2 * Diffie-Hellman implementation for PuTTY.
8 * The primes used in the group1 and group14 key exchange.
10 static const unsigned char P1
[] = {
11 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xC9, 0x0F, 0xDA, 0xA2,
12 0x21, 0x68, 0xC2, 0x34, 0xC4, 0xC6, 0x62, 0x8B, 0x80, 0xDC, 0x1C, 0xD1,
13 0x29, 0x02, 0x4E, 0x08, 0x8A, 0x67, 0xCC, 0x74, 0x02, 0x0B, 0xBE, 0xA6,
14 0x3B, 0x13, 0x9B, 0x22, 0x51, 0x4A, 0x08, 0x79, 0x8E, 0x34, 0x04, 0xDD,
15 0xEF, 0x95, 0x19, 0xB3, 0xCD, 0x3A, 0x43, 0x1B, 0x30, 0x2B, 0x0A, 0x6D,
16 0xF2, 0x5F, 0x14, 0x37, 0x4F, 0xE1, 0x35, 0x6D, 0x6D, 0x51, 0xC2, 0x45,
17 0xE4, 0x85, 0xB5, 0x76, 0x62, 0x5E, 0x7E, 0xC6, 0xF4, 0x4C, 0x42, 0xE9,
18 0xA6, 0x37, 0xED, 0x6B, 0x0B, 0xFF, 0x5C, 0xB6, 0xF4, 0x06, 0xB7, 0xED,
19 0xEE, 0x38, 0x6B, 0xFB, 0x5A, 0x89, 0x9F, 0xA5, 0xAE, 0x9F, 0x24, 0x11,
20 0x7C, 0x4B, 0x1F, 0xE6, 0x49, 0x28, 0x66, 0x51, 0xEC, 0xE6, 0x53, 0x81,
21 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
23 static const unsigned char P14
[] = {
24 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xC9, 0x0F, 0xDA, 0xA2,
25 0x21, 0x68, 0xC2, 0x34, 0xC4, 0xC6, 0x62, 0x8B, 0x80, 0xDC, 0x1C, 0xD1,
26 0x29, 0x02, 0x4E, 0x08, 0x8A, 0x67, 0xCC, 0x74, 0x02, 0x0B, 0xBE, 0xA6,
27 0x3B, 0x13, 0x9B, 0x22, 0x51, 0x4A, 0x08, 0x79, 0x8E, 0x34, 0x04, 0xDD,
28 0xEF, 0x95, 0x19, 0xB3, 0xCD, 0x3A, 0x43, 0x1B, 0x30, 0x2B, 0x0A, 0x6D,
29 0xF2, 0x5F, 0x14, 0x37, 0x4F, 0xE1, 0x35, 0x6D, 0x6D, 0x51, 0xC2, 0x45,
30 0xE4, 0x85, 0xB5, 0x76, 0x62, 0x5E, 0x7E, 0xC6, 0xF4, 0x4C, 0x42, 0xE9,
31 0xA6, 0x37, 0xED, 0x6B, 0x0B, 0xFF, 0x5C, 0xB6, 0xF4, 0x06, 0xB7, 0xED,
32 0xEE, 0x38, 0x6B, 0xFB, 0x5A, 0x89, 0x9F, 0xA5, 0xAE, 0x9F, 0x24, 0x11,
33 0x7C, 0x4B, 0x1F, 0xE6, 0x49, 0x28, 0x66, 0x51, 0xEC, 0xE4, 0x5B, 0x3D,
34 0xC2, 0x00, 0x7C, 0xB8, 0xA1, 0x63, 0xBF, 0x05, 0x98, 0xDA, 0x48, 0x36,
35 0x1C, 0x55, 0xD3, 0x9A, 0x69, 0x16, 0x3F, 0xA8, 0xFD, 0x24, 0xCF, 0x5F,
36 0x83, 0x65, 0x5D, 0x23, 0xDC, 0xA3, 0xAD, 0x96, 0x1C, 0x62, 0xF3, 0x56,
37 0x20, 0x85, 0x52, 0xBB, 0x9E, 0xD5, 0x29, 0x07, 0x70, 0x96, 0x96, 0x6D,
38 0x67, 0x0C, 0x35, 0x4E, 0x4A, 0xBC, 0x98, 0x04, 0xF1, 0x74, 0x6C, 0x08,
39 0xCA, 0x18, 0x21, 0x7C, 0x32, 0x90, 0x5E, 0x46, 0x2E, 0x36, 0xCE, 0x3B,
40 0xE3, 0x9E, 0x77, 0x2C, 0x18, 0x0E, 0x86, 0x03, 0x9B, 0x27, 0x83, 0xA2,
41 0xEC, 0x07, 0xA2, 0x8F, 0xB5, 0xC5, 0x5D, 0xF0, 0x6F, 0x4C, 0x52, 0xC9,
42 0xDE, 0x2B, 0xCB, 0xF6, 0x95, 0x58, 0x17, 0x18, 0x39, 0x95, 0x49, 0x7C,
43 0xEA, 0x95, 0x6A, 0xE5, 0x15, 0xD2, 0x26, 0x18, 0x98, 0xFA, 0x05, 0x10,
44 0x15, 0x72, 0x8E, 0x5A, 0x8A, 0xAC, 0xAA, 0x68, 0xFF, 0xFF, 0xFF, 0xFF,
45 0xFF, 0xFF, 0xFF, 0xFF
49 * The generator g = 2 (used for both group1 and group14).
