ox_ec.h | Developers

ox_ec.h

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Elliptic curve cryptography syscalls. More...

Data Structures

struct  cx_curve_weierstrass_s
 Weierstrass curve defined by y^3 = x^2 + a*x + b over GF(p). More...
struct  cx_curve_twisted_edwards_s
 Twisted Edwards curve defined by a*x^2 + y^2 = 1 + d*x2*y2 over GF(q). More...
struct  cx_curve_montgomery_s
 Montgomery curve defined by B*y^2= x^3 + A*x^2 + x over GF(q). More...
struct  cx_curve_domain_s
 Abstract type for elliptic curve domain. More...
struct  cx_ec_point_s
 Elliptic curve point. More...

Macros

#define CX_MAX_DOMAIN_LENGTH   66
 Largest domain parameters length. More...
#define HAVE_SECP256K1_CURVE
 Enables the Koblitz curve Secp256k1. More...
#define HAVE_SECP256R1_CURVE
 Enables the verifiably random curve Secp256r1. More...
#define HAVE_SECP384R1_CURVE
 Enables the verifiably random curve Secp384r1. More...
#define HAVE_SECP521R1_CURVE
 Enables the verifiably random curve Secp521r1. More...
#define HAVE_BRAINPOOL_P256R1_CURVE
 Enables the curve BrainpoolP256r1. More...
#define HAVE_BRAINPOOL_P256T1_CURVE
 Enables the twisted curve BrainpoolP256t1. More...
#define HAVE_BRAINPOOL_P320R1_CURVE
 Enables the curve BrainpoolP320r1. More...
#define HAVE_BRAINPOOL_P320T1_CURVE
 Enables the twisted curve BrainpoolP320t1. More...
#define HAVE_BRAINPOOL_P384R1_CURVE
 Enables the curve BrainpoolP384r1. More...
#define HAVE_BRAINPOOL_P384T1_CURVE
 Enables the twisted curve BrainpoolP384t1. More...
#define HAVE_BRAINPOOL_P512R1_CURVE
 Enables the curve BrainpoolP512r1. More...
#define HAVE_BRAINPOOL_P512T1_CURVE
 Enables the twisted curve BrainpoolP512t1. More...
#define HAVE_ED25519_CURVE
 Enables the twisted Edwards curve Ed25519. More...
#define HAVE_ED448_CURVE
 Enables the twisted Edwards curve Ed448. More...
#define HAVE_CV25519_CURVE
 Enables the Montgomery curve Curve25519. More...
#define HAVE_CV448_CURVE
 Enables the Montgomery curve Curve448. More...
#define HAVE_STARK256_CURVE
 Enables the Stark curve. More...
#define CX_ECCINFO_PARITY_ODD   1
 Indicates the parity of a point coordinate. More...
#define CX_ECCINFO_xGTn   2
#define CX_CURVE_256K1   CX_CURVE_SECP256K1
 Allowed identifier for Secp256k1. More...
#define CX_CURVE_256R1   CX_CURVE_SECP256R1
 Legacy identifier for Secp256r1. More...
#define CX_CURVE_NISTP256   CX_CURVE_SECP256R1
 Legacy identifier for Secp256r1. More...
#define CX_CURVE_NISTP384   CX_CURVE_SECP384R1
 Allowed identifier for Secp384r1. More...
#define CX_CURVE_NISTP521   CX_CURVE_SECP521R1
 Allowed identifier for Secp521r1. More...
#define CX_CURVE_RANGE(i, dom)
 Returns true if the curve identifier is in the specified range. More...
#define CX_CURVE_IS_WEIERSTRASS(c)
 Returns true if the curve is a short Weierstrass curve. More...
#define CX_CURVE_IS_TWISTED_EDWARDS(c)
 Returns true if the curve is a twisted Edwards curve. More...
#define CX_CURVE_IS_MONTGOMERY(c)
 Returns true if the curve is a Montgomery curve. More...
#define CX_CURVE_HEADER
 Curve domain parameters. More...

