1 /* crypto/ec/ec2_mult.c */
2 /* ====================================================================
3 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
5 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7 * to the OpenSSL project.
9 * The ECC Code is licensed pursuant to the OpenSSL open source
10 * license provided below.
12 * The software is originally written by Sheueling Chang Shantz and
13 * Douglas Stebila of Sun Microsystems Laboratories.
16 /* ====================================================================
17 * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
19 * Redistribution and use in source and binary forms, with or without
20 * modification, are permitted provided that the following conditions
23 * 1. Redistributions of source code must retain the above copyright
24 * notice, this list of conditions and the following disclaimer.
26 * 2. Redistributions in binary form must reproduce the above copyright
27 * notice, this list of conditions and the following disclaimer in
28 * the documentation and/or other materials provided with the
31 * 3. All advertising materials mentioning features or use of this
32 * software must display the following acknowledgment:
33 * "This product includes software developed by the OpenSSL Project
34 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
36 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
37 * endorse or promote products derived from this software without
38 * prior written permission. For written permission, please contact
39 * openssl-core@openssl.org.
41 * 5. Products derived from this software may not be called "OpenSSL"
42 * nor may "OpenSSL" appear in their names without prior written
43 * permission of the OpenSSL Project.
45 * 6. Redistributions of any form whatsoever must retain the following
47 * "This product includes software developed by the OpenSSL Project
48 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
50 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
51 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
52 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
53 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
54 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
55 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
56 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
57 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
58 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
59 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
60 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
61 * OF THE POSSIBILITY OF SUCH DAMAGE.
62 * ====================================================================
64 * This product includes cryptographic software written by Eric Young
65 * (eay@cryptsoft.com). This product includes software written by Tim
66 * Hudson (tjh@cryptsoft.com).
70 #include <openssl/err.h>
75 /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
77 * Uses algorithm Mdouble in appendix of
78 * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over
79 * GF(2^m) without precomputation".
80 * modified to not require precomputation of c=b^{2^{m-1}}.
82 static int gf2m_Mdouble(const EC_GROUP
*group
, BIGNUM
*x
, BIGNUM
*z
, BN_CTX
*ctx
)
87 /* Since Mdouble is static we can guarantee that ctx != NULL. */
90 if (t1
== NULL
) goto err
;
92 if (!group
->meth
->field_sqr(group
, x
, x
, ctx
)) goto err
;
93 if (!group
->meth
->field_sqr(group
, t1
, z
, ctx
)) goto err
;
94 if (!group
->meth
->field_mul(group
, z
, x
, t1
, ctx
)) goto err
;
95 if (!group
->meth
->field_sqr(group
, x
, x
, ctx
)) goto err
;
96 if (!group
->meth
->field_sqr(group
, t1
, t1
, ctx
)) goto err
;
97 if (!group
->meth
->field_mul(group
, t1
, &group
->b
, t1
, ctx
)) goto err
;
98 if (!BN_GF2m_add(x
, x
, t1
)) goto err
;
107 /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
108 * projective coordinates.
109 * Uses algorithm Madd in appendix of
110 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
111 * GF(2^m) without precomputation".
113 static int gf2m_Madd(const EC_GROUP
*group
, const BIGNUM
*x
, BIGNUM
*x1
, BIGNUM
*z1
,
114 const BIGNUM
*x2
, const BIGNUM
*z2
, BN_CTX
*ctx
)
119 /* Since Madd is static we can guarantee that ctx != NULL. */
121 t1
= BN_CTX_get(ctx
);
122 t2
= BN_CTX_get(ctx
);
123 if (t2
== NULL
) goto err
;
125 if (!BN_copy(t1
, x
)) goto err
;
126 if (!group
->meth
->field_mul(group
, x1
, x1
, z2
, ctx
)) goto err
;
127 if (!group
->meth
->field_mul(group
, z1
, z1
, x2
, ctx
)) goto err
;
128 if (!group
->meth
->field_mul(group
, t2
, x1
, z1
, ctx
)) goto err
;
129 if (!BN_GF2m_add(z1
, z1
, x1
)) goto err
;
130 if (!group
->meth
->field_sqr(group
, z1
, z1
, ctx
)) goto err
;
131 if (!group
->meth
->field_mul(group
, x1
, z1
, t1
, ctx
)) goto err
;
132 if (!BN_GF2m_add(x1
, x1
, t2
)) goto err
;
141 /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
142 * using Montgomery point multiplication algorithm Mxy() in appendix of
143 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
144 * GF(2^m) without precomputation".
