cosmopolitan/third_party/mbedtls/ecp_internal.h

#ifndef COSMOPOLITAN_THIRD_PARTY_MBEDTLS_ECP_INTERNAL_H_
#define COSMOPOLITAN_THIRD_PARTY_MBEDTLS_ECP_INTERNAL_H_
#include "third_party/mbedtls/config.h"
#include "third_party/mbedtls/ecp.h"

#if defined(MBEDTLS_ECP_INTERNAL_ALT)

/**
 * \brief           Indicate if the Elliptic Curve Point module extension can
 *                  handle the group.
 *
 * \param grp       The pointer to the elliptic curve group that will be the
 *                  basis of the cryptographic computations.
 *
 * \return          Non-zero if successful.
 */
unsigned char mbedtls_internal_ecp_grp_capable( const mbedtls_ecp_group *grp );

/**
 * \brief           Initialise the Elliptic Curve Point module extension.
 *
 *                  If mbedtls_internal_ecp_grp_capable returns true for a
 *                  group, this function has to be able to initialise the
 *                  module for it.
 *
 *                  This module can be a driver to a crypto hardware
 *                  accelerator, for which this could be an initialise function.
 *
 * \param grp       The pointer to the group the module needs to be
 *                  initialised for.
 *
 * \return          0 if successful.
 */
int mbedtls_internal_ecp_init( const mbedtls_ecp_group *grp );

/**
 * \brief           Frees and deallocates the Elliptic Curve Point module
 *                  extension.
 *
 * \param grp       The pointer to the group the module was initialised for.
 */
void mbedtls_internal_ecp_free( const mbedtls_ecp_group *grp );

#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)

#if defined(MBEDTLS_ECP_RANDOMIZE_JAC_ALT)
/**
 * \brief           Randomize jacobian coordinates:
 *                  (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l.
 *
 * \param grp       Pointer to the group representing the curve.
 *
 * \param pt        The point on the curve to be randomised, given with Jacobian
 *                  coordinates.
 *
 * \param f_rng     A function pointer to the random number generator.
 *
 * \param p_rng     A pointer to the random number generator state.
 *
 * \return          0 if successful.
 */
int mbedtls_internal_ecp_randomize_jac( const mbedtls_ecp_group *grp,
        mbedtls_ecp_point *pt, int (*f_rng)(void *, unsigned char *, size_t),
        void *p_rng );
#endif

#if defined(MBEDTLS_ECP_ADD_MIXED_ALT)
/**
 * \brief           Addition: R = P + Q, mixed affine-Jacobian coordinates.
 *
 *                  The coordinates of Q must be normalized (= affine),
 *                  but those of P don't need to. R is not normalized.
 *
 *                  This function is used only as a subrutine of
 *                  ecp_mul_comb().
 *
 *                  Special cases: (1) P or Q is zero, (2) R is zero,
 *                      (3) P == Q.
 *                  None of these cases can happen as intermediate step in
 *                  ecp_mul_comb():
 *                      - at each step, P, Q and R are multiples of the base
 *                      point, the factor being less than its order, so none of
 *                      them is zero;
 *                      - Q is an odd multiple of the base point, P an even
 *                      multiple, due to the choice of precomputed points in the
 *                      modified comb method.
 *                  So branches for these cases do not leak secret information.
 *
 *                  We accept Q->Z being unset (saving memory in tables) as
 *                  meaning 1.
 *
 *                  Cost in field operations if done by [5] 3.22:
 *                      1A := 8M + 3S
 *
 * \param grp       Pointer to the group representing the curve.
 *
 * \param R         Pointer to a point structure to hold the result.
 *
 * \param P         Pointer to the first summand, given with Jacobian
 *                  coordinates
 *
 * \param Q         Pointer to the second summand, given with affine
 *                  coordinates.
 *
 * \return          0 if successful.
 */
int mbedtls_internal_ecp_add_mixed( const mbedtls_ecp_group *grp,
                                    mbedtls_ecp_point *R,
                                    const mbedtls_ecp_point *P,
                                    const mbedtls_ecp_point *Q );
#endif

/**
 * \brief           Point doubling R = 2 P, Jacobian coordinates.
 *
 *                  Cost:   1D := 3M + 4S    (A ==  0)
 *                          4M + 4S          (A == -3)
 *                          3M + 6S + 1a     otherwise
 *                  when the implementation is based on the "dbl-1998-cmo-2"
 *                  doubling formulas in [8] and standard optimizations are
 *                  applied when curve parameter A is one of { 0, -3 }.
 *
 * \param grp       Pointer to the group representing the curve.
 *
 * \param R         Pointer to a point structure to hold the result.
 *
 * \param P         Pointer to the point that has to be doubled, given with
 *                  Jacobian coordinates.
 *
 * \return          0 if successful.
 */
#if defined(MBEDTLS_ECP_DOUBLE_JAC_ALT)
int mbedtls_internal_ecp_double_jac( const mbedtls_ecp_group *grp,
        mbedtls_ecp_point *R, const mbedtls_ecp_point *P );
#endif

