wiiqt/WiiQt/ec.cpp

// Copyright 2007,2008  Segher Boessenkool  <segher@kernel.crashing.org>
// Licensed under the terms of the GNU GPL, version 2
// http://www.gnu.org/licenses/old-licenses/gpl-2.0.txt

//#include <string.h>
//#include <stdio.h>

#include "tools.h"
#include "bn.h"
#include "sha1.h"

// y**2 + x*y = x**3 + x + b
/*static quint8 ec_b[30] = { 0x00, 0x66, 0x64, 0x7e, 0xde, 0x6c, 0x33, 0x2c, 0x7f, 0x8c, 0x09, 0x23, 0xbb, 0x58, 0x21,
                           0x3b, 0x33, 0x3b, 0x20, 0xe9, 0xce, 0x42, 0x81, 0xfe, 0x11, 0x5f, 0x7d, 0x8f, 0x90, 0xad };
*/
// order of the addition group of points
static quint8 ec_N[30] = { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                           0x13, 0xe9, 0x74, 0xe7, 0x2f, 0x8a, 0x69, 0x22, 0x03, 0x1d, 0x26, 0x03, 0xcf, 0xe0, 0xd7 };

// base point
static quint8 ec_G[60] = { 0x00, 0xfa, 0xc9, 0xdf, 0xcb, 0xac, 0x83, 0x13, 0xbb, 0x21, 0x39, 0xf1, 0xbb, 0x75, 0x5f,
                           0xef, 0x65, 0xbc, 0x39, 0x1f, 0x8b, 0x36, 0xf8, 0xf8, 0xeb, 0x73, 0x71, 0xfd, 0x55, 0x8b,
                           0x01, 0x00, 0x6a, 0x08, 0xa4, 0x19, 0x03, 0x35, 0x06, 0x78, 0xe5, 0x85, 0x28, 0xbe, 0xbf,
                           0x8a, 0x0b, 0xef, 0xf8, 0x67, 0xa7, 0xca, 0x36, 0x71, 0x6f, 0x7e, 0x01, 0xf8, 0x10, 0x52 };
/*
static void elt_print(char *name, quint8 *a)
{
    quint32 i;

	printf("%s = ", name);

	for (i = 0; i < 30; i++)
		printf("%02x", a[i]);

	printf("\n");
}
*/
static void elt_copy(quint8 *d, quint8 *a)
{
	memcpy(d, a, 30);
}

static void elt_zero(quint8 *d)
{
	memset(d, 0, 30);
}

static int elt_is_zero(quint8 *d)
{
    quint32 i;

	for (i = 0; i < 30; i++)
		if (d[i] != 0)
			return 0;

	return 1;
}

static void elt_add(quint8 *d, quint8 *a, quint8 *b)
{
    quint32 i;

	for (i = 0; i < 30; i++)
		d[i] = a[i] ^ b[i];
}

static void elt_mul_x(quint8 *d, quint8 *a)
{
    quint8 carry, x, y;
    quint32 i;

	carry = a[0] & 1;

	x = 0;
	for (i = 0; i < 29; i++) {
		y = a[i + 1];
		d[i] = x ^ (y >> 7);
		x = y << 1;
	}
	d[29] = x ^ carry;

	d[20] ^= carry << 2;
}

static void elt_mul(quint8 *d, quint8 *a, quint8 *b)
{
    quint32 i, n;
    quint8 mask;

	elt_zero(d);

	i = 0;
	mask = 1;
	for (n = 0; n < 233; n++) {
		elt_mul_x(d, d);

		if ((a[i] & mask) != 0)
			elt_add(d, d, b);

		mask >>= 1;
		if (mask == 0) {
			mask = 0x80;
			i++;
		}
	}
}

static const quint8 square[16] = { 0x00, 0x01, 0x04, 0x05, 0x10, 0x11, 0x14, 0x15, 0x40, 0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55 };

static void elt_square_to_wide(quint8 *d, quint8 *a)
{
    quint32 i;

	for (i = 0; i < 30; i++) {
		d[2*i] = square[a[i] >> 4];
		d[2*i + 1] = square[a[i] & 15];
	}
}

static void wide_reduce(quint8 *d)
{
    quint32 i;
    quint8 x;

	for (i = 0; i < 30; i++) {
		x = d[i];

		d[i + 19] ^= x >> 7;
		d[i + 20] ^= x << 1;

		d[i + 29] ^= x >> 1;
		d[i + 30] ^= x << 7;
	}

	x = d[30] & ~1;