147 * 1 if return value should be the point at infinity
150 static int gf2m_Mxy(const EC_GROUP
*group
, const BIGNUM
*x
, const BIGNUM
*y
, BIGNUM
*x1
,
151 BIGNUM
*z1
, BIGNUM
*x2
, BIGNUM
*z2
, BN_CTX
*ctx
)
153 BIGNUM
*t3
, *t4
, *t5
;
165 if (!BN_copy(x2
, x
)) return 0;
166 if (!BN_GF2m_add(z2
, x
, y
)) return 0;
170 /* Since Mxy is static we can guarantee that ctx != NULL. */
172 t3
= BN_CTX_get(ctx
);
173 t4
= BN_CTX_get(ctx
);
174 t5
= BN_CTX_get(ctx
);
175 if (t5
== NULL
) goto err
;
177 if (!BN_one(t5
)) goto err
;
179 if (!group
->meth
->field_mul(group
, t3
, z1
, z2
, ctx
)) goto err
;
181 if (!group
->meth
->field_mul(group
, z1
, z1
, x
, ctx
)) goto err
;
182 if (!BN_GF2m_add(z1
, z1
, x1
)) goto err
;
183 if (!group
->meth
->field_mul(group
, z2
, z2
, x
, ctx
)) goto err
;
184 if (!group
->meth
->field_mul(group
, x1
, z2
, x1
, ctx
)) goto err
;
185 if (!BN_GF2m_add(z2
, z2
, x2
)) goto err
;
187 if (!group
->meth
->field_mul(group
, z2
, z2
, z1
, ctx
)) goto err
;
188 if (!group
->meth
->field_sqr(group
, t4
, x
, ctx
)) goto err
;
189 if (!BN_GF2m_add(t4
, t4
, y
)) goto err
;
190 if (!group
->meth
->field_mul(group
, t4
, t4
, t3
, ctx
)) goto err
;
191 if (!BN_GF2m_add(t4
, t4
, z2
)) goto err
;
193 if (!group
->meth
->field_mul(group
, t3
, t3
, x
, ctx
)) goto err
;
194 if (!group
->meth
->field_div(group
, t3
, t5
, t3
, ctx
)) goto err
;
195 if (!group
->meth
->field_mul(group
, t4
, t3
, t4
, ctx
)) goto err
;
196 if (!group
->meth
->field_mul(group
, x2
, x1
, t3
, ctx
)) goto err
;
197 if (!BN_GF2m_add(z2
, x2
, x
)) goto err
;
199 if (!group
->meth
->field_mul(group
, z2
, z2
, t4
, ctx
)) goto err
;
200 if (!BN_GF2m_add(z2
, z2
, y
)) goto err
;
209 /* Computes scalar*point and stores the result in r.
210 * point can not equal r.
211 * Uses algorithm 2P of
212 * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
213 * GF(2^m) without precomputation".