Typedefs

typedef enum cx_curve_e cx_curve_t
 Convenience type. More...
typedef struct cx_curve_weierstrass_s cx_curve_weierstrass_t
 Convenience type. More...
typedef struct cx_curve_twisted_edwards_s cx_curve_twisted_edwards_t
 Convenience type. More...
typedef struct cx_curve_montgomery_s cx_curve_montgomery_t
 Convenience type. More...
typedef struct cx_curve_domain_s cx_curve_domain_t
 Convenience type. More...
typedef struct cx_ec_point_s cx_ecpoint_t
 Convenience type. More...
typedef enum cx_curve_dom_param_s cx_curve_dom_param_t

Enumerations

enum  cx_curve_e {
  CX_CURVE_NONE, CX_CURVE_WEIERSTRASS_START = 0x20, CX_CURVE_SECP256K1 = 0x21, CX_CURVE_SECP256R1 = 0x22,
  CX_CURVE_SECP384R1 = 0x23, CX_CURVE_SECP521R1 = 0x24, CX_CURVE_BrainPoolP256T1 = 0x31, CX_CURVE_BrainPoolP256R1 = 0x32,
  CX_CURVE_BrainPoolP320T1 = 0x33, CX_CURVE_BrainPoolP320R1 = 0x34, CX_CURVE_BrainPoolP384T1 = 0x35, CX_CURVE_BrainPoolP384R1 = 0x36,
  CX_CURVE_BrainPoolP512T1 = 0x37, CX_CURVE_BrainPoolP512R1 = 0x38, CX_CURVE_BLS12_381_G1 = 0x39, CX_CURVE_FRP256V1 = 0x41,
  CX_CURVE_Stark256 = 0x51, CX_CURVE_WEIERSTRASS_END = 0x6F, CX_CURVE_TWISTED_EDWARDS_START = 0x70, CX_CURVE_Ed25519 = 0x71,
  CX_CURVE_Ed448 = 0x72, CX_CURVE_TWISTED_EDWARDS_END = 0x7F, CX_CURVE_MONTGOMERY_START = 0x80, CX_CURVE_Curve25519 = 0x81,
  CX_CURVE_Curve448 = 0x82, CX_CURVE_MONTGOMERY_END = 0x8F
}
 List of supported elliptic curves. More...
enum  cx_curve_dom_param_s {
  CX_CURVE_PARAM_NONE = 0, CX_CURVE_PARAM_A = 1, CX_CURVE_PARAM_B = 2, CX_CURVE_PARAM_Field = 3,
  CX_CURVE_PARAM_Gx = 4, CX_CURVE_PARAM_Gy = 5, CX_CURVE_PARAM_Order = 6, CX_CURVE_PARAM_Cofactor = 7
}
 Identifiers of the domain parameters. More...

