3 * $Id: ec.c,v 1.10 2004/04/08 01:36:15 mdw Exp $
5 * Elliptic curve definitions
7 * (c) 2001 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Header files ------------------------------------------------------*/
34 /*----- Trivial wrappers --------------------------------------------------*/
36 /* --- @ec_samep@ --- *
38 * Arguments: @ec_curve *c, *d@ = two elliptic curves
40 * Returns: Nonzero if the curves are identical (not just isomorphic).
42 * Use: Checks for sameness of curves. This function does the full
43 * check, not just the curve-type-specific check done by the
44 * @sampep@ field operation.
47 int ec_samep(ec_curve
*c
, ec_curve
*d
)
49 return (field_samep(c
->f
, d
->f
) && c
->ops
== d
->ops
&& EC_SAMEP(c
, d
));
52 /* --- @ec_create@ --- *
54 * Arguments: @ec *p@ = pointer to an elliptic-curve point
56 * Returns: The argument @p@.
58 * Use: Initializes a new point. The initial value is the additive
59 * identity (which is universal for all curves).
62 ec
*ec_create(ec
*p
) { EC_CREATE(p
); return (p
); }
64 /* --- @ec_destroy@ --- *
66 * Arguments: @ec *p@ = pointer to an elliptic-curve point
70 * Use: Destroys a point, making it invalid.
73 void ec_destroy(ec
*p
) { EC_DESTROY(p
); }
75 /* --- @ec_atinf@ --- *
77 * Arguments: @const ec *p@ = pointer to a point
79 * Returns: Nonzero if %$p = O$% is the point at infinity, zero
83 int ec_atinf(const ec
*p
) { return (EC_ATINF(p
)); }
85 /* --- @ec_setinf@ --- *
87 * Arguments: @ec *p@ = pointer to a point
89 * Returns: The argument @p@.
91 * Use: Sets the given point to be the point %$O$% at infinity.
94 ec
*ec_setinf(ec
*p
) { EC_SETINF(p
); return (p
); }
96 /* --- @ec_copy@ --- *
98 * Arguments: @ec *d@ = pointer to destination point
99 * @const ec *p@ = pointer to source point
101 * Returns: The destination @d@.
103 * Use: Creates a copy of an elliptic curve point.
106 ec
*ec_copy(ec
*d
, const ec
*p
) { EC_COPY(d
, p
); return (d
); }
110 * Arguments: @const ec *p, *q@ = two points
112 * Returns: Nonzero if the points are equal. Compares external-format
116 int ec_eq(const ec
*p
, const ec
*q
) { return (EC_EQ(p
, q
)); }
118 /*----- Standard curve operations -----------------------------------------*/
120 /* --- @ec_stdsamep@ --- *
122 * Arguments: @ec_curve *c, *d@ = two elliptic curves
124 * Returns: Nonzero if the curves are identical (not just isomorphic).
126 * Use: Simple sameness check on @a@ and @b@ curve members.
129 int ec_stdsamep(ec_curve
*c
, ec_curve
*d
)
131 return (MP_EQ(c
->a
, d
->a
) && MP_EQ(c
->b
, d
->b
));
134 /* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- *
136 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
137 * @ec *d@ = pointer to the destination
138 * @const ec *p@ = pointer to a source point
140 * Returns: The destination @d@.
142 * Use: An identity operation if your curve has no internal
143 * representation. (The field internal representation is still
147 ec
*ec_idin(ec_curve
*c
, ec
*d
, const ec
*p
)
153 d
->x
= F_IN(f
, d
->x
, p
->x
);
154 d
->y
= F_IN(f
, d
->y
, p
->y
);
155 mp_drop(d
->z
); d
->z
= 0;
160 ec
*ec_idout(ec_curve
*c
, ec
*d
, const ec
*p
)
166 d
->x
= F_OUT(f
, d
->x
, p
->x
);
167 d
->y
= F_OUT(f
, d
->y
, p
->y
);
168 mp_drop(d
->z
); d
->z
= 0;
173 ec
*ec_idfix(ec_curve
*c
, ec
*d
, const ec
*p
)
179 /* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- *
181 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
182 * @ec *d@ = pointer to the destination
183 * @const ec *p@ = pointer to a source point
185 * Returns: The destination @d@.
187 * Use: Conversion functions if your curve operations use a
188 * projective representation.
