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  */
16 static int
17 has_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 
51 static int
52 crypto_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 
121 static void
122 edwards_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 
133 static int
134 crypto_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 
155 struct 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