Functions

SYSCALL cx_err_t cx_ecdomain_size (cx_curve_t curve, size_t *length)
 Gets the bit length of each parameter of the curve. More...
SYSCALL cx_err_t cx_ecdomain_parameters_length (cx_curve_t cv, size_t *length)
 Gets the byte length of each parameter of the curve. More...
SYSCALL cx_err_t cx_ecdomain_parameter (cx_curve_t cv, cx_curve_dom_param_t id, uint8_t *p, uint32_t p_len)
 Gets a specific parameter of the curve. More...
SYSCALL cx_err_t cx_ecdomain_parameter_bn (cx_curve_t cv, cx_curve_dom_param_t id, cx_bn_t p)
 Stores a specific parameter of the curve as a BN. More...
SYSCALL cx_err_t cx_ecdomain_generator (cx_curve_t cv, uint8_t *Gx, uint8_t *Gy, size_t len)
 Gets the generator of the curve. More...
SYSCALL cx_err_t cx_ecdomain_generator_bn (cx_curve_t cv, cx_ecpoint_t *P)
 Gets the generator of the curve and stores it in the point structure. More...
SYSCALL cx_err_t cx_ecpoint_alloc (cx_ecpoint_t *P, cx_curve_t cv)
 Allocates memory for a point on the curve. More...
SYSCALL cx_err_t cx_ecpoint_destroy (cx_ecpoint_t *P)
 Destroys a point on the curve. More...
SYSCALL cx_err_t cx_ecpoint_init (cx_ecpoint_t *P, const uint8_t *x, size_t x_len, const uint8_t *y, size_t y_len)
 Initializes a point on the curve. More...
SYSCALL cx_err_t cx_ecpoint_init_bn (cx_ecpoint_t *P, const cx_bn_t x, const cx_bn_t y)
 Initializes a point on the curve with the BN indexes of the coordinates. More...
SYSCALL cx_err_t cx_ecpoint_export (const cx_ecpoint_t *P, uint8_t *x, size_t x_len, uint8_t *y, size_t y_len)
 Exports a point. More...
SYSCALL cx_err_t cx_ecpoint_export_bn (const cx_ecpoint_t *P, cx_bn_t *x, cx_bn_t *y)
 Exports a point using BN indexes of the coordinates. More...
SYSCALL cx_err_t cx_ecpoint_compress (const cx_ecpoint_t *P, uint8_t *xy_compressed, size_t xy_compressed_len, uint32_t *sign)
 Computes the compressed form of a point. More...
SYSCALL cx_err_t cx_ecpoint_decompress (cx_ecpoint_t *P, const uint8_t *xy_compressed, size_t xy_compressed_len, uint32_t sign)
 Computes the affine coordinates of a point given its compressed form. More...
SYSCALL cx_err_t cx_ecpoint_add (cx_ecpoint_t *R, const cx_ecpoint_t *P, const cx_ecpoint_t *Q)
 Adds two points on a curve. More...
SYSCALL cx_err_t cx_ecpoint_neg (cx_ecpoint_t *P)
 Computes the opposite of a point. More...
SYSCALL cx_err_t cx_ecpoint_rnd_scalarmul (cx_ecpoint_t *P, const uint8_t *k, size_t k_len)
 Performs a secure scalar multiplication. More...
SYSCALL cx_err_t cx_ecpoint_rnd_scalarmul_bn (cx_ecpoint_t *P, const cx_bn_t bn_k)
 Performs a secure scalar multiplication given the BN index of the scalar. More...
SYSCALL cx_err_t cx_ecpoint_rnd_fixed_scalarmul (cx_ecpoint_t *P, const uint8_t *k, size_t k_len)
 Performs a secure scalar multiplication with a fixed scalar length. More...
SYSCALL cx_err_t cx_ecpoint_scalarmul (cx_ecpoint_t *P, const uint8_t *k, size_t k_len)
 Performs a scalar multiplication. More...
SYSCALL cx_err_t cx_ecpoint_scalarmul_bn (cx_ecpoint_t *P, const cx_bn_t bn_k)
 Performs a scalar multiplication given the BN index of the scalar. More...
SYSCALL cx_err_t cx_ecpoint_double_scalarmul (cx_ecpoint_t *R, cx_ecpoint_t *P, cx_ecpoint_t *Q, const uint8_t *k, size_t k_len, const uint8_t *r, size_t r_len)
 Performs a double scalar multiplication. More...
SYSCALL cx_err_t cx_ecpoint_double_scalarmul_bn (cx_ecpoint_t *R, cx_ecpoint_t *P, cx_ecpoint_t *Q, const cx_bn_t bn_k, const cx_bn_t bn_r)
 Performs a double scalar multiplication given the BN indexes of the scalars. More...
SYSCALL cx_err_t cx_ecpoint_cmp (const cx_ecpoint_t *P, const cx_ecpoint_t *Q, bool *is_equal)
 Compares two points on the same curve. More...
SYSCALL cx_err_t cx_ecpoint_is_on_curve (const cx_ecpoint_t *R, bool *is_on_curve)
 Checks whether a given point is on the curve. More...
SYSCALL cx_err_t cx_ecpoint_is_at_infinity (const cx_ecpoint_t *R, bool *is_at_infinity)
 Checks whether a given point is the point at infinity. More...

Detailed Description

Elliptic curve cryptography syscalls.

This file contains elliptic curves definitions and functions.

Macro Definition Documentation

CX_CURVE_256K1

#define CX_CURVE_256K1   CX_CURVE_SECP256K1

Allowed identifier for Secp256k1.

CX_CURVE_256R1

#define CX_CURVE_256R1   CX_CURVE_SECP256R1

Legacy identifier for Secp256r1.

CX_CURVE_HEADER

#define CX_CURVE_HEADER
Value:
cx_curve_t curve; \
unsigned int bit_size; \
unsigned int length; \
const uint8_t *a; \
const uint8_t *b; \
const uint8_t *p; \
const uint8_t *Gx; \
const uint8_t *Gy; \
const uint8_t *n; \
const uint8_t *h; \
const uint8_t *Hn; \
const uint8_t *Hp; \
enum cx_curve_e cx_curve_t
Convenience type.
Definition: ox_ec.h:241

Curve domain parameters.