/**
 * \brief           Normalize jacobian coordinates of an array of (pointers to)
 *                  points.
 *
 *                  Using Montgomery's trick to perform only one inversion mod P
 *                  the cost is:
 *                      1N(t) := 1I + (6t - 3)M + 1S
 *                  (See for example Algorithm 10.3.4. in [9])
 *
 *                  This function is used only as a subrutine of
 *                  ecp_mul_comb().
 *
 *                  Warning: fails (returning an error) if one of the points is
 *                  zero!
 *                  This should never happen, see choice of w in ecp_mul_comb().
 *
 * \param grp       Pointer to the group representing the curve.
 *
 * \param T         Array of pointers to the points to normalise.
 *
 * \param t_len     Number of elements in the array.
 *
 * \return          0 if successful,
 *                      an error if one of the points is zero.
 */
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_MANY_ALT)
int mbedtls_internal_ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
        mbedtls_ecp_point *T[], size_t t_len );
#endif

/**
 * \brief           Normalize jacobian coordinates so that Z == 0 || Z == 1.
 *
 *                  Cost in field operations if done by [5] 3.2.1:
 *                      1N := 1I + 3M + 1S
 *
 * \param grp       Pointer to the group representing the curve.
 *
 * \param pt        pointer to the point to be normalised. This is an
 *                  input/output parameter.
 *
 * \return          0 if successful.
 */
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
int mbedtls_internal_ecp_normalize_jac( const mbedtls_ecp_group *grp,
                                        mbedtls_ecp_point *pt );
#endif

#endif /* MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */

#if defined(MBEDTLS_ECP_MONTGOMERY_ENABLED)

#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
int mbedtls_internal_ecp_double_add_mxz( const mbedtls_ecp_group *grp,
        mbedtls_ecp_point *R, mbedtls_ecp_point *S, const mbedtls_ecp_point *P,
        const mbedtls_ecp_point *Q, const mbedtls_mpi *d );
#endif

/**
 * \brief           Randomize projective x/z coordinates:
 *                      (X, Z) -> (l X, l Z) for random l
 *
 * \param grp       pointer to the group representing the curve
 *
 * \param P         the point on the curve to be randomised given with
 *                  projective coordinates. This is an input/output parameter.
 *
 * \param f_rng     a function pointer to the random number generator
 *
 * \param p_rng     a pointer to the random number generator state
 *
 * \return          0 if successful
 */
#if defined(MBEDTLS_ECP_RANDOMIZE_MXZ_ALT)
int mbedtls_internal_ecp_randomize_mxz( const mbedtls_ecp_group *grp,
                                        mbedtls_ecp_point *P, 
                                        int (*f_rng)(void *, unsigned char *, size_t),
                                        void *p_rng );
#endif

/**
 * \brief           Normalize Montgomery x/z coordinates: X = X/Z, Z = 1.
 *
 * \param grp       pointer to the group representing the curve
 *
 * \param P         pointer to the point to be normalised. This is an
 *                  input/output parameter.
 *
 * \return          0 if successful
 */
#if defined(MBEDTLS_ECP_NORMALIZE_MXZ_ALT)
int mbedtls_internal_ecp_normalize_mxz( const mbedtls_ecp_group *grp,
                                        mbedtls_ecp_point *P );
#endif

#endif /* MBEDTLS_ECP_MONTGOMERY_ENABLED */

#endif /* MBEDTLS_ECP_INTERNAL_ALT */

void secp256r1( uint64_t[8] );
void secp384r1( uint64_t[12] );

int mbedtls_p256_double_jac( const mbedtls_ecp_group *,
                             const mbedtls_ecp_point *,
                             mbedtls_ecp_point * );
int mbedtls_p256_add_mixed( const mbedtls_ecp_group *,
                            const mbedtls_ecp_point *,
                            const mbedtls_ecp_point *,
                            mbedtls_ecp_point * );
int mbedtls_p256_normalize_jac( const mbedtls_ecp_group *,
                                mbedtls_ecp_point * );
int mbedtls_p256_normalize_jac_many( const mbedtls_ecp_group *,
                                     mbedtls_ecp_point *[], size_t );

int mbedtls_p384_double_jac( const mbedtls_ecp_group *,
                             const mbedtls_ecp_point *,
                             mbedtls_ecp_point * );
int mbedtls_p384_add_mixed( const mbedtls_ecp_group *,
                            const mbedtls_ecp_point *,
                            const mbedtls_ecp_point *,
                            mbedtls_ecp_point * );
int mbedtls_p384_normalize_jac( const mbedtls_ecp_group *,
                                mbedtls_ecp_point * );
int mbedtls_p384_normalize_jac_many( const mbedtls_ecp_group *,
                                     mbedtls_ecp_point *[], size_t );

void mbedtls_p384_mod( uint64_t X[12] );

#endif /* COSMOPOLITAN_THIRD_PARTY_MBEDTLS_ECP_INTERNAL_H_ */