weierstrass.h

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#ifndef _IPXE_WEIERSTRASS_H
#define _IPXE_WEIERSTRASS_H

/** @file
 *
 * Weierstrass elliptic curves
 *
 */

FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );

#include <ipxe/bigint.h>
#include <ipxe/crypto.h>

/** Number of axes in Weierstrass curve point representation */
#define WEIERSTRASS_AXES 2

/**
 * Maximum multiple of field prime encountered during calculations
 *
 * Calculations are performed using values modulo a small multiple of
 * the field prime, rather than modulo the field prime itself.  This
 * allows explicit reductions after additions, subtractions, and
 * relaxed Montgomery multiplications to be omitted entirely, provided
 * that we keep careful track of the field prime multiple for each
 * intermediate value.
 *
 * Relaxed Montgomery multiplication will produce a result in the
 * range t < (1+m/k)N, where m is this maximum multiple of the field
 * prime, and k is the constant in R > kN representing the leading
 * zero padding in the big integer representation of the field prime.
 * We choose to set k=m so that multiplications will always produce a
 * result in the range t < 2N.
 *
 * This is expressed as the base-two logarithm of the multiple
 * (rounded up), to simplify compile-time calculations.
 */
#define WEIERSTRASS_MAX_MULTIPLE_LOG2 5 /* maximum reached is mod 20N */

/**
 * Determine number of elements in scalar values for a Weierstrass curve
 *
 * @v len               Length of field prime, in bytes
 * @ret size            Number of elements
 */
#define weierstrass_size( len )                                         \
        bigint_required_size ( (len) +                                  \
                               ( ( WEIERSTRASS_MAX_MULTIPLE_LOG2 + 7 )  \
                                 / 8 ) )

/**
 * Define a Weierstrass projective co-ordinate type
 *
 * @v size              Number of elements in scalar values
 * @ret weierstrass_t   Projective co-ordinate type
 */
#define weierstrass_t( size )                                           \
        union {                                                         \
                bigint_t ( size ) axis[3];                              \
                struct {                                                \
                        bigint_t ( size ) x;                            \
                        bigint_t ( size ) y;                            \
                        bigint_t ( size ) z;                            \
                };                                                      \
                bigint_t ( size * 3 ) all;                              \
        }

/** Indexes for stored multiples of the field prime */
enum weierstrass_multiple {
        WEIERSTRASS_N = 0,
        WEIERSTRASS_2N,
        WEIERSTRASS_4N,
        WEIERSTRASS_NUM_MULTIPLES
};

/** Number of cached in Montgomery form for each Weierstrass curve */
#define WEIERSTRASS_NUM_MONT 3

/** Number of cached big integers for each Weierstrass curve */
#define WEIERSTRASS_NUM_CACHED                                          \
        ( WEIERSTRASS_NUM_MULTIPLES +                                   \
          1 /* fermat */ + 1 /* mont */ +                               \
          WEIERSTRASS_NUM_MONT )

/**
 * A Weierstrass elliptic curve
 *
 * This is an elliptic curve y^2 = x^3 + ax + b
 */
struct weierstrass_curve {
        /** Number of elements in scalar values */
        const unsigned int size;
        /** Curve name */
        const char *name;
        /** Length of raw scalar values */
        size_t len;
        /** Field prime */
        const uint8_t *prime_raw;
        /** Constant "a" */
        const uint8_t *a_raw;
        /** Constant "b" */
        const uint8_t *b_raw;
        /** Base point */
        const uint8_t *base;

        /** Cached field prime "N" (and multiples thereof) */
        bigint_element_t *prime[WEIERSTRASS_NUM_CACHED];
        /** Cached constant "N-2" (for Fermat's little theorem) */
        bigint_element_t *fermat;
        /** Cached Montgomery constant (R^2 mod N) */
        bigint_element_t *square;
        /** Cached constants in Montgomery form */
        union {
                struct {
                        /** Cached constant "1", in Montgomery form */
                        bigint_element_t *one;
                        /** Cached constant "a", in Montgomery form */
                        bigint_element_t *a;
                        /** Cached constant "3b", in Montgomery form */
                        bigint_element_t *b3;
                };
                bigint_element_t *mont[WEIERSTRASS_NUM_MONT];
        };
};

extern int weierstrass_multiply ( struct weierstrass_curve *curve,
                                  const void *base, const void *scalar,
                                  void *result );

/** Define a Weierstrass curve */
#define WEIERSTRASS_CURVE( _name, _curve, _len, _prime, _a, _b, _base ) \
        static bigint_t ( weierstrass_size(_len) )                      \
                _name ## _cache[WEIERSTRASS_NUM_CACHED];                \
        static struct weierstrass_curve _name ## _weierstrass = {       \
                .size = weierstrass_size(_len),                         \
                .name = #_name,                                         \
                .len = (_len),                                          \
                .prime_raw = (_prime),                                  \
                .a_raw = (_a),                                          \
                .b_raw = (_b),                                          \
                .base = (_base),                                        \
                .prime = {                                              \
                        (_name ## _cache)[0].element,                   \
                        (_name ## _cache)[1].element,                   \
                        (_name ## _cache)[2].element,                   \
                },                                                      \
                .fermat = (_name ## _cache)[3].element,                 \
                .square = (_name ## _cache)[4].element,                 \
                .one = (_name ## _cache)[5].element,                    \
                .a = (_name ## _cache)[6].element,                      \
                .b3 = (_name ## _cache)[7].element,                     \
        };                                                              \
        static int _name ## _multiply ( const void *base,               \
                                        const void *scalar,             \
                                        void *result ) {                \
                return weierstrass_multiply ( &_name ## _weierstrass,   \
                                              base, scalar, result );   \
        }                                                               \
        struct elliptic_curve _curve = {                                \
                .name = #_name,                                         \
                .pointsize = ( WEIERSTRASS_AXES * (_len) ),             \
                .keysize = (_len),                                      \
                .multiply = _name ## _multiply,                         \
        }

#endif /* _IPXE_WEIERSTRASS_H */