The parameters are common to cx_curve_weierstrass_s, cx_curve_twisted_edwards_s, and cx_curve_montgomery_s.

  • curve: Curve identifier. See cx_curve_e
  • bit_size: Curve size in bits
  • length: Component lenth in bytes
  • a: a coefficient of the curve equation
  • b: b (Weierstrass or Montgomery) or d (twisted Edwards) coefficient of the curve equation
  • p: Prime specifying the base field
  • Gx: x-coordinate of the base point
  • Gy: y-coordinate of the base point
  • n: Curve order: order of the group generated by G
  • h: Cofactor i.e. h = |E(GF(p))|/n
  • Hn: Second Montgomery constant for the curve order
  • Hp: Second Montgomery constant for the field characteristic p

CX_CURVE_IS_MONTGOMERY

#define CX_CURVE_IS_MONTGOMERY (   c)

Returns true if the curve is a Montgomery curve.

CX_CURVE_IS_TWISTED_EDWARDS

#define CX_CURVE_IS_TWISTED_EDWARDS (   c)

Returns true if the curve is a twisted Edwards curve.

CX_CURVE_IS_WEIERSTRASS

#define CX_CURVE_IS_WEIERSTRASS (   c)

Returns true if the curve is a short Weierstrass curve.

CX_CURVE_NISTP256

#define CX_CURVE_NISTP256   CX_CURVE_SECP256R1

Legacy identifier for Secp256r1.

CX_CURVE_NISTP384

#define CX_CURVE_NISTP384   CX_CURVE_SECP384R1

Allowed identifier for Secp384r1.

CX_CURVE_NISTP521

#define CX_CURVE_NISTP521   CX_CURVE_SECP521R1

Allowed identifier for Secp521r1.

CX_CURVE_RANGE

#define CX_CURVE_RANGE (   i,
  dom 
)

Returns true if the curve identifier is in the specified range.

CX_ECCINFO_PARITY_ODD

#define CX_ECCINFO_PARITY_ODD   1

Indicates the parity of a point coordinate.

CX_ECCINFO_xGTn

#define CX_ECCINFO_xGTn   2

CX_MAX_DOMAIN_LENGTH

#define CX_MAX_DOMAIN_LENGTH   66

Largest domain parameters length.

HAVE_BRAINPOOL_P256R1_CURVE

#define HAVE_BRAINPOOL_P256R1_CURVE

Enables the curve BrainpoolP256r1.

HAVE_BRAINPOOL_P256T1_CURVE

#define HAVE_BRAINPOOL_P256T1_CURVE

Enables the twisted curve BrainpoolP256t1.

HAVE_BRAINPOOL_P320R1_CURVE

#define HAVE_BRAINPOOL_P320R1_CURVE

Enables the curve BrainpoolP320r1.

HAVE_BRAINPOOL_P320T1_CURVE

#define HAVE_BRAINPOOL_P320T1_CURVE

Enables the twisted curve BrainpoolP320t1.

HAVE_BRAINPOOL_P384R1_CURVE

#define HAVE_BRAINPOOL_P384R1_CURVE

Enables the curve BrainpoolP384r1.

HAVE_BRAINPOOL_P384T1_CURVE

#define HAVE_BRAINPOOL_P384T1_CURVE

Enables the twisted curve BrainpoolP384t1.

HAVE_BRAINPOOL_P512R1_CURVE

#define HAVE_BRAINPOOL_P512R1_CURVE

Enables the curve BrainpoolP512r1.

HAVE_BRAINPOOL_P512T1_CURVE

#define HAVE_BRAINPOOL_P512T1_CURVE

Enables the twisted curve BrainpoolP512t1.

HAVE_CV25519_CURVE

#define HAVE_CV25519_CURVE

Enables the Montgomery curve Curve25519.

HAVE_CV448_CURVE

#define HAVE_CV448_CURVE

Enables the Montgomery curve Curve448.

HAVE_ED25519_CURVE

#define HAVE_ED25519_CURVE

Enables the twisted Edwards curve Ed25519.

HAVE_ED448_CURVE

#define HAVE_ED448_CURVE

Enables the twisted Edwards curve Ed448.

HAVE_SECP256K1_CURVE

#define HAVE_SECP256K1_CURVE

Enables the Koblitz curve Secp256k1.

