp_init(&tmp)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
|
|
goto ERR;
|
|
}
|
|
|
|
ERR:
|
|
mp_clear(&tmp);
|
|
return res;
|
|
}
|
|
|
|
|
|
/* computes a = 2**b
|
|
*
|
|
* Simple algorithm which zeroes the int, grows it then just sets one bit
|
|
* as required.
|
|
*/
|
|
static int mp_2expt (mp_int * a, int b)
|
|
{
|
|
int res;
|
|
|
|
/* zero a as per default */
|
|
mp_zero (a);
|
|
|
|
/* grow a to accommodate the single bit */
|
|
if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* set the used count of where the bit will go */
|
|
a->used = b / DIGIT_BIT + 1;
|
|
|
|
/* put the single bit in its place */
|
|
a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* pre-calculate the value required for Barrett reduction
|
|
* For a given modulus "b" it calulates the value required in "a"
|
|
*/
|
|
static int mp_reduce_setup (mp_int * a, mp_int * b)
|
|
{
|
|
int res;
|
|
|
|
if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
return mp_div (a, b, a, NULL);
|
|
}
|
|
|
|
|
|
/* reduces x mod m, assumes 0 < x < m**2, mu is
|
|
* precomputed via mp_reduce_setup.
|
|
* From HAC pp.604 Algorithm 14.42
|
|
*/
|
|
static int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
|
|
{
|
|
mp_int q;
|
|
int res, um = m->used;
|
|
|
|
/* q = x */
|
|
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* q1 = x / b**(k-1) */
|
|
mp_rshd (&q, um - 1);
|
|
|
|
/* according to HAC this optimization is ok */
|
|
if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
|
|
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
} else {
|
|
#ifdef BN_S_MP_MUL_HIGH_DIGS_C
|
|
if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
|
|
if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
#else
|
|
{
|
|
#error mp_reduce would always fail
|
|
res = MP_VAL;
|
|
goto CLEANUP;
|
|
}
|
|
#endif
|
|
}
|
|
|
|
/* q3 = q2 / b**(k+1) */
|
|
mp_rshd (&q, um + 1);
|
|
|
|
/* x = x mod b**(k+1), quick (no division) */
|
|
if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* q = q * m mod b**(k+1), quick (no division) */
|
|
if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* x = x - q */
|
|
if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
|
|
/* If x < 0, add b**(k+1) to it */
|
|
if (mp_cmp_d (x, 0) == MP_LT) {
|
|
mp_set (&q, 1);
|
|
if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
if ((res = mp_add (x, &q, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
/* Back off if it's too big */
|
|
while (mp_cmp (x, m) != MP_LT) {
|
|
if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
|
|
goto CLEANUP;
|
|
}
|
|
}
|
|
|
|
CLEANUP:
|
|
mp_clear (&q);
|
|
|
|
return res;
|
|
}
|
|
|
|
|
|
/* multiplies |a| * |b| and only computes up to digs digits of result
|
|
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
|
|
* many digits of output are created.
|
|
*/
|
|
static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int res, pa, pb, ix, iy;
|
|
mp_digit u;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
#ifdef BN_FAST_S_MP_MUL_DIGS_C
|
|
/* can we use the fast multiplier? */
|
|
if (((digs) < MP_WARRAY) &&
|
|
MIN (a->used, b->used) <
|
|
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
return fast_s_mp_mul_digs (a, b, c, digs);
|
|
}
|
|
#endif
|
|
|
|
if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
t.used = digs;
|
|
|
|
/* compute the digits of the product directly */
|
|
pa = a->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* set the carry to zero */
|
|
u = 0;
|
|
|
|
/* limit ourselves to making digs digits of output */
|
|
pb = MIN (b->used, digs - ix);
|
|
|
|
/* setup some aliases */
|
|
/* copy of the digit from a used within the nested loop */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* an alias for the destination shifted ix places */
|
|
tmpt = t.dp + ix;
|
|
|
|
/* an alias for the digits of b */
|
|
tmpy = b->dp;
|
|
|
|
/* compute the columns of the output and propagate the carry */
|
|
for (iy = 0; iy < pb; iy++) {
|
|
/* compute the column as a mp_word */
|
|
r = ((mp_word)*tmpt) +
|
|
((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
|
((mp_word) u);
|
|
|
|
/* the new column is the lower part of the result */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get the carry word from the result */
|
|
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
/* set carry if it is placed below digs */
|
|
if (ix + iy < digs) {
|
|
*tmpt = u;
|
|
}
|
|
}
|
|
|
|
mp_clamp (&t);
|
|
mp_exch (&t, c);
|
|
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef BN_FAST_S_MP_MUL_DIGS_C
|
|
/* Fast (comba) multiplier
|
|
*
|
|
* This is the fast column-array [comba] multiplier. It is
|
|
* designed to compute the columns of the product first
|
|
* then handle the carries afterwards. This has the effect
|
|
* of making the nested loops that compute the columns very
|
|
* simple and schedulable on super-scalar processors.