	d[49] ^= x >> 7;
	d[50] ^= x << 1;

	d[59] ^= x >> 1;

	d[30] &= 1;
}

static void elt_square(quint8 *d, quint8 *a)
{
    quint8 wide[60];

	elt_square_to_wide(wide, a);
	wide_reduce(wide);

	elt_copy(d, wide + 30);
}

static void itoh_tsujii(quint8 *d, quint8 *a, quint8 *b, quint32 j)
{
    quint8 t[30];

	elt_copy(t, a);
	while (j--) {
		elt_square(d, t);
		elt_copy(t, d);
	}

	elt_mul(d, t, b);
}

static void elt_inv(quint8 *d, quint8 *a)
{
    quint8 t[30];
    quint8 s[30];

	itoh_tsujii(t, a, a, 1);
	itoh_tsujii(s, t, a, 1);
	itoh_tsujii(t, s, s, 3);
	itoh_tsujii(s, t, a, 1);
	itoh_tsujii(t, s, s, 7);
	itoh_tsujii(s, t, t, 14);
	itoh_tsujii(t, s, a, 1);
	itoh_tsujii(s, t, t, 29);
	itoh_tsujii(t, s, s, 58);
	itoh_tsujii(s, t, t, 116);
	elt_square(d, s);
}
/*
static int point_is_on_curve(quint8 *p)
{
    quint8 s[30], t[30];
    quint8 *x, *y;

	x = p;
	y = p + 30;

	elt_square(t, x);
	elt_mul(s, t, x);

	elt_add(s, s, t);

	elt_square(t, y);
	elt_add(s, s, t);

	elt_mul(t, x, y);
	elt_add(s, s, t);

	elt_add(s, s, ec_b);

	return elt_is_zero(s);
}
*/
static int point_is_zero(quint8 *p)
{
	return elt_is_zero(p) && elt_is_zero(p + 30);
}

static void point_double(quint8 *r, quint8 *p)
{
    quint8 s[30], t[30];
    quint8 *px, *py, *rx, *ry;

	px = p;
	py = p + 30;
	rx = r;
	ry = r + 30;

	if (elt_is_zero(px)) {
		elt_zero(rx);
		elt_zero(ry);

		return;
	}

	elt_inv(t, px);
	elt_mul(s, py, t);
	elt_add(s, s, px);

	elt_square(t, px);

	elt_square(rx, s);
	elt_add(rx, rx, s);
	rx[29] ^= 1;

	elt_mul(ry, s, rx);
	elt_add(ry, ry, rx);
	elt_add(ry, ry, t);
}

static void point_add(quint8 *r, quint8 *p, quint8 *q)
{
    quint8 s[30], t[30], u[30];
    quint8 *px, *py, *qx, *qy, *rx, *ry;

	px = p;
	py = p + 30;
	qx = q;
	qy = q + 30;
	rx = r;
	ry = r + 30;

	if (point_is_zero(p)) {
		elt_copy(rx, qx);
		elt_copy(ry, qy);
		return;
	}

	if (point_is_zero(q)) {
		elt_copy(rx, px);
		elt_copy(ry, py);
		return;
	}

	elt_add(u, px, qx);

	if (elt_is_zero(u)) {
		elt_add(u, py, qy);
		if (elt_is_zero(u))
			point_double(r, p);
		else {
			elt_zero(rx);
			elt_zero(ry);
		}

		return;
	}

	elt_inv(t, u);
	elt_add(u, py, qy);
	elt_mul(s, t, u);

	elt_square(t, s);
	elt_add(t, t, s);
	elt_add(t, t, qx);
	t[29] ^= 1;

	elt_mul(u, s, t);
	elt_add(s, u, py);
	elt_add(rx, t, px);
	elt_add(ry, s, rx);
}

static void point_mul(quint8 *d, quint8 *a, quint8 *b)	// a is bignum
{
    quint32 i;
    quint8 mask;

	elt_zero(d);
	elt_zero(d + 30);

	for (i = 0; i < 30; i++)
		for (mask = 0x80; mask != 0; mask >>= 1) {
			point_double(d, d);
			if ((a[i] & mask) != 0)
				point_add(d, d, b);
		}
}

void generate_ecdsa(quint8 *R, quint8 *S, quint8 *k, quint8 *hash)
{
    quint8 e[30];
    quint8 kk[30];
    quint8 m[30];
    quint8 minv[30];
    quint8 mG[60];
    //FILE *fp;

	elt_zero(e);
	memcpy(e + 10, hash, 20);
    memset( &m, 0, sizeof( m ) );