215 static int ec_GF2m_montgomery_point_multiply(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
216 const EC_POINT
*point
, BN_CTX
*ctx
)
218 BIGNUM
*x1
, *x2
, *z1
, *z2
;
224 ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY
, EC_R_INVALID_ARGUMENT
);
228 /* if result should be point at infinity */
229 if ((scalar
== NULL
) || BN_is_zero(scalar
) || (point
== NULL
) ||
230 EC_POINT_is_at_infinity(group
, point
))
232 return EC_POINT_set_to_infinity(group
, r
);
235 /* only support affine coordinates */
236 if (!point
->Z_is_one
) return 0;
238 /* Since point_multiply is static we can guarantee that ctx != NULL. */
240 x1
= BN_CTX_get(ctx
);
241 z1
= BN_CTX_get(ctx
);
242 if (z1
== NULL
) goto err
;
247 if (!BN_GF2m_mod_arr(x1
, &point
->X
, group
->poly
)) goto err
; /* x1 = x */
248 if (!BN_one(z1
)) goto err
; /* z1 = 1 */
249 if (!group
->meth
->field_sqr(group
, z2
, x1
, ctx
)) goto err
; /* z2 = x1^2 = x^2 */
250 if (!group
->meth
->field_sqr(group
, x2
, z2
, ctx
)) goto err
;
251 if (!BN_GF2m_add(x2
, x2
, &group
->b
)) goto err
; /* x2 = x^4 + b */
253 /* find top most bit and go one past it */
254 i
= scalar
->top
- 1; j
= BN_BITS2
- 1;
256 while (!(scalar
->d
[i
] & mask
)) { mask
>>= 1; j
--; }
258 /* if top most bit was at word break, go to next word */
261 i
--; j
= BN_BITS2
- 1;
269 if (scalar
->d
[i
] & mask
)
271 if (!gf2m_Madd(group
, &point
->X
, x1
, z1
, x2
, z2
, ctx
)) goto err
;
272 if (!gf2m_Mdouble(group
, x2
, z2
, ctx
)) goto err
;
276 if (!gf2m_Madd(group
, &point
->X
, x2
, z2
, x1
, z1
, ctx
)) goto err
;
277 if (!gf2m_Mdouble(group
, x1
, z1
, ctx
)) goto err
;
285 /* convert out of "projective" coordinates */
286 i
= gf2m_Mxy(group
, &point
->X
, &point
->Y
, x1
, z1
, x2
, z2
, ctx
);
287 if (i
== 0) goto err
;
290 if (!EC_POINT_set_to_infinity(group
, r
)) goto err
;
294 if (!BN_one(&r
->Z
)) goto err
;
298 /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
299 BN_set_negative(&r
->X
, 0);
300 BN_set_negative(&r
->Y
, 0);
311 * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
312 * gracefully ignoring NULL scalar values.
314 int ec_GF2m_simple_mul(const EC_GROUP
*group
, EC_POINT
*r
, const BIGNUM
*scalar
,
315 size_t num
, const EC_POINT
*points
[], const BIGNUM
*scalars
[], BN_CTX
*ctx
)
317 BN_CTX
*new_ctx
= NULL
;
324 ctx
= new_ctx
= BN_CTX_new();
329 /* This implementation is more efficient than the wNAF implementation for 2
330 * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points,
331 * or if we can perform a fast multiplication based on precomputation.
333 if ((scalar
&& (num
> 1)) || (num
> 2) || (num
== 0 && EC_GROUP_have_precompute_mult(group
)))
335 ret
= ec_wNAF_mul(group
, r
, scalar
, num
, points
, scalars
, ctx
);
339 if ((p
= EC_POINT_new(group
)) == NULL
) goto err
;
341 if (!EC_POINT_set_to_infinity(group
, r
)) goto err
;
345 if (!ec_GF2m_montgomery_point_multiply(group
, p
, scalar
, group
->generator
, ctx
)) goto err
;
346 if (BN_is_negative(scalar
))
347 if (!group
->meth
->invert(group
, p
, ctx
)) goto err
;
348 if (!group
->meth
->add(group
, r
, r
, p
, ctx
)) goto err
;
351 for (i
= 0; i
< num
; i
++)
353 if (!ec_GF2m_montgomery_point_multiply(group
, p
, scalars
[i
], points
[i
], ctx
)) goto err
;
354 if (BN_is_negative(scalars
[i
]))
355 if (!group
->meth
->invert(group
, p
, ctx
)) goto err
;
356 if (!group
->meth
->add(group
, r
, r
, p
, ctx
)) goto err
;
362 if (p
) EC_POINT_free(p
);
364 BN_CTX_free(new_ctx
);
369 /* Precomputation for point multiplication: fall back to wNAF methods
370 * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
372 int ec_GF2m_precompute_mult(EC_GROUP
*group
, BN_CTX
*ctx
)
374 return ec_wNAF_precompute_mult(group
, ctx
);
377 int ec_GF2m_have_precompute_mult(const EC_GROUP
*group
)
379 return ec_wNAF_have_precompute_mult(group
);