|
|
*
|
|
* This has been modified to produce a variable number of
|
|
* digits of output so if say only a half-product is required
|
|
* you don't have to compute the upper half (a feature
|
|
* required for fast Barrett reduction).
|
|
*
|
|
* Based on Algorithm 14.12 on pp.595 of HAC.
|
|
*
|
|
*/
|
|
static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY];
|
|
register mp_word _W;
|
|
|
|
/* grow the destination as required */
|
|
if (c->alloc < digs) {
|
|
if ((res = mp_grow (c, digs)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
pa = MIN(digs, a->used + b->used);
|
|
|
|
/* clear the carry */
|
|
_W = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty;
|
|
int iy;
|
|
mp_digit *tmpx, *tmpy;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(b->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = b->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(a->used-tx, ty+1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; ++iz) {
|
|
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
|
|
|
}
|
|
|
|
/* store term */
|
|
W[ix] = ((mp_digit)_W) & MP_MASK;
|
|
|
|
/* make next carry */
|
|
_W = _W >> ((mp_word)DIGIT_BIT);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = c->used;
|
|
c->used = pa;
|
|
|
|
{
|
|
register mp_digit *tmpc;
|
|
tmpc = c->dp;
|
|
for (ix = 0; ix < pa+1; ix++) {
|
|
/* now extract the previous digit [below the carry] */
|
|
*tmpc++ = W[ix];
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
for (; ix < olduse; ix++) {
|
|
*tmpc++ = 0;
|
|
}
|
|
}
|
|
mp_clamp (c);
|
|
return MP_OKAY;
|
|
}
|
|
#endif /* BN_FAST_S_MP_MUL_DIGS_C */
|
|
|
|
|
|
/* init an mp_init for a given size */
|
|
static int mp_init_size (mp_int * a, int size)
|
|
{
|
|
int x;
|
|
|
|
/* pad size so there are always extra digits */
|
|
size += (MP_PREC * 2) - (size % MP_PREC);
|
|
|
|
/* alloc mem */
|
|
a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
|
|
if (a->dp == NULL) {
|
|
return MP_MEM;
|
|
}
|
|
|
|
/* set the members */
|
|
a->used = 0;
|
|
a->alloc = size;
|
|
a->sign = MP_ZPOS;
|
|
|
|
/* zero the digits */
|
|
for (x = 0; x < size; x++) {
|
|
a->dp[x] = 0;
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
|
|
static int s_mp_sqr (mp_int * a, mp_int * b)
|
|
{
|
|
mp_int t;
|
|
int res, ix, iy, pa;
|
|
mp_word r;
|
|
mp_digit u, tmpx, *tmpt;
|
|
|
|
pa = a->used;
|
|
if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
|
|
/* default used is maximum possible size */
|
|
t.used = 2*pa + 1;
|
|
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* first calculate the digit at 2*ix */
|
|
/* calculate double precision result */
|
|
r = ((mp_word) t.dp[2*ix]) +
|
|
((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
|
|
|
|
/* store lower part in result */
|
|
t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get the carry */
|
|
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
|
|
/* left hand side of A[ix] * A[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias for where to store the results */
|
|
tmpt = t.dp + (2*ix + 1);
|
|
|
|
for (iy = ix + 1; iy < pa; iy++) {
|
|
/* first calculate the product */
|
|
r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
|
|
|
|
/* now calculate the double precision result, note we use
|
|
* addition instead of *2 since it's easier to optimize
|
|
*/
|
|
r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
|
|
|
|
/* store lower part */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* get carry */
|
|
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
/* propagate upwards */
|
|
while (u != ((mp_digit) 0)) {
|
|
r = ((mp_word) *tmpt) + ((mp_word) u);
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
}
|
|
|
|
mp_clamp (&t);
|
|
mp_exch (&t, b);
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
/* multiplies |a| * |b| and does not compute the lower digs digits
|
|
* [meant to get the higher part of the product]
|
|
*/
|
|
static int s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
|
|
{
|
|
mp_int t;
|
|
int res, pa, pb, ix, iy;
|
|
mp_digit u;
|
|
mp_word r;
|
|
mp_digit tmpx, *tmpt, *tmpy;
|
|
|
|
/* can we use the fast multiplier? */
|
|
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
|
|
if (((a->used + b->used + 1) < MP_WARRAY)
|
|
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
return fast_s_mp_mul_high_digs (a, b, c, digs);
|
|
}
|
|
#endif
|
|
|
|
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
t.used = a->used + b->used + 1;
|
|
|
|
pa = a->used;
|
|
pb = b->used;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
/* clear the carry */
|
|
u = 0;
|
|
|
|
/* left hand side of A[ix] * B[iy] */
|
|
tmpx = a->dp[ix];
|
|
|
|
/* alias to the address of where the digits will be stored */
|
|
tmpt = &(t.dp[digs]);
|
|
|
|
/* alias for where to read the right hand side from */
|
|
tmpy = b->dp + (digs - ix);
|
|
|
|
for (iy = digs - ix; iy < pb; iy++) {
|
|
/* calculate the double precision result */
|
|
r = ((mp_word)*tmpt) +
|
|
((mp_word)tmpx) * ((mp_word)*tmpy++) +
|
|
((mp_word) u);
|
|
|
|
/* get the lower part */
|
|
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* carry the carry */
|
|
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
*tmpt = u;
|
|
}
|
|
mp_clamp (&t);
|
|
mp_exch (&t, c);
|
|
mp_clear (&t);
|
|
return MP_OKAY;
|
|
}
|
|
|
|
|
|
#ifdef BN_MP_MONTGOMERY_SETUP_C
|
|
/* setups the montgomery reduction stuff */
|
|
static int
|
|
mp_montgomery_setup (mp_int * n, mp_digit * rho)
|
|
{
|
|
mp_digit x, b;
|
|
|
|
/* fast inversion mod 2**k
|
|
*
|
|
* Based on the fact that
|
|
*
|
|
* XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
|
|
* => 2*X*A - X*X*A*A = 1
|
|
* => 2*(1) - (1) = 1
|
|
*/
|
|
b = n->dp[0];
|
|
|
|
if ((b & 1) == 0) {
|
|
return MP_VAL;
|
|
}
|
|
|
|
x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**8 */
|
|
#if !defined(MP_8BIT)
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**16 */
|
|
#endif
|
|
#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**32 */
|
|
#endif
|
|
#ifdef MP_64BIT
|
|
x *= 2 - b * x; /* here x*a==1 mod 2**64 */
|
|
#endif
|
|
|
|
/* rho = -1/m mod b */
|
|
*rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
|
/* computes xR**-1 == x (mod N) via Montgomery Reduction
|
|
*
|
|
* This is an optimized implementation of montgomery_reduce
|
|
* which uses the comba method to quickly calculate the columns of the
|
|
* reduction.
|
|
*
|
|
* Based on Algorithm 14.32 on pp.601 of HAC.
|
|
*/
|
|
static int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
|
|
{
|
|
int ix, res, olduse;
|
|
mp_word W[MP_WARRAY];
|
|
|
|
/* get old used count */
|
|
olduse = x->used;
|
|
|
|
/* grow a as required */
|
|
if (x->alloc < n->used + 1) {
|
|
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* first we have to get the digits of the input into
|
|
* an array of double precision words W[...]
