Mbed TLS v2.28.8
Loading...
Searching...
No Matches
mbedtls_ecp_group Struct Reference

The ECP group structure. More...

#include <ecp.h>

Collaboration diagram for mbedtls_ecp_group:

Data Fields

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_pointT
 
size_t T_size
 

Detailed Description

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 (G) for a prime-order subgroup is fixed.

For Short Weierstrass, this subgroup is the whole curve, and its cardinality is denoted by N. Our code requires that 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 A without setting it to the authentic value for curves with A = -3(SECP256R1, etc), in which case you need to load A by yourself when using domain parameters directly, for example:

CHECK_RETURN(mbedtls_ecp_group_load(&grp, grp_id));
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:
int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
Perform a signed subtraction of an MPI and an integer: X = A - b.
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
Make a copy of an MPI.
void mbedtls_mpi_init(mbedtls_mpi *X)
Initialize an MPI context.
void mbedtls_mpi_free(mbedtls_mpi *X)
This function frees the components of an MPI context.
void mbedtls_ecp_group_init(mbedtls_ecp_group *grp)
This function initializes an ECP group context without loading any domain parameters.
int mbedtls_ecp_group_load(mbedtls_ecp_group *grp, mbedtls_ecp_group_id id)
This function sets up an ECP group context from a standardized set of domain parameters.
void mbedtls_ecp_group_free(mbedtls_ecp_group *grp)
This function frees the components of an ECP group.
static int mbedtls_ecp_group_a_is_minus_3(const mbedtls_ecp_group *grp)
This function checks if domain parameter A of the curve is -3.
Definition ecp.h:1024
mbedtls_mpi A
Definition ecp.h:273

For Montgomery curves, we do not store A, but (A + 2) / 4, which is the quantity used in the formulas. Additionally, nbits is not the size of N but the required size for private keys.

If modp is NULL, reduction modulo P is done using a generic algorithm. Otherwise, modp must point to a function that takes an mbedtls_mpi in the range of 0..2^(2*pbits)-1, and transforms it in-place to an integer which is congruent mod P to the given MPI, and is close enough to 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.

Note
Alternative implementations must keep the group IDs distinct. If two group structures have the same ID, then they must be identical.

Definition at line 270 of file ecp.h.

Field Documentation

◆ A

mbedtls_mpi mbedtls_ecp_group::A

For Short Weierstrass: A in the equation. Note that 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.

Definition at line 273 of file ecp.h.

Referenced by mbedtls_ecp_group_a_is_minus_3().

◆ B

mbedtls_mpi mbedtls_ecp_group::B

For Short Weierstrass: B in the equation. For Montgomery curves: unused.

Definition at line 278 of file ecp.h.

◆ G

mbedtls_ecp_point mbedtls_ecp_group::G

The generator of the subgroup used.

Definition at line 280 of file ecp.h.

◆ h

unsigned int mbedtls_ecp_group::h

Definition at line 286 of file ecp.h.

◆ id

mbedtls_ecp_group_id mbedtls_ecp_group::id

An internal group identifier.

Definition at line 271 of file ecp.h.

◆ modp

int(* mbedtls_ecp_group::modp) (mbedtls_mpi *)

The function for fast pseudo-reduction mod P (see above).

Definition at line 287 of file ecp.h.

◆ N

mbedtls_mpi mbedtls_ecp_group::N

The order of G.

Definition at line 281 of file ecp.h.

◆ nbits

size_t mbedtls_ecp_group::nbits

For Short Weierstrass: The number of bits in P. For Montgomery curves: the number of bits in the private keys.

Definition at line 283 of file ecp.h.

◆ P

mbedtls_mpi mbedtls_ecp_group::P

The prime modulus of the base field.

Definition at line 272 of file ecp.h.

◆ pbits

size_t mbedtls_ecp_group::pbits

The number of bits in P.

Definition at line 282 of file ecp.h.

◆ T

mbedtls_ecp_point* mbedtls_ecp_group::T

Pre-computed points for ecp_mul_comb().

Definition at line 292 of file ecp.h.

◆ t_data

void* mbedtls_ecp_group::t_data

Unused.

Definition at line 291 of file ecp.h.

◆ t_post

int(* mbedtls_ecp_group::t_post) (mbedtls_ecp_point *, void *)

Unused.

Definition at line 290 of file ecp.h.

◆ t_pre

int(* mbedtls_ecp_group::t_pre) (mbedtls_ecp_point *, void *)

Unused.

Definition at line 289 of file ecp.h.

◆ T_size

size_t mbedtls_ecp_group::T_size

The number of pre-computed points.

Definition at line 293 of file ecp.h.


The documentation for this struct was generated from the following file: