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Dependencies:   esp8266-driver

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ecp_internal.h File Reference
Functions

ecp_internal.h File Reference

Function declarations for alternative implementation of elliptic curve point arithmetic. More...

Go to the source code of this file.

Functions

unsigned char mbedtls_internal_ecp_grp_capable (const mbedtls_ecp_group *grp)
 Indicate if the Elliptic Curve Point module extension can handle the group.
int mbedtls_internal_ecp_init (const mbedtls_ecp_group *grp)
 Initialise the Elliptic Curve Point module extension.
void mbedtls_internal_ecp_free (const mbedtls_ecp_group *grp)
 Frees and deallocates the Elliptic Curve Point module extension.
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)
 Randomize jacobian coordinates: (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l.
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)
 Addition: R = P + Q, mixed affine-Jacobian coordinates.
int mbedtls_internal_ecp_double_jac (const mbedtls_ecp_group *grp, mbedtls_ecp_point *R, const mbedtls_ecp_point *P)
 Point doubling R = 2 P, Jacobian coordinates.
int mbedtls_internal_ecp_normalize_jac_many (const mbedtls_ecp_group *grp, mbedtls_ecp_point *T[], size_t t_len)
 Normalize jacobian coordinates of an array of (pointers to) points.
int mbedtls_internal_ecp_normalize_jac (const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt)
 Normalize jacobian coordinates so that Z == 0 || Z == 1.
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)
 Randomize projective x/z coordinates: (X, Z) -> (l X, l Z) for random l.
int mbedtls_internal_ecp_normalize_mxz (const mbedtls_ecp_group *grp, mbedtls_ecp_point *P)
 Normalize Montgomery x/z coordinates: X = X/Z, Z = 1.

Detailed Description

Function declarations for alternative implementation of elliptic curve point arithmetic.

Definition in file ecp_internal.h.

Function Documentation

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 
)

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

Parameters:
grpPointer to the group representing the curve.
RPointer to a point structure to hold the result.
PPointer to the first summand, given with Jacobian coordinates
QPointer to the second summand, given with affine coordinates.
Returns:
0 if successful.
int mbedtls_internal_ecp_double_jac ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  R,
const mbedtls_ecp_point *  P 
)

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 }.

Parameters:
grpPointer to the group representing the curve.
RPointer to a point structure to hold the result.
PPointer to the point that has to be doubled, given with Jacobian coordinates.
Returns:
0 if successful.
void mbedtls_internal_ecp_free ( const mbedtls_ecp_group *  grp )

Frees and deallocates the Elliptic Curve Point module extension.

Parameters:
grpThe pointer to the group the module was initialised for.
unsigned char mbedtls_internal_ecp_grp_capable ( const mbedtls_ecp_group *  grp )

Indicate if the Elliptic Curve Point module extension can handle the group.

Parameters:
grpThe pointer to the elliptic curve group that will be the basis of the cryptographic computations.
Returns:
Non-zero if successful.
int mbedtls_internal_ecp_init ( const mbedtls_ecp_group *  grp )

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.

Parameters:
grpThe pointer to the group the module needs to be initialised for.
Returns:
0 if successful.
int mbedtls_internal_ecp_normalize_jac ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  pt 
)

Normalize jacobian coordinates so that Z == 0 || Z == 1.

Cost in field operations if done by [5] 3.2.1: 1N := 1I + 3M + 1S

Parameters:
grpPointer to the group representing the curve.
ptpointer to the point to be normalised. This is an input/output parameter.
Returns:
0 if successful.
int mbedtls_internal_ecp_normalize_jac_many ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  T[],
size_t  t_len 
)

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().

Parameters:
grpPointer to the group representing the curve.
TArray of pointers to the points to normalise.
t_lenNumber of elements in the array.
Returns:
0 if successful, an error if one of the points is zero.
int mbedtls_internal_ecp_normalize_mxz ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  P 
)

Normalize Montgomery x/z coordinates: X = X/Z, Z = 1.

Parameters:
grppointer to the group representing the curve
Ppointer to the point to be normalised. This is an input/output parameter.
Returns:
0 if successful
int mbedtls_internal_ecp_randomize_jac ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  pt,
int(*)(void *, unsigned char *, size_t)  f_rng,
void *  p_rng 
)

Randomize jacobian coordinates: (X, Y, Z) -> (l^2 X, l^3 Y, l Z) for random l.

Parameters:
grpPointer to the group representing the curve.
ptThe point on the curve to be randomised, given with Jacobian coordinates.
f_rngA function pointer to the random number generator.
p_rngA pointer to the random number generator state.
Returns:
0 if successful.
int mbedtls_internal_ecp_randomize_mxz ( const mbedtls_ecp_group *  grp,
mbedtls_ecp_point *  P,
int(*)(void *, unsigned char *, size_t)  f_rng,
void *  p_rng 
)

Randomize projective x/z coordinates: (X, Z) -> (l X, l Z) for random l.

Parameters:
grppointer to the group representing the curve
Pthe point on the curve to be randomised given with projective coordinates. This is an input/output parameter.
f_rnga function pointer to the random number generator
p_rnga pointer to the random number generator state
Returns:
0 if successful
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