|
|
*/
|
|
{
|
|
register mp_word *_W;
|
|
register mp_digit *tmpx;
|
|
|
|
/* alias for the W[] array */
|
|
_W = W;
|
|
|
|
/* alias for the digits of x*/
|
|
tmpx = x->dp;
|
|
|
|
/* copy the digits of a into W[0..a->used-1] */
|
|
for (ix = 0; ix < x->used; ix++) {
|
|
*_W++ = *tmpx++;
|
|
}
|
|
|
|
/* zero the high words of W[a->used..m->used*2] */
|
|
for (; ix < n->used * 2 + 1; ix++) {
|
|
*_W++ = 0;
|
|
}
|
|
}
|
|
|
|
/* now we proceed to zero successive digits
|
|
* from the least significant upwards
|
|
*/
|
|
for (ix = 0; ix < n->used; ix++) {
|
|
/* mu = ai * m' mod b
|
|
*
|
|
* We avoid a double precision multiplication (which isn't required)
|
|
* by casting the value down to a mp_digit. Note this requires
|
|
* that W[ix-1] have the carry cleared (see after the inner loop)
|
|
*/
|
|
register mp_digit mu;
|
|
mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
|
|
|
|
/* a = a + mu * m * b**i
|
|
*
|
|
* This is computed in place and on the fly. The multiplication
|
|
* by b**i is handled by offseting which columns the results
|
|
* are added to.
|
|
*
|
|
* Note the comba method normally doesn't handle carries in the
|
|
* inner loop In this case we fix the carry from the previous
|
|
* column since the Montgomery reduction requires digits of the
|
|
* result (so far) [see above] to work. This is
|
|
* handled by fixing up one carry after the inner loop. The
|
|
* carry fixups are done in order so after these loops the
|
|
* first m->used words of W[] have the carries fixed
|
|
*/
|
|
{
|
|
register int iy;
|
|
register mp_digit *tmpn;
|
|
register mp_word *_W;
|
|
|
|
/* alias for the digits of the modulus */
|
|
tmpn = n->dp;
|
|
|
|
/* Alias for the columns set by an offset of ix */
|
|
_W = W + ix;
|
|
|
|
/* inner loop */
|
|
for (iy = 0; iy < n->used; iy++) {
|
|
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
|
|
}
|
|
}
|
|
|
|
/* now fix carry for next digit, W[ix+1] */
|
|
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
/* now we have to propagate the carries and
|
|
* shift the words downward [all those least
|
|
* significant digits we zeroed].
|
|
*/
|
|
{
|
|
register mp_digit *tmpx;
|
|
register mp_word *_W, *_W1;
|
|
|
|
/* nox fix rest of carries */
|
|
|
|
/* alias for current word */
|
|
_W1 = W + ix;
|
|
|
|
/* alias for next word, where the carry goes */
|
|
_W = W + ++ix;
|
|
|
|
for (; ix <= n->used * 2 + 1; ix++) {
|
|
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
|
|
}
|
|
|
|
/* copy out, A = A/b**n
|
|
*
|
|
* The result is A/b**n but instead of converting from an
|
|
* array of mp_word to mp_digit than calling mp_rshd
|
|
* we just copy them in the right order
|
|
*/
|
|
|
|
/* alias for destination word */
|
|
tmpx = x->dp;
|
|
|
|
/* alias for shifted double precision result */
|
|
_W = W + n->used;
|
|
|
|
for (ix = 0; ix < n->used + 1; ix++) {
|
|
*tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
|
|
}
|
|
|
|
/* zero oldused digits, if the input a was larger than
|
|
* m->used+1 we'll have to clear the digits
|
|
*/
|
|
for (; ix < olduse; ix++) {
|
|
*tmpx++ = 0;
|
|
}
|
|
}
|
|
|
|
/* set the max used and clamp */
|
|
x->used = n->used + 1;
|
|
mp_clamp (x);
|
|
|
|
/* if A >= m then A = A - m */
|
|
if (mp_cmp_mag (x, n) != MP_LT) {
|
|
return s_mp_sub (x, n, x);
|
|
}
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_MP_MUL_2_C
|
|
/* b = a*2 */
|
|
static int mp_mul_2(mp_int * a, mp_int * b)
|
|
{
|
|
int x, res, oldused;
|
|
|
|
/* grow to accommodate result */
|
|
if (b->alloc < a->used + 1) {
|
|
if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
oldused = b->used;
|
|
b->used = a->used;
|
|
|
|
{
|
|
register mp_digit r, rr, *tmpa, *tmpb;
|
|
|
|
/* alias for source */
|
|
tmpa = a->dp;
|
|
|
|
/* alias for dest */
|
|
tmpb = b->dp;
|
|
|
|
/* carry */
|
|
r = 0;
|
|
for (x = 0; x < a->used; x++) {
|
|
|
|
/* get what will be the *next* carry bit from the
|
|
* MSB of the current digit
|
|
*/
|
|
rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
|
|
|
|
/* now shift up this digit, add in the carry [from the previous] */
|
|
*tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
|
|
|
|
/* copy the carry that would be from the source
|
|
* digit into the next iteration
|
|
*/
|
|
r = rr;
|
|
}
|
|
|
|
/* new leading digit? */
|
|
if (r != 0) {
|
|
/* add a MSB which is always 1 at this point */
|
|
*tmpb = 1;
|
|
++(b->used);
|
|
}
|
|
|
|
/* now zero any excess digits on the destination
|
|
* that we didn't write to
|
|
*/
|
|
tmpb = b->dp + b->used;
|
|
for (x = b->used; x < oldused; x++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
b->sign = a->sign;
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
|
/*
|
|
* shifts with subtractions when the result is greater than b.
|
|
*
|
|
* The method is slightly modified to shift B unconditionally up to just under
|
|
* the leading bit of b. This saves a lot of multiple precision shifting.
|
|
*/
|
|
static int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
|
|
{
|
|
int x, bits, res;
|
|
|
|
/* how many bits of last digit does b use */
|
|
bits = mp_count_bits (b) % DIGIT_BIT;
|
|
|
|
if (b->used > 1) {
|
|
if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
} else {
|
|
mp_set(a, 1);
|
|
bits = 1;
|
|
}
|
|
|
|
|
|
/* now compute C = A * B mod b */
|
|
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
|
|
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
if (mp_cmp_mag (a, b) != MP_LT) {
|
|
if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
}
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_MP_EXPTMOD_FAST_C
|
|
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
|
|
*
|
|
* Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
|
|
* The value of k changes based on the size of the exponent.
|
|
*
|
|
* Uses Montgomery or Diminished Radix reduction [whichever appropriate]
|
|
*/
|
|
|
|
static int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
|
|
{
|
|
mp_int M[TAB_SIZE], res;
|
|
mp_digit buf, mp;
|
|
int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
|
|
|
|
/* use a pointer to the reduction algorithm. This allows us to use
|
|
* one of many reduction algorithms without modding the guts of
|
|
* the code with if statements everywhere.
|
|
*/
|
|
int (*redux)(mp_int*,mp_int*,mp_digit);
|
|
|
|
/* find window size */
|
|
x = mp_count_bits (X);
|
|
if (x <= 7) {
|
|
winsize = 2;
|
|
} else if (x <= 36) {
|
|
winsize = 3;
|
|
} else if (x <= 140) {
|
|
winsize = 4;
|
|
} else if (x <= 450) {
|
|
winsize = 5;
|
|
} else if (x <= 1303) {
|
|
winsize = 6;
|
|
} else if (x <= 3529) {
|
|
winsize = 7;
|
|
} else {
|
|
winsize = 8;
|
|
}
|
|
|
|
#ifdef MP_LOW_MEM
|
|
if (winsize > 5) {
|
|
winsize = 5;
|
|
}
|
|
#endif
|
|
|
|
/* init M array */
|
|
/* init first cell */
|
|
if ((err = mp_init(&M[1])) != MP_OKAY) {
|
|
return err;
|
|
}
|
|
|
|
/* now init the second half of the array */
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
if ((err = mp_init(&M[x])) != MP_OKAY) {
|
|
for (y = 1<<(winsize-1); y < x; y++) {
|
|
mp_clear (&M[y]);
|
|
}
|
|
mp_clear(&M[1]);
|
|
return err;
|
|
}
|
|
}
|
|
|
|
/* determine and setup reduction code */
|
|
if (redmode == 0) {
|
|
#ifdef BN_MP_MONTGOMERY_SETUP_C
|
|
/* now setup montgomery */
|
|
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
|
|
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
|
|
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
|
|
if (((P->used * 2 + 1) < MP_WARRAY) &&
|
|
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
|
|
redux = fast_mp_montgomery_reduce;
|
|
} else
|
|
#endif
|
|
{
|
|
#ifdef BN_MP_MONTGOMERY_REDUCE_C
|
|
/* use slower baseline Montgomery method */
|
|
redux = mp_montgomery_reduce;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
}
|
|
} else if (redmode == 1) {
|
|
#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
|
|
/* setup DR reduction for moduli of the form B**k - b */
|
|
mp_dr_setup(P, &mp);
|
|
redux = mp_dr_reduce;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
} else {
|
|
#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
|
|
/* setup DR reduction for moduli of the form 2**k - b */
|
|
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
redux = mp_reduce_2k;
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_M;
|
|
#endif
|
|
}
|
|
|
|
/* setup result */
|
|
if ((err = mp_init (&res)) != MP_OKAY) {
|
|
goto LBL_M;
|
|
}
|
|
|
|
/* create M table
|
|
*
|
|
|
|
*
|
|
