3 * $Id: ec.c,v 1.3 2002/01/13 13:48:44 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 /*----- Revision history --------------------------------------------------*
33 * Revision 1.3 2002/01/13 13:48:44 mdw
36 * Revision 1.2 2001/05/07 17:29:44 mdw
37 * Treat projective coordinates as an internal representation. Various
38 * minor interface changes.
40 * Revision 1.1 2001/04/29 18:12:33 mdw
45 /*----- Header files ------------------------------------------------------*/
50 /*----- Trivial wrappers --------------------------------------------------*/
52 /* --- @ec_create@ --- *
54 * Arguments: @ec *p@ = pointer to an elliptic-curve point
58 * Use: Initializes a new point. The initial value is the additive
59 * identity (which is universal for all curves).
62 void ec_create(ec
*p
) { EC_CREATE(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
91 * Use: Sets the given point to be the point %$O$% at infinity.
94 void ec_setinf(ec
*p
) { EC_SETINF(p
); }
96 /* --- @ec_copy@ --- *
98 * Arguments: @ec *d@ = pointer to destination point
99 * @const ec *p@ = pointer to source point
103 * Use: Creates a copy of an elliptic curve point.
106 void ec_copy(ec
*d
, const ec
*p
) { EC_COPY(d
, p
); }
108 /*----- Standard curve operations -----------------------------------------*/
110 /* --- @ec_idin@, @ec_idout@ --- *
112 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
113 * @ec *d@ = pointer to the destination
114 * @const ec *p@ = pointer to a source point
116 * Returns: The destination @d@.
118 * Use: An identity operation if your curve has no internal
119 * representation. (The field internal representation is still
123 ec
*ec_idin(ec_curve
*c
, ec
*d
, const ec
*p
)
129 d
->x
= F_IN(f
, d
->x
, p
->x
);
130 d
->y
= F_IN(f
, d
->y
, p
->y
);
131 mp_drop(d
->z
); d
->z
= 0;
136 ec
*ec_idout(ec_curve
*c
, ec
*d
, const ec
*p
)
142 d
->x
= F_OUT(f
, d
->x
, p
->x
);
143 d
->y
= F_OUT(f
, d
->y
, p
->y
);
144 mp_drop(d
->z
); d
->z
= 0;
149 /* --- @ec_projin@, @ec_projout@ --- *
151 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
152 * @ec *d@ = pointer to the destination
153 * @const ec *p@ = pointer to a source point
155 * Returns: The destination @d@.
157 * Use: Conversion functions if your curve operations use a
158 * projective representation.
161 ec
*ec_projin(ec_curve
*c
, ec
*d
, const ec
*p
)
167 d
->x
= F_IN(f
, d
->x
, p
->x
);
168 d
->y
= F_IN(f
, d
->y
, p
->y
);
169 mp_drop(d
->z
); d
->z
= MP_COPY(f
->one
);
174 ec
*ec_projout(ec_curve
*c
, ec
*d
, const ec
*p
)
181 z
= F_INV(f
, MP_NEW
, p
->z
);
182 x
= F_MUL(f
, d
->x
, p
->x
, z
);
183 y
= F_MUL(f
, d
->y
, p
->y
, z
);
186 d
->x
= F_OUT(f
, x
, x
);
187 d
->y
= F_OUT(f
, y
, y
);
193 /* --- @ec_stdsub@ --- *
195 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
196 * @ec *d@ = pointer to the destination
197 * @const ec *a, *b@ = the operand points
199 * Returns: The destination @d@.
201 * Use: Standard point subtraction operation, in terms of negation
202 * and addition. This isn't as efficient as a ready-made
203 * subtraction operator.
206 ec
*ec_stdsub(ec_curve
*c
, ec
*d
, const ec
*a
, const ec
*b
)
215 /*----- Real arithmetic ---------------------------------------------------*/
217 /* --- @ec_find@ --- *
219 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
220 * @ec *d@ = pointer to the destination point
221 * @mp *x@ = a possible x-coordinate
223 * Returns: Zero if OK, nonzero if there isn't a point there.
225 * Use: Finds a point on an elliptic curve with a given x-coordinate.
228 ec
*ec_find(ec_curve
*c
, ec
*d
, mp
*x
)
230 x
= F_IN(c
->f
, MP_NEW
, x
);
231 if ((d
= EC_FIND(c
, d
, x
)) != 0)
237 /* --- @ec_add@ --- *
239 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
240 * @ec *d@ = pointer to the destination point
241 * @const ec *p, *q@ = pointers to the operand points
245 * Use: Adds two points on an elliptic curve.
248 ec
*ec_add(ec_curve
*c
, ec
*d
, const ec
*p
, const ec
*q
)
250 ec pp
= EC_INIT
, qq
= EC_INIT
;
253 EC_ADD(c
, d
, &pp
, &qq
);
260 /* --- @ec_dbl@ --- *
262 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
263 * @ec *d@ = pointer to the destination point
264 * @const ec *p@ = pointer to the operand point
268 * Use: Doubles a point on an elliptic curve.
271 ec
*ec_dbl(ec_curve
*c
, ec
*d
, const ec
*p
)
275 return (EC_OUT(c
, d
, d
));
278 /* --- @ec_imul@, @ec_mul@ --- *
280 * Arguments: @ec_curve *c@ = pointer to an elliptic curve
281 * @ec *d@ = pointer to the destination point
282 * @const ec *p@ = pointer to the generator point
283 * @mp *n@ = integer multiplier
285 * Returns: The destination @d@.
287 * Use: Multiplies a point by a scalar, returning %$n p$%. The
288 * @imul@ variant uses internal representations for argument
292 ec
*ec_imul(ec_curve
*c
, ec
*d
, const ec
*p
, mp
*n
)
297 if (t
.x
&& (n
->f
& MP_BURN
))
303 else if (MP_LEN(n
) < EXP_THRESH
)
304 EXP_SIMPLE(&d
, t
, n
);
306 EXP_WINDOW(&d
, t
, n
);
310 ec
*ec_mul(ec_curve
*c
, ec
*d
, const ec
*p
, mp
*n
)
314 return (EC_OUT(c
, d
, d
));
317 /*----- That's all, folks -------------------------------------------------*/