HAVE_SECP256R1_CURVE

#define HAVE_SECP256R1_CURVE

Enables the verifiably random curve Secp256r1.

HAVE_SECP384R1_CURVE

#define HAVE_SECP384R1_CURVE

Enables the verifiably random curve Secp384r1.

HAVE_SECP521R1_CURVE

#define HAVE_SECP521R1_CURVE

Enables the verifiably random curve Secp521r1.

HAVE_STARK256_CURVE

#define HAVE_STARK256_CURVE

Enables the Stark curve.

Typedef Documentation

cx_curve_dom_param_t

cx_curve_domain_t

Convenience type.

See cx_curve_domain_s.

cx_curve_montgomery_t

Convenience type.

See cx_curve_montgomery_s.

cx_curve_t

typedef enum cx_curve_e cx_curve_t

Convenience type.

See cx_curve_e.

cx_curve_twisted_edwards_t

cx_curve_weierstrass_t

cx_ecpoint_t

typedef struct cx_ec_point_s cx_ecpoint_t

Convenience type.

See cx_ec_point_s.

Enumeration Type Documentation

cx_curve_dom_param_s

Identifiers of the domain parameters.

Enumerator
CX_CURVE_PARAM_NONE 

No parameter.

CX_CURVE_PARAM_A 

First coefficient of the curve.

CX_CURVE_PARAM_B 

Second coefficient of the curve.

CX_CURVE_PARAM_Field 

Curve field.

CX_CURVE_PARAM_Gx 

x-coordinate of the curve's generator

CX_CURVE_PARAM_Gy 

y-coordinate of the curve's generator

CX_CURVE_PARAM_Order 

Order of the generator.

CX_CURVE_PARAM_Cofactor 

Cofactor.

cx_curve_e

enum cx_curve_e

List of supported elliptic curves.

Enumerator
CX_CURVE_NONE 

Undefined curve.

CX_CURVE_WEIERSTRASS_START 

Low limit (not included) of Weierstrass curve ID.

CX_CURVE_SECP256K1 

Secp256k1.

CX_CURVE_SECP256R1 

Secp256r1.

CX_CURVE_SECP384R1 

Secp384r1.

CX_CURVE_SECP521R1 

Secp521r1.

CX_CURVE_BrainPoolP256T1 

BrainpoolP256t1.

CX_CURVE_BrainPoolP256R1 

BrainpoolP256r1.

CX_CURVE_BrainPoolP320T1 

BrainpoolP320t1.

CX_CURVE_BrainPoolP320R1 

BrainpoolP320r1.

CX_CURVE_BrainPoolP384T1 

BrainpoolP384t1.

CX_CURVE_BrainPoolP384R1 

Brainpool384r1.

CX_CURVE_BrainPoolP512T1 

BrainpoolP512t1.

CX_CURVE_BrainPoolP512R1 

BrainpoolP512r1.

CX_CURVE_BLS12_381_G1 

BLS12-381 G1.

CX_CURVE_FRP256V1 

ANSSI FRP256.

CX_CURVE_Stark256 

Stark.

CX_CURVE_WEIERSTRASS_END 

High limit (not included) of Weierstrass curve ID.

CX_CURVE_TWISTED_EDWARDS_START 

Low limit (not included) of Twisted Edwards curve ID.

CX_CURVE_Ed25519 

Ed25519.

CX_CURVE_Ed448 

Ed448.

CX_CURVE_TWISTED_EDWARDS_END 

High limit (not included) of Twisted Edwards curve ID.

CX_CURVE_MONTGOMERY_START 

Low limit (not included) of Montgomery curve ID.

CX_CURVE_Curve25519 

Curve25519.

CX_CURVE_Curve448 

Curve448.

CX_CURVE_MONTGOMERY_END 

High limit (not included) of Montgomery curve ID.

Function Documentation

cx_ecdomain_generator()

SYSCALL cx_err_t cx_ecdomain_generator ( cx_curve_t  cv,
uint8_t *  Gx,
uint8_t *  Gy,
size_t  len 
)

Gets the generator of the curve.

Parameters
[in]cvCurve identifier.
[out]GxBuffer to store the x-coordinate of the generator.
[out]GyBuffer to store the y-coordinate of the generator.
[in]lenByte length of each coordinate.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE
  • CX_INVALID_PARAMETER

cx_ecdomain_generator_bn()

SYSCALL cx_err_t cx_ecdomain_generator_bn ( cx_curve_t  cv,
cx_ecpoint_t P 
)

Gets the generator of the curve and stores it in the point structure.