* The first half of the table is not computed though accept for M[0] and M[1]
|
|
*/
|
|
|
|
if (redmode == 0) {
|
|
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
|
|
/* now we need R mod m */
|
|
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
#else
|
|
err = MP_VAL;
|
|
goto LBL_RES;
|
|
#endif
|
|
|
|
/* now set M[1] to G * R mod m */
|
|
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
} else {
|
|
mp_set(&res, 1);
|
|
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
|
|
if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
for (x = 0; x < (winsize - 1); x++) {
|
|
if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* create upper table */
|
|
for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
|
|
if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* set initial mode and bit cnt */
|
|
mode = 0;
|
|
bitcnt = 1;
|
|
buf = 0;
|
|
digidx = X->used - 1;
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
|
|
for (;;) {
|
|
/* grab next digit as required */
|
|
if (--bitcnt == 0) {
|
|
/* if digidx == -1 we are out of digits so break */
|
|
if (digidx == -1) {
|
|
break;
|
|
}
|
|
/* read next digit and reset bitcnt */
|
|
buf = X->dp[digidx--];
|
|
bitcnt = (int)DIGIT_BIT;
|
|
}
|
|
|
|
/* grab the next msb from the exponent */
|
|
y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
|
|
buf <<= (mp_digit)1;
|
|
|
|
/* if the bit is zero and mode == 0 then we ignore it
|
|
* These represent the leading zero bits before the first 1 bit
|
|
* in the exponent. Technically this opt is not required but it
|
|
* does lower the # of trivial squaring/reductions used
|
|
*/
|
|
if (mode == 0 && y == 0) {
|
|
continue;
|
|
}
|
|
|
|
/* if the bit is zero and mode == 1 then we square */
|
|
if (mode == 1 && y == 0) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
continue;
|
|
}
|
|
|
|
/* else we add it to the window */
|
|
bitbuf |= (y << (winsize - ++bitcpy));
|
|
mode = 2;
|
|
|
|
if (bitcpy == winsize) {
|
|
/* ok window is filled so square as required and multiply */
|
|
/* square first */
|
|
for (x = 0; x < winsize; x++) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* empty window and reset */
|
|
bitcpy = 0;
|
|
bitbuf = 0;
|
|
mode = 1;
|
|
}
|
|
}
|
|
|
|
/* if bits remain then square/multiply */
|
|
if (mode == 2 && bitcpy > 0) {
|
|
/* square then multiply if the bit is set */
|
|
for (x = 0; x < bitcpy; x++) {
|
|
if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
|
|
/* get next bit of the window */
|
|
bitbuf <<= 1;
|
|
if ((bitbuf & (1 << winsize)) != 0) {
|
|
/* then multiply */
|
|
if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
if ((err = redux (&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (redmode == 0) {
|
|
/* fixup result if Montgomery reduction is used
|
|
* recall that any value in a Montgomery system is
|
|
* actually multiplied by R mod n. So we have
|
|
* to reduce one more time to cancel out the factor
|
|
* of R.
|
|
*/
|
|
if ((err = redux(&res, P, mp)) != MP_OKAY) {
|
|
goto LBL_RES;
|
|
}
|
|
}
|
|
|
|
/* swap res with Y */
|
|
mp_exch (&res, Y);
|
|
err = MP_OKAY;
|
|
LBL_RES:mp_clear (&res);
|
|
LBL_M:
|
|
mp_clear(&M[1]);
|
|
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
|
|
mp_clear (&M[x]);
|
|
}
|
|
return err;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_FAST_S_MP_SQR_C
|
|
/* the jist of squaring...
|
|
* you do like mult except the offset of the tmpx [one that
|
|
* starts closer to zero] can't equal the offset of tmpy.
|
|
* So basically you set up iy like before then you min it with
|
|
* (ty-tx) so that it never happens. You double all those
|
|
* you add in the inner loop
|
|
|
|
After that loop you do the squares and add them in.
