/*

 a tiny-ecdh implementation for the ez80 CPU

## CURVE SPEC ##
using curve secp224k1
define curve T = (p, a, b, G, n, h), where
finite field Fp is defined by:
	p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFE56D
	f(x) = 2^224 − 2^32 − 2^12 − 2^11 − 2^9 − 2^7 − 2^4 − 2 − 1
curve E: y^2 = x^3 + ax + b over Fp is defined by:
	a = 00000000 00000000 00000000 00000000 00000000 00000000 00000000
	b = 00000000 00000000 00000000 00000000 00000000 00000000 00000005
	G(x) = A1455B33 4DF099DF 30FC28A1 69A467E9 E47075A9 0F7E650E B6B7A45C
	G(y) = 7E089FED 7FBA3442 82CAFBD6 F7E319F7 C0B0BD59 E2CA4BDB 556D61A5
	n = 00000000 00000000 00000000 0001DCE8 D2EC6184 CAF0A971 769FB1F7
	h = 01

## KEYGEN ## generate key pair (d, Q)
d is secret. Assert d in range [1, n-1] (random).
Q = d*G
output (d, Q)

## PUBKEY VALID ##
assert Q != infinity point
assert xQ, yQ are of degree <= m-1
assert nQ = infinity point
if h = 1, skip final assertion

## SECRET COMPUTE ##
inputs:
	private key d(alice) associated with T(alice)
	public key Q(bob) associated with T(bob)
P = (x, y) = h * d(alice) * Q(bob)
if P = infinite point, invalid
output x as shared secret field
(optional, but recommended) pass x to a KDF to generate symmetric key
 */

#define ECC_PRV_KEY_SIZE	28
#define ECC_PUB_KEY_SIZE	(ECC_PRV_KEY_SIZE<<1)
#define CURVE_DEGREE		224

#define PTFM_WORD_SIZE		sizeof(uint8_t)
#define ECC_GF_LEN			(ECC_PRV_KEY_SIZE / PTFM_WORD_SIZE)

// main type definitions for variables
typedef uint32_t vec_t[ECC_GF_LEN];	// should be 24 bytes
struct Point {
	vec_t x;
	vec_t y;
};
struct Curve {
	vec_t polynomial;
	vec_t coeff_a;
	vec_t coeff_b;
	Point base;
	vec_t b_order;
	uint8_t cofactor;
};


Curve secp224k1 = {
	{0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFE56D},	// p
	{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000},	// a
	{0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000005},	// b
	{
		{0xA1455B33, 0x4DF099DF, 0x30FC28A1, 0x69A467E9, 0xE47075A9, 0x0F7E650E, 0xB6B7A45C},
		{0x7E089FED, 0x7FBA3442, 0x82CAFBD6, 0xF7E319F7, 0xC0B0BD59, 0xE2CA4BDB, 0x556D61A5}
	},		// G (x, y)
	{0x00000000, 0x00000000, 0x00000000, 0x0001DCE8, 0xD2EC6184, 0xCAF0A971, 0x769FB1F7},	// n
	1
};