191 ec
*ec_projin(ec_curve
*c
, ec
*d
, const ec
*p
)
197 d
->x
= F_IN(f
, d
->x
, p
->x
);
198 d
->y
= F_IN(f
, d
->y
, p
->y
);
199 mp_drop(d
->z
); d
->z
= MP_COPY(f
->one
);
204 ec
*ec_projout(ec_curve
*c
, ec
*d
, const ec
*p
)
211 z
= F_INV(f
, MP_NEW
, p
->z
);
212 zz
= F_SQR(f
, MP_NEW
, z
);
213 z
= F_MUL(f
, z
, zz
, z
);
214 x
= F_MUL(f
, d
->x
, p
->x
, zz
);
215 y
= F_MUL(f
, d
->y
, p
->y
, z
);
219 d
->x
= F_OUT(f
, x
, x
);
220 d
->y
= F_OUT(f
, y
, y
);
226 ec
*ec_projfix(ec_curve
*c
, ec
*d
, const ec
*p
)
230 else if (d
->z
== c
->f
->one
)
235 z
= F_INV(f
, MP_NEW
, p
->z
);
236 zz
= F_SQR(f
, MP_NEW
, z
);
237 z
= F_MUL(f
, z
, zz
, z
);
238 d
->x
= F_MUL(f
, d
->x
, p
->x
, zz
);
239 d
->y
= F_MUL(f
, d
->y
, p
->y
, z
);
243 d
->z
= MP_COPY(f
->one
);
248 /* --- @ec_stdsub@ --- *
250 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
251 * @ec *d@ = pointer to the destination
252 * @const ec *p, *q@ = the operand points
254 * Returns: The destination @d@.
256 * Use: Standard point subtraction operation, in terms of negation
257 * and addition. This isn't as efficient as a ready-made
258 * subtraction operator.
261 ec
*ec_stdsub(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
271 /*----- Creating curves ---------------------------------------------------*/
273 /* --- @ec_destroycurve@ --- *
275 * Arguments: @ec_curve *c@ = pointer to an ellptic curve
279 * Use: Destroys a description of an elliptic curve.
282 void ec_destroycurve(ec_curve
*c
) { c
->ops
->destroy(c
); }
284 /*----- Real arithmetic ---------------------------------------------------*/
286 /* --- @ec_find@ --- *
288 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
289 * @ec *d@ = pointer to the destination point
290 * @mp *x@ = a possible x-coordinate
292 * Returns: Zero if OK, nonzero if there isn't a point there.
294 * Use: Finds a point on an elliptic curve with a given x-coordinate.
297 ec
*ec_find(ec_curve
*c
, ec
*d
, mp
*x
)
299 x
= F_IN(c
->f
, MP_NEW
, x
);
300 if ((d
= EC_FIND(c
, d
, x
)) != 0)
306 /* --- @ec_neg@ --- *
308 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
309 * @ec *d@ = pointer to the destination point
310 * @const ec *p@ = pointer to the operand point
312 * Returns: The destination point.
314 * Use: Computes the negation of the given point.
317 ec
*ec_neg(ec_curve
*c
, ec
*d
, const ec
*p
)
321 return (EC_OUT(c
, d
, d
));
324 /* --- @ec_add@ --- *
326 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
327 * @ec *d@ = pointer to the destination point
328 * @const ec *p, *q@ = pointers to the operand points
332 * Use: Adds two points on an elliptic curve.
335 ec
*ec_add(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
337 ec pp
= EC_INIT
, qq
= EC_INIT
;
340 EC_ADD(c
, d
, &pp
, &qq
);
347 /* --- @ec_sub@ --- *
349 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
350 * @ec *d@ = pointer to the destination point
351 * @const ec *p, *q@ = pointers to the operand points
353 * Returns: The destination @d@.
355 * Use: Subtracts one point from another on an elliptic curve.
358 ec
*ec_sub(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
360 ec pp
= EC_INIT
, qq
= EC_INIT
;
363 EC_SUB(c
, d
, &pp
, &qq
);
370 /* --- @ec_dbl@ --- *
372 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
373 * @ec *d@ = pointer to the destination point
374 * @const ec *p@ = pointer to the operand point
378 * Use: Doubles a point on an elliptic curve.
381 ec
*ec_dbl(ec_curve
*c
, ec
*d
, const ec
*p
)
385 return (EC_OUT(c
, d
, d
));
388 /* --- @ec_check@ --- *
390 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
391 * @const ec *p@ = pointer to the point
393 * Returns: Zero if OK, nonzero if this is an invalid point.
395 * Use: Checks that a point is actually on an elliptic curve.
398 int ec_check(ec_curve
*c
, const ec
*p
)
406 rc
= EC_CHECK(c
, &t
);
411 /* --- @ec_rand@ --- *
413 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
414 * @ec *d@ = pointer to the destination point
415 * @grand *r@ = random number source
417 * Returns: The destination @d@.
419 * Use: Finds a random point on the given curve.
422 ec
*ec_rand(ec_curve
*c
, ec
*d
, grand
*r
)
425 do x
= F_RAND(c
->f
, x
, r
); while (!EC_FIND(c
, d
, x
));
427 if (grand_range(r
, 2)) EC_NEG(c
, d
, d
);
428 return (EC_OUT(c
, d
, d
));
431 /*----- That's all, folks -------------------------------------------------*/