Parameters
[in]cvCurve identifier.
[out]PPointer to the structure where to store the generator.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_INVALID_PARAMETER_SIZE
  • CX_EC_INVALID_POINT

cx_ecdomain_parameter()

SYSCALL cx_err_t cx_ecdomain_parameter ( cx_curve_t  cv,
cx_curve_dom_param_t  id,
uint8_t *  p,
uint32_t  p_len 
)

Gets a specific parameter of the curve.

Parameters
[in]cvCurve identifier.
[in]idParameter identifier.
[out]pBuffer where to store the parameter.
[in]p_lenLength of the buffer.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE
  • CX_INVALID_PARAMETER

cx_ecdomain_parameter_bn()

SYSCALL cx_err_t cx_ecdomain_parameter_bn ( cx_curve_t  cv,
cx_curve_dom_param_t  id,
cx_bn_t  p 
)

Stores a specific parameter of the curve as a BN.

Parameters
[in]cvCurve identifier.
[in]idParameter identifier.
[out]pBN where to store the parameter.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_INVALID_PARAMETER_SIZE

cx_ecdomain_parameters_length()

SYSCALL cx_err_t cx_ecdomain_parameters_length ( cx_curve_t  cv,
size_t *  length 
)

Gets the byte length of each parameter of the curve.

Parameters
[in]cvCurve identifier.
[out]lengthByte length of each parameter.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE

cx_ecdomain_size()

SYSCALL cx_err_t cx_ecdomain_size ( cx_curve_t  curve,
size_t *  length 
)

Gets the bit length of each parameter of the curve.

Parameters
[in]curveCurve identifier.
[out]lengthBit length of each parameter.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE

cx_ecpoint_add()

SYSCALL cx_err_t cx_ecpoint_add ( cx_ecpoint_t R,
const cx_ecpoint_t P,
const cx_ecpoint_t Q 
)

Adds two points on a curve.

Each point should not be the point at infinity. If one of the point is the point at infinity then the function returns a CX_EC_INFINITE_POINT error.

Parameters
[out]RPointer to the result point.
[in]PPointer to the first point to add. The point must be on the curve.
[in]QPointer to the second point to add. The point must be on the curve.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INVALID_POINT
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_alloc()

SYSCALL cx_err_t cx_ecpoint_alloc ( cx_ecpoint_t P,
cx_curve_t  cv 
)

Allocates memory for a point on the curve.

Parameters
[in]PPointer to a point.
[in]cvCurve on which the point is defined.
Returns
Error code:
  • CX_OK on success
  • CX_EC_INVALID_CURVE
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_MEMORY_FULL

cx_ecpoint_cmp()

SYSCALL cx_err_t cx_ecpoint_cmp ( const cx_ecpoint_t P,
const cx_ecpoint_t Q,
bool *  is_equal 
)

Compares two points on the same curve.

Parameters
[in]PFirst point to compare.
[in]QSecond point to compare.
[out]is_equalBoolean which indicates whether the two points are equal or not:
  • 1 if the points are equal
  • 0 otherwise
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_compress()

SYSCALL cx_err_t cx_ecpoint_compress ( const cx_ecpoint_t P,
uint8_t *  xy_compressed,
size_t  xy_compressed_len,
uint32_t *  sign 
)

Computes the compressed form of a point.

The compressed form depends on the curve type. For a Weierstrass or a Montgomery curve, the compressed form consists of the x-coordinate and a prefix. For a Twisted Edwards curve the compressed form consists of a y-coordinate and a prefix.

Parameters
[in]PPointer to the point to be compressed.
[out]xy_compressedBuffer to hold the compressed coordinate.
[in]xy_compressed_lenLength of the compressed coordinate in bytes. This should be equal to the length of one coordinate.
[out]signPointer to the sign of the hidden coordinate: correspond to the least significant bit of the y-coordinate for a Weierstrass or Montgomery curve and of the x-coordinate for a Twisted Edwards curve.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_decompress()

SYSCALL cx_err_t cx_ecpoint_decompress ( cx_ecpoint_t P,
const uint8_t *  xy_compressed,
size_t  xy_compressed_len,
uint32_t  sign 
)

Computes the affine coordinates of a point given its compressed form.

