ecc.h File Reference

 Calculations on elliptic curve secp256r1

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#include <stdint.h>

Go to the source code of this file.

Macros
#define	ecc_is_valid_key(key, order)   (ecc_compare(order, key) == 1)
	Checks if a (random) number is valid as scalar on elliptic curve secp256r1. More...

Functions
int32_t	ecc_compare (const uint32_t *a, const uint32_t *b)
	Compares the value of a with the value of b. More...
void	ecc_ec_mult (uint32_t *resultx, uint32_t *resulty, const uint32_t *px, const uint32_t *py, const uint32_t *secret)
	ECC scalar multiplication on elliptic curve secp256r1. More...

Detailed Description

 Calculations on elliptic curve secp256r1

This is a efficient ECC implementation on the secp256r1 curve for 32 Bit CPU architectures. It provides basic operations on the secp256r1 curve and support for ECDH and ECDSA.

Author

Lars Schmertmann Small.nosp@m.Lars.nosp@m.@t-on.nosp@m.line.nosp@m..de Jens Trillmann jtril.nosp@m.lma@.nosp@m.infor.nosp@m.mati.nosp@m.k.uni.nosp@m.-bre.nosp@m.men.d.nosp@m.e

Definition in file ecc.h.

Macro Definition Documentation

#define ecc_is_valid_key	(		key,
			order
	)		(ecc_compare(order, key) == 1)

Checks if a (random) number is valid as scalar on elliptic curve secp256r1.

A (random) number is only usable as scalar on elliptic curve secp256r1 if it is lower than the order of the curve. For the check, you need to provide the order of elliptic curve secp256r1.

uint32_t order[8] = {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF};

Parameters

key	The (random) number to check for usability
order	The order of elliptic curve secp256r1

Returns

1 if key is valid

Definition at line 68 of file ecc.h.

Function Documentation

int32_t ecc_compare	(	const uint32_t *	a,
		const uint32_t *	b
	)

Compares the value of a with the value of b.

This function is only public because its needed for the macro ecc_is_valid_key. It does a comparison of two 256 bit numbers. The return values are 1, 0 or -1.

Parameters

a	First number
b	Second number

Returns

1 if a is greater than b 0 if a is equal to b -1 if a is less than b

Definition at line 112 of file ecc.c.

void ecc_ec_mult	(	uint32_t *	resultx,
		uint32_t *	resulty,
		const uint32_t *	px,
		const uint32_t *	py,
		const uint32_t *	secret
	)

ECC scalar multiplication on elliptic curve secp256r1.

This function does a scalar multiplication on elliptic curve secp256r1. For an Elliptic curve Diffie–Hellman you need two multiplications. First one with the base point of elliptic curve secp256r1 you need to provide.

uint32_t base_x[8] = {0xd898c296, 0xf4a13945, 0x2deb33a0, 0x77037d81, 0x63a440f2, 0xf8bce6e5, 0xe12c4247, 0x6b17d1f2}; uint32_t base_y[8] = {0x37bf51f5, 0xcbb64068, 0x6b315ece, 0x2bce3357, 0x7c0f9e16, 0x8ee7eb4a, 0xfe1a7f9b, 0x4fe342e2};

Parameters

resultx	Pointer to memory to store the x-coordinate of the result
resulty	Pointer to memory to store the y-coordinate of the result
px	x-coordinate of the point to multiply with scalar
py	y-coordinate of the point to multiply with scalar
secret	Scalar for multiplication with elliptic curve point

Definition at line 124 of file ecc.c.