1#include <tommath.h>
2#ifdef BN_FAST_MP_INVMOD_C
3/* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
16 */
17
18/* computes the modular inverse via binary extended euclidean algorithm,
19 * that is c = 1/a mod b
20 *
21 * Based on slow invmod except this is optimized for the case where b is
22 * odd as per HAC Note 14.64 on pp. 610
23 */
24int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
25{
26  mp_int  x, y, u, v, B, D;
27  int     res, neg;
28
29  /* 2. [modified] b must be odd   */
30  if (mp_iseven (b) == 1) {
31    return MP_VAL;
32  }
33
34  /* init all our temps */
35  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
36     return res;
37  }
38
39  /* x == modulus, y == value to invert */
40  if ((res = mp_copy (b, &x)) != MP_OKAY) {
41    goto LBL_ERR;
42  }
43
44  /* we need y = |a| */
45  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
46    goto LBL_ERR;
47  }
48
49  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
50  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
51    goto LBL_ERR;
52  }
53  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
54    goto LBL_ERR;
55  }
56  mp_set (&D, 1);
57
58top:
59  /* 4.  while u is even do */
60  while (mp_iseven (&u) == 1) {
61    /* 4.1 u = u/2 */
62    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
63      goto LBL_ERR;
64    }
65    /* 4.2 if B is odd then */
66    if (mp_isodd (&B) == 1) {
67      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
68        goto LBL_ERR;
69      }
70    }
71    /* B = B/2 */
72    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
73      goto LBL_ERR;
74    }
75  }
76
77  /* 5.  while v is even do */
78  while (mp_iseven (&v) == 1) {
79    /* 5.1 v = v/2 */
80    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
81      goto LBL_ERR;
82    }
83    /* 5.2 if D is odd then */
84    if (mp_isodd (&D) == 1) {
85      /* D = (D-x)/2 */
86      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
87        goto LBL_ERR;
88      }
89    }
90    /* D = D/2 */
91    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
92      goto LBL_ERR;
93    }
94  }
95
96  /* 6.  if u >= v then */
97  if (mp_cmp (&u, &v) != MP_LT) {
98    /* u = u - v, B = B - D */
99    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
100      goto LBL_ERR;
101    }
102
103    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
104      goto LBL_ERR;
105    }
106  } else {
107    /* v - v - u, D = D - B */
108    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
109      goto LBL_ERR;
110    }
111
112    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
113      goto LBL_ERR;
114    }
115  }
116
117  /* if not zero goto step 4 */
118  if (mp_iszero (&u) == 0) {
119    goto top;
120  }
121
122  /* now a = C, b = D, gcd == g*v */
123
124  /* if v != 1 then there is no inverse */
125  if (mp_cmp_d (&v, 1) != MP_EQ) {
126    res = MP_VAL;
127    goto LBL_ERR;
128  }
129
130  /* b is now the inverse */
131  neg = a->sign;
132  while (D.sign == MP_NEG) {
133    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
134      goto LBL_ERR;
135    }
136  }
137  mp_exch (&D, c);
138  c->sign = neg;
139  res = MP_OKAY;
140
141LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
142  return res;
143}
144#endif
145
146/* $Source$ */
147/* $Revision$ */
148/* $Date$ */
149