    QTime midnight( 0, 0, 0 );
    qsrand( midnight.secsTo( QTime::currentTime() ) );
    for( quint16 i = 0; i < 15; i++ )
    {
        quint16 rn = qrand() % 0xffff;
        memcpy( (char*)&m + ( i * 2 ), &rn, 2 );
        //qDebug() << "m:" << i;
        //hexdump( (void*)&m, 30 );
    }


    //fp = fopen("/dev/random", "rb");
    //if (fread(m, sizeof m, 1, fp) != 1)
        //fatal("reading random");
    //fclose(fp);
	m[0] = 0;

	//	R = (mG).x

	point_mul(mG, m, ec_G);
	elt_copy(R, mG);
	if (bn_compare(R, ec_N, 30) >= 0)
		bn_sub_modulus(R, ec_N, 30);

	//	S = m**-1*(e + Rk) (mod N)

	elt_copy(kk, k);
	if (bn_compare(kk, ec_N, 30) >= 0)
		bn_sub_modulus(kk, ec_N, 30);
	bn_mul(S, R, kk, ec_N, 30);
	bn_add(kk, S, e, ec_N, 30);
	bn_inv(minv, m, ec_N, 30);
	bn_mul(S, minv, kk, ec_N, 30);
}

int check_ecdsa(quint8 *Q, quint8 *R, quint8 *S, quint8 *hash)
{
    quint8 Sinv[30];
    quint8 e[30];
    quint8 w1[30], w2[30];
    quint8 r1[60], r2[60];

	bn_inv(Sinv, S, ec_N, 30);

	elt_zero(e);
	memcpy(e + 10, hash, 20);

	bn_mul(w1, e, Sinv, ec_N, 30);
	bn_mul(w2, R, Sinv, ec_N, 30);

	point_mul(r1, w1, ec_G);
	point_mul(r2, w2, Q);

	point_add(r1, r1, r2);

	if (bn_compare(r1, ec_N, 30) >= 0)
		bn_sub_modulus(r1, ec_N, 30);

	return (bn_compare(r1, R, 30) == 0);
}

void ec_priv_to_pub(quint8 *k, quint8 *Q)
{
	point_mul(Q, k, ec_G);
}

int check_ec(quint8 *ng, quint8 *ap, quint8 *sig, quint8 *sig_hash)
{
    //qDebug() << QByteArray( (const char*)ng, 0x10 ).toHex();
    //qDebug() << QByteArray( (const char*)ap, 0x10 ).toHex();
    //qDebug() << QByteArray( (const char*)sig, 0x10 ).toHex();
    //qDebug() << QByteArray( (const char*)sig_hash, 0x10 ).toHex();
    quint8 ap_hash[20];
    quint8 *ng_Q, *ap_R, *ap_S;
    quint8 *ap_Q, *sig_R, *sig_S;

    ng_Q = ng + 0x0108;
    ap_R = ap + 0x04;
    ap_S = ap + 0x22;


    SHA1Context sha;
    SHA1Reset( &sha );
    SHA1Input( &sha, (const unsigned char*)ap + 0x80, 0x100 );
    SHA1Result( &sha );

    for( int i = 0; i < 5 ; i++ )
    {
        quint32 part = qFromBigEndian( sha.Message_Digest[ i ] );
        memcpy( (char*)&ap_hash + ( i * 4 ), &part, 4 );
    }
    ap_Q = ap + 0x0108;
    sig_R = sig;
    sig_S = sig + 30;

    return check_ecdsa(ng_Q, ap_R, ap_S, ap_hash)
           && check_ecdsa(ap_Q, sig_R, sig_S, sig_hash);
}

void make_ec_cert( quint8 *cert, quint8 *sig, char *signer, char *name, quint8 *priv, quint32 key_id )
{
    //qDebug() << "make_ec_cert";
	memset( cert, 0, 0x180 );
    quint32 tmp = qFromBigEndian( (quint32)0x10002 );
	memcpy( (char*)cert, (const void*)&tmp, 4 );
	memcpy( cert + 4, sig, 60 );
	strcpy( (char*)cert + 0x80, signer );
    tmp = qFromBigEndian( (quint32)2 );
	memcpy( (char*)cert + 0xc0, (const void*)&tmp, 4 );
	strcpy( (char*)cert + 0xc4, name );
    tmp = qFromBigEndian( key_id );
	memcpy( (char*)cert + 0x104, (const void*)&tmp, 4 );
    ec_priv_to_pub( priv, cert + 0x108 );
}