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comparison tomsfastmath/src/numtheory/fp_invmod.c @ 643:a362b62d38b2 dropbear-tfm

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Add tomsfastmath from git rev bfa4582842bc3bab42e4be4aed5703437049502a with Makefile.in renamed
author Matt Johnston <matt@ucc.asn.au>
date Wed, 23 Nov 2011 18:10:20 +0700
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642:33fd2f3499d2 643:a362b62d38b2
1 /* TomsFastMath, a fast ISO C bignum library.
2 *
3 * This project is meant to fill in where LibTomMath
4 * falls short. That is speed ;-)
5 *
6 * This project is public domain and free for all purposes.
7 *
8 * Tom St Denis, [email protected]
9 */
10 #include <tfm.h>
11
12 static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
13 {
14 fp_int x, y, u, v, A, B, C, D;
15 int res;
16
17 /* b cannot be negative */
18 if (b->sign == FP_NEG || fp_iszero(b) == 1) {
19 return FP_VAL;
20 }
21
22 /* init temps */
23 fp_init(&x); fp_init(&y);
24 fp_init(&u); fp_init(&v);
25 fp_init(&A); fp_init(&B);
26 fp_init(&C); fp_init(&D);
27
28 /* x = a, y = b */
29 if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
30 return res;
31 }
32 fp_copy(b, &y);
33
34 /* 2. [modified] if x,y are both even then return an error! */
35 if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
36 return FP_VAL;
37 }
38
39 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
40 fp_copy (&x, &u);
41 fp_copy (&y, &v);
42 fp_set (&A, 1);
43 fp_set (&D, 1);
44
45 top:
46 /* 4. while u is even do */
47 while (fp_iseven (&u) == 1) {
48 /* 4.1 u = u/2 */
49 fp_div_2 (&u, &u);
50
51 /* 4.2 if A or B is odd then */
52 if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
53 /* A = (A+y)/2, B = (B-x)/2 */
54 fp_add (&A, &y, &A);
55 fp_sub (&B, &x, &B);
56 }
57 /* A = A/2, B = B/2 */
58 fp_div_2 (&A, &A);
59 fp_div_2 (&B, &B);
60 }
61
62 /* 5. while v is even do */
63 while (fp_iseven (&v) == 1) {
64 /* 5.1 v = v/2 */
65 fp_div_2 (&v, &v);
66
67 /* 5.2 if C or D is odd then */
68 if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
69 /* C = (C+y)/2, D = (D-x)/2 */
70 fp_add (&C, &y, &C);
71 fp_sub (&D, &x, &D);
72 }
73 /* C = C/2, D = D/2 */
74 fp_div_2 (&C, &C);
75 fp_div_2 (&D, &D);
76 }
77
78 /* 6. if u >= v then */
79 if (fp_cmp (&u, &v) != FP_LT) {
80 /* u = u - v, A = A - C, B = B - D */
81 fp_sub (&u, &v, &u);
82 fp_sub (&A, &C, &A);
83 fp_sub (&B, &D, &B);
84 } else {
85 /* v - v - u, C = C - A, D = D - B */
86 fp_sub (&v, &u, &v);
87 fp_sub (&C, &A, &C);
88 fp_sub (&D, &B, &D);
89 }
90
91 /* if not zero goto step 4 */
92 if (fp_iszero (&u) == 0)
93 goto top;
94
95 /* now a = C, b = D, gcd == g*v */
96
97 /* if v != 1 then there is no inverse */
98 if (fp_cmp_d (&v, 1) != FP_EQ) {
99 return FP_VAL;
100 }
101
102 /* if its too low */
103 while (fp_cmp_d(&C, 0) == FP_LT) {
104 fp_add(&C, b, &C);
105 }
106
107 /* too big */
108 while (fp_cmp_mag(&C, b) != FP_LT) {
109 fp_sub(&C, b, &C);
110 }
111
112 /* C is now the inverse */
113 fp_copy(&C, c);
114 return FP_OKAY;
115 }
116
117 /* c = 1/a (mod b) for odd b only */
118 int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
119 {
120 fp_int x, y, u, v, B, D;
121 int neg;
122
123 /* 2. [modified] b must be odd */
124 if (fp_iseven (b) == FP_YES) {
125 return fp_invmod_slow(a,b,c);
126 }
127
128 /* init all our temps */
129 fp_init(&x); fp_init(&y);
130 fp_init(&u); fp_init(&v);
131 fp_init(&B); fp_init(&D);
132
133 /* x == modulus, y == value to invert */
134 fp_copy(b, &x);
135
136 /* we need y = |a| */
137 fp_abs(a, &y);
138
139 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
140 fp_copy(&x, &u);
141 fp_copy(&y, &v);
142 fp_set (&D, 1);
143
144 top:
145 /* 4. while u is even do */
146 while (fp_iseven (&u) == FP_YES) {
147 /* 4.1 u = u/2 */
148 fp_div_2 (&u, &u);
149
150 /* 4.2 if B is odd then */
151 if (fp_isodd (&B) == FP_YES) {
152 fp_sub (&B, &x, &B);
153 }
154 /* B = B/2 */
155 fp_div_2 (&B, &B);
156 }
157
158 /* 5. while v is even do */
159 while (fp_iseven (&v) == FP_YES) {
160 /* 5.1 v = v/2 */
161 fp_div_2 (&v, &v);
162
163 /* 5.2 if D is odd then */
164 if (fp_isodd (&D) == FP_YES) {
165 /* D = (D-x)/2 */
166 fp_sub (&D, &x, &D);
167 }
168 /* D = D/2 */
169 fp_div_2 (&D, &D);
170 }
171
172 /* 6. if u >= v then */
173 if (fp_cmp (&u, &v) != FP_LT) {
174 /* u = u - v, B = B - D */
175 fp_sub (&u, &v, &u);
176 fp_sub (&B, &D, &B);
177 } else {
178 /* v - v - u, D = D - B */
179 fp_sub (&v, &u, &v);
180 fp_sub (&D, &B, &D);
181 }
182
183 /* if not zero goto step 4 */
184 if (fp_iszero (&u) == FP_NO) {
185 goto top;
186 }
187
188 /* now a = C, b = D, gcd == g*v */
189
190 /* if v != 1 then there is no inverse */
191 if (fp_cmp_d (&v, 1) != FP_EQ) {
192 return FP_VAL;
193 }
194
195 /* b is now the inverse */
196 neg = a->sign;
197 while (D.sign == FP_NEG) {
198 fp_add (&D, b, &D);
199 }
200 fp_copy (&D, c);
201 c->sign = neg;
202 return FP_OKAY;
203 }
204
205 /* $Source$ */
206 /* $Revision$ */
207 /* $Date$ */