1
2#include <stddef.h>
3#include <stdint.h>
4
5#include "../scalarmult_curve25519.h"
6#include "export.h"
7#include "private/ed25519_ref10.h"
8#include "utils.h"
9#include "x25519_ref10.h"
10
11/*
12 * Reject small order points early to mitigate the implications of
13 * unexpected optimizations that would affect the ref10 code.
14 * See https://eprint.iacr.org/2017/806.pdf for reference.
15 */
16static int
17has_small_order(const unsigned char s[32])
18{
19    CRYPTO_ALIGN(16)
20    static const unsigned char blacklist[][32] = {
21        { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
22        { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
23        { 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00 },
24        { 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57 },
25        { 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f },
26        { 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f },
27        { 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f },
28        { 0xcd, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x80 },
29        { 0x4c, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0xd7 },
30        { 0xd9, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff },
31        { 0xda, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff },
32        { 0xdb, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff }
33    };
34    unsigned char c[12] = { 0 };
35    unsigned int  k;
36    size_t        i, j;
37
38    COMPILER_ASSERT(12 == sizeof blacklist / sizeof blacklist[0]);
39    for (j = 0; j < 32; j++) {
40        for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) {
41            c[i] |= s[j] ^ blacklist[i][j];
42        }
43    }
44    k = 0;
45    for (i = 0; i < sizeof blacklist / sizeof blacklist[0]; i++) {
46        k |= (c[i] - 1);
47    }
48    return (int) ((k >> 8) & 1);
49}
50
51static int
52crypto_scalarmult_curve25519_ref10(unsigned char *q,
53                                   const unsigned char *n,
54                                   const unsigned char *p)
55{
56    unsigned char *t = q;
57    unsigned int   i;
58    fe25519        x1;
59    fe25519        x2;
60    fe25519        z2;
61    fe25519        x3;
62    fe25519        z3;
63    fe25519        tmp0;
64    fe25519        tmp1;
65    int            pos;
66    unsigned int   swap;
67    unsigned int   b;
68
69    if (has_small_order(p)) {
70        return -1;
71    }
72    for (i = 0; i < 32; i++) {
73        t[i] = n[i];
74    }
75    t[0] &= 248;
76    t[31] &= 127;
77    t[31] |= 64;
78    fe25519_frombytes(x1, p);
79    fe25519_1(x2);
80    fe25519_0(z2);
81    fe25519_copy(x3, x1);
82    fe25519_1(z3);
83
84    swap = 0;
85    for (pos = 254; pos >= 0; --pos) {
86        b = t[pos / 8] >> (pos & 7);
87        b &= 1;
88        swap ^= b;
89        fe25519_cswap(x2, x3, swap);
90        fe25519_cswap(z2, z3, swap);
91        swap = b;
92        fe25519_sub(tmp0, x3, z3);
93        fe25519_sub(tmp1, x2, z2);
94        fe25519_add(x2, x2, z2);
95        fe25519_add(z2, x3, z3);
96        fe25519_mul(z3, tmp0, x2);
97        fe25519_mul(z2, z2, tmp1);
98        fe25519_sq(tmp0, tmp1);
99        fe25519_sq(tmp1, x2);
100        fe25519_add(x3, z3, z2);
101        fe25519_sub(z2, z3, z2);
102        fe25519_mul(x2, tmp1, tmp0);
103        fe25519_sub(tmp1, tmp1, tmp0);
104        fe25519_sq(z2, z2);
105        fe25519_scalar_product(z3, tmp1, 121666);
106        fe25519_sq(x3, x3);
107        fe25519_add(tmp0, tmp0, z3);
108        fe25519_mul(z3, x1, z2);
109        fe25519_mul(z2, tmp1, tmp0);
110    }
111    fe25519_cswap(x2, x3, swap);
112    fe25519_cswap(z2, z3, swap);
113
114    fe25519_invert(z2, z2);
115    fe25519_mul(x2, x2, z2);
116    fe25519_tobytes(q, x2);
117
118    return 0;
119}
120
121static void
122edwards_to_montgomery(fe25519 montgomeryX, const fe25519 edwardsY, const fe25519 edwardsZ)
123{
124    fe25519 tempX;
125    fe25519 tempZ;
126
127    fe25519_add(tempX, edwardsZ, edwardsY);
128    fe25519_sub(tempZ, edwardsZ, edwardsY);
129    fe25519_invert(tempZ, tempZ);
130    fe25519_mul(montgomeryX, tempX, tempZ);
131}
132
133static int
134crypto_scalarmult_curve25519_ref10_base(unsigned char *q,
135                                        const unsigned char *n)
136{
137    unsigned char *t = q;
138    ge25519_p3     A;
139    fe25519        pk;
140    unsigned int   i;
141
142    for (i = 0; i < 32; i++) {
143        t[i] = n[i];
144    }
145    t[0] &= 248;
146    t[31] &= 127;
147    t[31] |= 64;
148    ge25519_scalarmult_base(&A, t);
149    edwards_to_montgomery(pk, A.Y, A.Z);
150    fe25519_tobytes(q, pk);
151
152    return 0;
153}
154
155struct crypto_scalarmult_curve25519_implementation
156    crypto_scalarmult_curve25519_ref10_implementation = {
157        SODIUM_C99(.mult =) crypto_scalarmult_curve25519_ref10,
158        SODIUM_C99(.mult_base =) crypto_scalarmult_curve25519_ref10_base
159    };
160