Parameters
[out]PPointer to the point.
[in]xy_compressedPointer to the buffer holding the compressed coordinate.
[in]xy_compressed_lenLength of the compressed coordinate in bytes. This should be equal to the length of one coordinate.
[in]signSign of the coordinate to recover.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_MEMORY_FULL
  • CX_NO_RESIDUE

cx_ecpoint_destroy()

SYSCALL cx_err_t cx_ecpoint_destroy ( cx_ecpoint_t P)

Destroys a point on the curve.

Parameters
[in]PPointer to the point to destroy. If the pointer is NULL, nothing is done.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_INTERNAL_ERROR

cx_ecpoint_double_scalarmul()

SYSCALL cx_err_t cx_ecpoint_double_scalarmul ( cx_ecpoint_t R,
cx_ecpoint_t P,
cx_ecpoint_t Q,
const uint8_t *  k,
size_t  k_len,
const uint8_t *  r,
size_t  r_len 
)

Performs a double scalar multiplication.

This implements the Straus-Shamir algorithm for computing R = [k]P + [r]Q. This should be used only for non-secret computations.

Parameters
[out]RPointer to the result.
[in]PPointer to the first point.
[in]QPointer to the second point.
[in]kPointer to the first scalar.
[in]k_lenLength of the first scalar.
[in]rPointer to the second scalar.
[in]r_lenLength of the second scalar.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_MEMORY_FULL
  • CX_EC_INFINITE_POINT

cx_ecpoint_double_scalarmul_bn()

SYSCALL cx_err_t cx_ecpoint_double_scalarmul_bn ( cx_ecpoint_t R,
cx_ecpoint_t P,
cx_ecpoint_t Q,
const cx_bn_t  bn_k,
const cx_bn_t  bn_r 
)

Performs a double scalar multiplication given the BN indexes of the scalars.

This implements the Straus-Shamir algorithm for computing R = [k]P + [r]Q. This should be used only for non-secret computations.

Parameters
[out]RPointer to the result.
[in]PPointer to the first point.
[in]QPointer to the second point.
[in]bn_kBN index of the first scalar.
[in]bn_rBN index of the second scalar.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_MEMORY_FULL
  • CX_EC_INFINITE_POINT

cx_ecpoint_export()

SYSCALL cx_err_t cx_ecpoint_export ( const cx_ecpoint_t P,
uint8_t *  x,
size_t  x_len,
uint8_t *  y,
size_t  y_len 
)

Exports a point.

Fills two distinct buffers with the x-coordinate and the y-coordinate of the point. If the point is not in affine representation, it will be normalized first.

Parameters
[in]PPointer to the point to export.
[out]xBuffer for the x-coordinate.
[in]x_lenLength of the x buffer.
[out]yBuffer for the y-coordinate.
[in]y_lenLength of the y buffer.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_export_bn()

SYSCALL cx_err_t cx_ecpoint_export_bn ( const cx_ecpoint_t P,
cx_bn_t x,
cx_bn_t y 
)

Exports a point using BN indexes of the coordinates.

Parameters
[in]PPointer to the point to export.
[out]xPointer to the BN index of the x-coordinate.
[out]yPointer to the BN index of the y-coordinate.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_init()

SYSCALL cx_err_t cx_ecpoint_init ( cx_ecpoint_t P,
const uint8_t *  x,
size_t  x_len,
const uint8_t *  y,
size_t  y_len 
)

Initializes a point on the curve.

Parameters
[in]PPointer to the point to initialize.
[in]xx-coordinate of the point. This must belong to the curve field.
[in]x_lenLength of the x-coordinate. This must be at most equal to the curve's domain number of bytes.
[in]yy-coordinate of the point. This must belong to the curve field.
[in]y_lenLength of the y-coordinate. This must be at most equal to the curve's domain number of bytes.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE

cx_ecpoint_init_bn()

SYSCALL cx_err_t cx_ecpoint_init_bn ( cx_ecpoint_t P,
const cx_bn_t  x,
const cx_bn_t  y 
)

Initializes a point on the curve with the BN indexes of the coordinates.

Parameters
[in]PPointer to the point to initialize.
[in]xBN index of the x-coordinate. The coordinate must belong to the base field.
[in]yBN index of the y-coordinate. The coordinate must belong to the base field.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE

cx_ecpoint_is_at_infinity()

SYSCALL cx_err_t cx_ecpoint_is_at_infinity ( const cx_ecpoint_t R,
bool *  is_at_infinity 
)

Checks whether a given point is the point at infinity.

