|
2
|
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
|
|
2 * |
|
|
3 * LibTomMath is a library that provides multiple-precision |
|
|
4 * integer arithmetic as well as number theoretic functionality. |
|
|
5 * |
|
|
6 * The library was designed directly after the MPI library by |
|
|
7 * Michael Fromberger but has been written from scratch with |
|
|
8 * additional optimizations in place. |
|
|
9 * |
|
|
10 * The library is free for all purposes without any express |
|
|
11 * guarantee it works. |
|
|
12 * |
|
|
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
|
|
14 */ |
|
|
15 #include <tommath.h> |
|
|
16 |
|
|
17 /* Check if remainders are possible squares - fast exclude non-squares */ |
|
|
18 static const char rem_128[128] = { |
|
|
19 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
20 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
21 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
22 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
23 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
24 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
25 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, |
|
|
26 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 |
|
|
27 }; |
|
|
28 |
|
|
29 static const char rem_105[105] = { |
|
|
30 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, |
|
|
31 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, |
|
|
32 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, |
|
|
33 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, |
|
|
34 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, |
|
|
35 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, |
|
|
36 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1 |
|
|
37 }; |
|
|
38 |
|
|
39 /* Store non-zero to ret if arg is square, and zero if not */ |
|
|
40 int mp_is_square(mp_int *arg,int *ret) |
|
|
41 { |
|
|
42 int res; |
|
|
43 mp_digit c; |
|
|
44 mp_int t; |
|
|
45 unsigned long r; |
|
|
46 |
|
|
47 /* Default to Non-square :) */ |
|
|
48 *ret = MP_NO; |
|
|
49 |
|
|
50 if (arg->sign == MP_NEG) { |
|
|
51 return MP_VAL; |
|
|
52 } |
|
|
53 |
|
|
54 /* digits used? (TSD) */ |
|
|
55 if (arg->used == 0) { |
|
|
56 return MP_OKAY; |
|
|
57 } |
|
|
58 |
|
|
59 /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */ |
|
|
60 if (rem_128[127 & DIGIT(arg,0)] == 1) { |
|
|
61 return MP_OKAY; |
|
|
62 } |
|
|
63 |
|
|
64 /* Next check mod 105 (3*5*7) */ |
|
|
65 if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) { |
|
|
66 return res; |
|
|
67 } |
|
|
68 if (rem_105[c] == 1) { |
|
|
69 return MP_OKAY; |
|
|
70 } |
|
|
71 |
|
|
72 /* product of primes less than 2^31 */ |
|
|
73 if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { |
|
|
74 return res; |
|
|
75 } |
|
|
76 if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) { |
|
|
77 goto ERR; |
|
|
78 } |
|
|
79 r = mp_get_int(&t); |
|
|
80 /* Check for other prime modules, note it's not an ERROR but we must |
|
|
81 * free "t" so the easiest way is to goto ERR. We know that res |
|
|
82 * is already equal to MP_OKAY from the mp_mod call |
|
|
83 */ |
|
|
84 if ( (1L<<(r%11)) & 0x5C4L ) goto ERR; |
|
|
85 if ( (1L<<(r%13)) & 0x9E4L ) goto ERR; |
|
|
86 if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR; |
|
|
87 if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR; |
|
|
88 if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR; |
|
|
89 if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR; |
|
|
90 if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR; |
|
|
91 |
|
|
92 /* Final check - is sqr(sqrt(arg)) == arg ? */ |
|
|
93 if ((res = mp_sqrt(arg,&t)) != MP_OKAY) { |
|
|
94 goto ERR; |
|
|
95 } |
|
|
96 if ((res = mp_sqr(&t,&t)) != MP_OKAY) { |
|
|
97 goto ERR; |
|
|
98 } |
|
|
99 |
|
|
100 *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO; |
|
|
101 ERR:mp_clear(&t); |
|
|
102 return res; |
|
|
103 } |