|
|
*/
|
|
|
|
static int fast_s_mp_sqr (mp_int * a, mp_int * b)
|
|
{
|
|
int olduse, res, pa, ix, iz;
|
|
mp_digit W[MP_WARRAY], *tmpx;
|
|
mp_word W1;
|
|
|
|
/* grow the destination as required */
|
|
pa = a->used + a->used;
|
|
if (b->alloc < pa) {
|
|
if ((res = mp_grow (b, pa)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* number of output digits to produce */
|
|
W1 = 0;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
int tx, ty, iy;
|
|
mp_word _W;
|
|
mp_digit *tmpy;
|
|
|
|
/* clear counter */
|
|
_W = 0;
|
|
|
|
/* get offsets into the two bignums */
|
|
ty = MIN(a->used-1, ix);
|
|
tx = ix - ty;
|
|
|
|
/* setup temp aliases */
|
|
tmpx = a->dp + tx;
|
|
tmpy = a->dp + ty;
|
|
|
|
/* this is the number of times the loop will iterrate, essentially
|
|
while (tx++ < a->used && ty-- >= 0) { ... }
|
|
*/
|
|
iy = MIN(a->used-tx, ty+1);
|
|
|
|
/* now for squaring tx can never equal ty
|
|
* we halve the distance since they approach at a rate of 2x
|
|
* and we have to round because odd cases need to be executed
|
|
*/
|
|
iy = MIN(iy, (ty-tx+1)>>1);
|
|
|
|
/* execute loop */
|
|
for (iz = 0; iz < iy; iz++) {
|
|
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
|
|
}
|
|
|
|
/* double the inner product and add carry */
|
|
_W = _W + _W + W1;
|
|
|
|
/* even columns have the square term in them */
|
|
if ((ix&1) == 0) {
|
|
_W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
|
|
}
|
|
|
|
/* store it */
|
|
W[ix] = (mp_digit)(_W & MP_MASK);
|
|
|
|
/* make next carry */
|
|
W1 = _W >> ((mp_word)DIGIT_BIT);
|
|
}
|
|
|
|
/* setup dest */
|
|
olduse = b->used;
|
|
b->used = a->used+a->used;
|
|
|
|
{
|
|
mp_digit *tmpb;
|
|
tmpb = b->dp;
|
|
for (ix = 0; ix < pa; ix++) {
|
|
*tmpb++ = W[ix] & MP_MASK;
|
|
}
|
|
|
|
/* clear unused digits [that existed in the old copy of c] */
|
|
for (; ix < olduse; ix++) {
|
|
*tmpb++ = 0;
|
|
}
|
|
}
|
|
mp_clamp (b);
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|
|
|
|
|
|
#ifdef BN_MP_MUL_D_C
|
|
/* multiply by a digit */
|
|
static int
|
|
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
|
|
{
|
|
mp_digit u, *tmpa, *tmpc;
|
|
mp_word r;
|
|
int ix, res, olduse;
|
|
|
|
/* make sure c is big enough to hold a*b */
|
|
if (c->alloc < a->used + 1) {
|
|
if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
|
|
return res;
|
|
}
|
|
}
|
|
|
|
/* get the original destinations used count */
|
|
olduse = c->used;
|
|
|
|
/* set the sign */
|
|
c->sign = a->sign;
|
|
|
|
/* alias for a->dp [source] */
|
|
tmpa = a->dp;
|
|
|
|
/* alias for c->dp [dest] */
|
|
tmpc = c->dp;
|
|
|
|
/* zero carry */
|
|
u = 0;
|
|
|
|
/* compute columns */
|
|
for (ix = 0; ix < a->used; ix++) {
|
|
/* compute product and carry sum for this term */
|
|
r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
|
|
|
|
/* mask off higher bits to get a single digit */
|
|
*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
|
|
|
|
/* send carry into next iteration */
|
|
u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
|
|
}
|
|
|
|
/* store final carry [if any] and increment ix offset */
|
|
*tmpc++ = u;
|
|
++ix;
|
|
|
|
/* now zero digits above the top */
|
|
while (ix++ < olduse) {
|
|
*tmpc++ = 0;
|
|
}
|
|
|
|
/* set used count */
|
|
c->used = a->used + 1;
|
|
mp_clamp(c);
|
|
|
|
return MP_OKAY;
|
|
}
|
|
#endif
|