The point at infinity has a z-coordinate equal to 0.

Parameters
[in]RPointer to the point to check.
[out]is_at_infinityBoolean which indicates whether the point is at infinity or not:
  • 1 if the point is at infinity
  • 0 otherwise
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE

cx_ecpoint_is_on_curve()

SYSCALL cx_err_t cx_ecpoint_is_on_curve ( const cx_ecpoint_t R,
bool *  is_on_curve 
)

Checks whether a given point is on the curve.

Parameters
[in]RPointer to the point to check.
[out]is_on_curveBoolean which indicates whether the point is on the curve or not:
  • 1 if the point is on the curve
  • 0 otherwise
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_neg()

SYSCALL cx_err_t cx_ecpoint_neg ( cx_ecpoint_t P)

Computes the opposite of a point.

The point should not be the point at infinity, otherwise the function returns a CX_EC_INFINITE_POINT error.

Parameters
[in,out]PPointer to a point of the curve. This will hold the result.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_CURVE
  • CX_EC_INVALID_POINT
  • CX_MEMORY_FULL
  • CX_EC_INFINITE_POINT

cx_ecpoint_rnd_fixed_scalarmul()

SYSCALL cx_err_t cx_ecpoint_rnd_fixed_scalarmul ( cx_ecpoint_t P,
const uint8_t *  k,
size_t  k_len 
)

Performs a secure scalar multiplication with a fixed scalar length.

Parameters
[in,out]PPointer to a point on a curve. This will hold the result.
[in]kPointer to the scalar. The scalar is an integer at least equal to 0 and at most equal to the order of the curve minus 1.
[in]k_lenLength of the scalar. This should be equal to the domain length.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_rnd_scalarmul()

SYSCALL cx_err_t cx_ecpoint_rnd_scalarmul ( cx_ecpoint_t P,
const uint8_t *  k,
size_t  k_len 
)

Performs a secure scalar multiplication.

Parameters
[in,out]PPointer to a point on a curve. This will hold the result.
[in]kPointer to the scalar. The scalar is an integer at least equal to 0 and at most equal to the order of the curve minus 1.
[in]k_lenLength of the scalar. This should be equal to the domain length.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_rnd_scalarmul_bn()

SYSCALL cx_err_t cx_ecpoint_rnd_scalarmul_bn ( cx_ecpoint_t P,
const cx_bn_t  bn_k 
)

Performs a secure scalar multiplication given the BN index of the scalar.

Parameters
[in,out]PPointer to a point on a curve. This will hold the result.
[in]bn_kBN index of the scalar. The scalar is an integer at least equal to 0 and at most equal to the order of the curve minus 1.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_scalarmul()

SYSCALL cx_err_t cx_ecpoint_scalarmul ( cx_ecpoint_t P,
const uint8_t *  k,
size_t  k_len 
)

Performs a scalar multiplication.

Warning
This should be called only for non critical purposes. It is recommended to use cx_ecpoint_rnd_scalarmul or cx_ecpoint_rnd_fixed_scalarmul rather than this function.
Parameters
[in,out]PPointer to a point on a curve. This will hold the result.
[in]kPointer to the scalar. The scalar is an integer at least equal to 0 and at most equal to the order of the curve minus 1.
[in]k_lenLength of the scalar.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

cx_ecpoint_scalarmul_bn()

SYSCALL cx_err_t cx_ecpoint_scalarmul_bn ( cx_ecpoint_t P,
const cx_bn_t  bn_k 
)

Performs a scalar multiplication given the BN index of the scalar.

Warning
This should be called only for non critical purposes. It is recommended to use cx_ecpoint_rnd_scalarmul_bn rather than this function.
Parameters
[in,out]PPointer to a point on a curve. This will hold the result.
[in]bn_kBN index of the scalar. The scalar is an integer at least equal to 0 and at most equal to the order of the curve minus 1.
Returns
Error code:
  • CX_OK on success
  • CX_NOT_LOCKED
  • CX_INVALID_PARAMETER
  • CX_EC_INVALID_POINT
  • CX_EC_INVALID_CURVE
  • CX_EC_INFINITE_POINT
  • CX_MEMORY_FULL

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