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mbedtls_ecp_group struct
The ECP group structure. We consider two types of curve equations: Short Weierstrass: y^2 = x^3 + A x + B mod P (SEC1 + RFC-4492) Montgomery: y^2 = x^3 + A x^2 + x mod P (Curve25519, Curve448) In both cases, the generator (\p G) for a prime-order subgroup is fixed. For Short Weierstrass, this subgroup is the whole curve, and its cardinality is denoted by \p N. Our code requires that \p N is an odd prime as mbedtls_ecp_mul() requires an odd number, and mbedtls_ecdsa_sign() requires that it is prime for blinding purposes. The default implementation only initializes \p A without setting it to the authentic value for curves with A = -3(SECP256R1, etc), in which case you need to load \p A by yourself when using domain parameters directly, for example: \code mbedtls_mpi_init(&A); mbedtls_ecp_group_init(&grp); CHECK_RETURN(mbedtls_ecp_group_load(&grp, grp_id)); if (mbedtls_ecp_group_a_is_minus_3(&grp)) { CHECK_RETURN(mbedtls_mpi_sub_int(&A, &grp.P, 3)); } else { CHECK_RETURN(mbedtls_mpi_copy(&A, &grp.A)); } do_something_with_a(&A); cleanup: mbedtls_mpi_free(&A); mbedtls_ecp_group_free(&grp); \endcode For Montgomery curves, we do not store \p A, but (A + 2) / 4, which is the quantity used in the formulas. Additionally, \p nbits is not the size of \p N but the required size for private keys. If \p modp is NULL, reduction modulo \p P is done using a generic algorithm. Otherwise, \p modp must point to a function that takes an \p mbedtls_mpi in the range of 0..2^(2*pbits)-1, and transforms it in-place to an integer which is congruent mod \p P to the given MPI, and is close enough to \p pbits in size, so that it may be efficiently brought in the 0..P-1 range by a few additions or subtractions. Therefore, it is only an approximative modular reduction. It must return 0 on success and non-zero on failure.
Syntax
typedef struct mbedtls_ecp_group
{
mbedtls_ecp_group_id id;
mbedtls_mpi P;
mbedtls_mpi A;
mbedtls_mpi B;
mbedtls_ecp_point G;
mbedtls_mpi N;
size_t pbits;
size_t nbits;
unsigned int h;
int (*modp)(mbedtls_mpi *);
int (*t_pre)(mbedtls_ecp_point *, void *);
int (*t_post)(mbedtls_ecp_point *, void *);
void *t_data;
mbedtls_ecp_point *T;
size_t T_size;
}
mbedtls_ecp_group;
Fields
Field
Declared as
Description
For Short Weierstrass: \p A in the equation. Note that \p A is not set to the authentic value in some cases. Refer to detailed description of ::mbedtls_ecp_group if using domain parameters in the structure. For Montgomery curves: (A + 2) / 4.
For Short Weierstrass: \p B in the equation. For Montgomery curves: unused.
size_t
For Short Weierstrass: The number of bits in \p P. For Montgomery curves: the number of bits in the private keys.
The function for fast pseudo-reduction mod \p P (see above).
Related Functions
Found 58 other functions taking a mbedtls_ecp_group
argument:
Function
Description
This function sets up an ECP group context from a standardized set of domain parameters.
This function frees the components of an ECP group.
This function performs multiplication of a point by an integer: \p R = \p m * \p P in a restartable way. \see mbedtls_ecp_mul()
This function checks that a point is a valid public key on this curve. It only checks that the point is non-zero, has valid coordinates and lies on the curve. It does not verify that it is indeed a multiple of \c G. This additional check is computationally more expensive, is not required by standards, and should not be necessary if the group used has a small cofactor. In particular, it is useless for the NIST groups which all have a cofactor of 1.
This function initializes an ECP group context without loading any domain parameters.
This function generates a private key.
This function performs a scalar multiplication of a point by an integer: \p R = \p m * \p P. It is not thread-safe to use same group in multiple threads.
This function checks that an \c mbedtls_mpi is a valid private key for this curve.
This function imports a point from unsigned binary data.
This function imports a point from a TLS ECPoint record.
This function exports a point as a TLS ECPoint record defined in RFC 4492, Section 5.4.
This function copies the contents of group \p src into group \p dst.
This function generates an ECP keypair.
This function performs multiplication and addition of two points by integers: \p R = \p m * \p P + \p n * \p Q in a restartable way. \see \c mbedtls_ecp_muladd()
This function generates an ECDH keypair on an elliptic curve. This function performs the first of two core computations implemented during the ECDH key exchange. The second core computation is performed by mbedtls_ecdh_compute_shared(). \see ecp.h
This function exports a point into unsigned binary data.
This function exports an elliptic curve as a TLS ECParameters record as defined in RFC 4492, Section 5.4.
This function generates a keypair with a configurable base point.
This function computes the shared secret. This function performs the second of two core computations implemented during the ECDH key exchange. The first core computation is performed by mbedtls_ecdh_gen_public(). \see ecp.h
This function sets up an ECP group context from a TLS ECParameters record as defined in RFC 4492, Section 5.4.
This function performs multiplication and addition of two points by integers: \p R = \p m * \p P + \p n * \p Q It is not thread-safe to use same group in multiple threads.
This function computes the ECDSA signature of a previously-hashed message. \see ecp.h
This function verifies the ECDSA signature of a previously-hashed message. \see ecp.h
This function checks if domain parameter A of the curve is \c -3.