51 static const unsigned char G
[] = { 2 };
53 static const struct ssh_kex ssh_diffiehellman_group1_sha1
= {
54 "diffie-hellman-group1-sha1", "group1",
55 P1
, G
, lenof(P1
), lenof(G
), &ssh_sha1
58 static const struct ssh_kex
*const group1_list
[] = {
59 &ssh_diffiehellman_group1_sha1
62 const struct ssh_kexes ssh_diffiehellman_group1
= {
63 sizeof(group1_list
) / sizeof(*group1_list
),
67 static const struct ssh_kex ssh_diffiehellman_group14_sha1
= {
68 "diffie-hellman-group14-sha1", "group14",
69 P14
, G
, lenof(P14
), lenof(G
), &ssh_sha1
72 static const struct ssh_kex
*const group14_list
[] = {
73 &ssh_diffiehellman_group14_sha1
76 const struct ssh_kexes ssh_diffiehellman_group14
= {
77 sizeof(group14_list
) / sizeof(*group14_list
),
81 static const struct ssh_kex ssh_diffiehellman_gex_sha256
= {
82 "diffie-hellman-group-exchange-sha256", NULL
,
83 NULL
, NULL
, 0, 0, &ssh_sha256
86 static const struct ssh_kex ssh_diffiehellman_gex_sha1
= {
87 "diffie-hellman-group-exchange-sha1", NULL
,
88 NULL
, NULL
, 0, 0, &ssh_sha1
91 static const struct ssh_kex
*const gex_list
[] = {
92 &ssh_diffiehellman_gex_sha256
,
93 &ssh_diffiehellman_gex_sha1
96 const struct ssh_kexes ssh_diffiehellman_gex
= {
97 sizeof(gex_list
) / sizeof(*gex_list
),
105 Bignum x
, e
, p
, q
, qmask
, g
;
109 * Common DH initialisation.
111 static void dh_init(struct dh_ctx
*ctx
)
113 ctx
->q
= bignum_rshift(ctx
->p
, 1);
114 ctx
->qmask
= bignum_bitmask(ctx
->q
);
115 ctx
->x
= ctx
->e
= NULL
;
119 * Initialise DH for a standard group.
121 void *dh_setup_group(const struct ssh_kex
*kex
)
123 struct dh_ctx
*ctx
= snew(struct dh_ctx
);
124 ctx
->p
= bignum_from_bytes(kex
->pdata
, kex
->plen
);
125 ctx
->g
= bignum_from_bytes(kex
->gdata
, kex
->glen
);
131 * Initialise DH for a server-supplied group.
133 void *dh_setup_gex(Bignum pval
, Bignum gval
)
135 struct dh_ctx
*ctx
= snew(struct dh_ctx
);
136 ctx
->p
= copybn(pval
);
137 ctx
->g
= copybn(gval
);
143 * Clean up and free a context.
145 void dh_cleanup(void *handle
)
147 struct dh_ctx
*ctx
= (struct dh_ctx
*)handle
;
158 * DH stage 1: invent a number x between 1 and q, and compute e =
159 * g^x mod p. Return e.
161 * If `nbits' is greater than zero, it is used as an upper limit
162 * for the number of bits in x. This is safe provided that (a) you
163 * use twice as many bits in x as the number of bits you expect to
164 * use in your session key, and (b) the DH group is a safe prime
165 * (which SSH demands that it must be).
167 * P. C. van Oorschot, M. J. Wiener
168 * "On Diffie-Hellman Key Agreement with Short Exponents".
169 * Advances in Cryptology: Proceedings of Eurocrypt '96
170 * Springer-Verlag, May 1996.
172 Bignum
dh_create_e(void *handle
, int nbits
)
174 struct dh_ctx
*ctx
= (struct dh_ctx
*)handle
;
180 nbytes
= ssh1_bignum_length(ctx
->qmask
);
181 buf
= snewn(nbytes
, unsigned char);
185 * Create a potential x, by ANDing a string of random bytes
190 if (nbits
== 0 || nbits
> bignum_bitcount(ctx
->qmask
)) {
191 ssh1_write_bignum(buf
, ctx
->qmask
);
192 for (i
= 2; i
< nbytes
; i
++)
193 buf
[i
] &= random_byte();
194 ssh1_read_bignum(buf
, nbytes
, &ctx
->x
); /* can't fail */
197 ctx
->x
= bn_power_2(nbits
);
199 for (i
= 0; i
< nbits
; i
++) {
204 bignum_set_bit(ctx
->x
, i
, b
& 1);
209 } while (bignum_cmp(ctx
->x
, One
) <= 0 || bignum_cmp(ctx
->x
, ctx
->q
) >= 0);
214 * Done. Now compute e = g^x mod p.
216 ctx
->e
= modpow(ctx
->g
, ctx
->x
, ctx
->p
);
222 * DH stage 2: given a number f, compute K = f^x mod p.
224 Bignum
dh_find_K(void *handle
, Bignum f
)
226 struct dh_ctx
*ctx
= (struct dh_ctx
*)handle
;
228 ret
= modpow(f
, ctx
->x
, ctx
->p
);