예제 #1
0
void fb_slv_basic(fb_t c, const fb_t a) {
	int i;
	fb_t t0;

	fb_null(t0);

	TRY {
		fb_new(t0);

		fb_copy(t0, a);
		fb_copy(c, a);

		for (i = 0; i < (FB_BITS - 1) / 2; i++) {
			fb_sqr(c, c);
			fb_sqr(c, c);
			fb_add(c, c, t0);
		}

		fb_add_dig(c, c, fb_trc(c));
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
	}
}
예제 #2
0
/**
 * Precomputes half-traces for z^i with odd i.
 *
 * @throw ERR_NO_MEMORY if there is no available memory.
 */
static void find_solve() {
	int i, j, k, l;
	fb_t t0;

	fb_null(t0);

	TRY {
		fb_new(t0);

		l = 0;
		for (i = 0; i < FB_BITS; i += 8, l++) {
			for (j = 0; j < 16; j++) {
				fb_zero(t0);
				for (k = 0; k < 4; k++) {
					if (j & (1 << k)) {
						fb_set_bit(t0, i + 2 * k + 1, 1);
					}
				}
				fb_copy(fb_half[l][j], t0);
				for (k = 0; k < (FB_BITS - 1) / 2; k++) {
					fb_sqr(fb_half[l][j], fb_half[l][j]);
					fb_sqr(fb_half[l][j], fb_half[l][j]);
					fb_add(fb_half[l][j], fb_half[l][j], t0);
				}
			}
			fb_rsh(fb_half[l][j], fb_half[l][j], 1);
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
	}
}
예제 #3
0
파일: relic_eb_pck.c 프로젝트: ekr/hacrypto
int eb_upk(eb_t r, const eb_t p) {
	fb_t t0, t1;
	int res = 0;

	fb_null(t0);
	fb_null(t1);

	TRY {
		fb_new(t0);
		fb_new(t1);

		eb_rhs(t1, p);

		if (eb_curve_is_super()) {
			/* t0 = c^2. */
			fb_sqr(t0, eb_curve_get_c());
			/* t0 = 1/c^2. */
			fb_inv(t0, t0);
			/* t0 = t1/c^2. */
			fb_mul(t0, t0, t1);
			res = (fb_trc(t0) == 0);
			/* Solve t1^2 + t1 = t0. */
			fb_slv(t1, t0);
			/* If this is not the correct solution, try the other. */
			if (fb_get_bit(t1, 0) != fb_get_bit(p->y, 0)) {
				fb_add_dig(t1, t1, 1);
			}
			/* x3 = x1, y3 = t1 * c, z3 = 1. */
			fb_mul(r->y, t1, eb_curve_get_c());
		} else {
			fb_sqr(t0, p->x);
			/* t0 = 1/x1^2. */
			fb_inv(t0, t0);
			/* t0 = t1/x1^2. */
			fb_mul(t0, t0, t1);
			res = (fb_trc(t0) == 0);
			/* Solve t1^2 + t1 = t0. */
			fb_slv(t1, t0);
			/* If this is not the correct solution, try the other. */
			if (fb_get_bit(t1, 0) != fb_get_bit(p->y, 0)) {
				fb_add_dig(t1, t1, 1);
			}
			/* x3 = x1, y3 = t1 * x1, z3 = 1. */
			fb_mul(r->y, t1, p->x);
		}
		fb_copy(r->x, p->x);
		fb_set_dig(r->z, 1);

		r->norm = 1;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
	}
	return res;
}
예제 #4
0
void fb_invn_low(dig_t *c, dig_t *a) {
	int i, j, x, y, u[11];
	fb_t table[11];

	int len, *chain = fb_poly_get_chain(&len);

	u[0] = 1;
	u[1] = 2;
	fb_copy(table[0], a);
	fb_sqr(table[1], table[0]);
	fb_mul(table[1], table[1], table[0]);

	u[2] = u[1] + u[0];
	fb_sqr(table[2], table[1]);
	fb_mul(table[2], table[2], table[0]);

	u[3] = u[2] + u[1];
	fb_sqr(table[3], table[2]);
	for (j = 1; j < u[1]; j++) {
		fb_sqr(table[3], table[3]);
	}
	fb_mul(table[3], table[3], table[1]);

	u[4] = 2 * u[3];
	fb_sqr(table[4], table[3]);
	for (j = 1; j < u[3]; j++) {
		fb_sqr(table[4], table[4]);
	}
	fb_mul(table[4], table[4], table[3]);

	u[5] = u[4] + u[3];
	fb_sqr(table[5], table[4]);
	for (j = 1; j < u[3]; j++) {
		fb_sqr(table[5], table[5]);
	}
	fb_mul(table[5], table[5], table[3]);

	u[6] = u[5] + u[4];
	fb_itr(table[6], table[5], u[4], inv_tab[4]);
	fb_mul(table[6], table[6], table[4]);

	u[7] = 2 * u[6];
	fb_itr(table[7], table[6], u[6], inv_tab[6]);
	fb_mul(table[7], table[7], table[6]);

	u[8] = u[7] + u[6];
	fb_itr(table[8], table[7], u[6], inv_tab[6]);
	fb_mul(table[8], table[8], table[6]);

	u[9] = u[8] + u[7];
	fb_itr(table[9], table[8], u[8], inv_tab[7]);
	fb_mul(table[9], table[9], table[7]);

	u[10] = 2 * u[9];
	fb_itr(table[10], table[9], u[9], inv_tab[9]);
	fb_mul(table[10], table[10], table[9]);

	fb_sqr(c, table[10]);
}
예제 #5
0
int eb_is_valid(const eb_t p) {
	eb_t t;
	fb_t lhs;
	int r = 0;

	eb_null(t);
	fb_null(lhs);

	TRY {
		eb_new(t);
		fb_new(lhs);

		eb_norm(t, p);

		fb_mul(lhs, t->x, t->y);
		eb_rhs(t->x, t);
		fb_sqr(t->y, t->y);
		fb_add(lhs, lhs, t->y);
		r = (fb_cmp(lhs, t->x) == CMP_EQ) || eb_is_infty(p);
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		eb_free(t);
		fb_free(lhs);
	}
	return r;
}
예제 #6
0
void fb2_inv(fb2_t c, fb2_t a) {
	fb_t a0, a1, m0, m1;

	fb_null(a0);
	fb_null(a1);
	fb_null(m0);
	fb_null(m1);

	TRY {
		fb_new(a0);
		fb_new(a1);
		fb_new(m0);
		fb_new(m1);

		fb_add(a0, a[0], a[1]);
		fb_sqr(m0, a[0]);
		fb_mul(m1, a0, a[1]);
		fb_add(a1, m0, m1);
		fb_inv(a1, a1);
		fb_mul(c[0], a0, a1);
		fb_mul(c[1], a[1], a1);
	} CATCH_ANY {
		THROW(ERR_CAUGHT);
	} FINALLY {
		fb_free(a0);
		fb_free(a1);
		fb_free(m0);
		fb_free(m1);
	}
}
예제 #7
0
void fb_srt_basic(fb_t c, const fb_t a) {
	if (c != a) {
		fb_copy(c, a);
	}

	for (int i = 1; i < FB_BITS; i++) {
		fb_sqr(c, c);
	}
}
예제 #8
0
void eb_rhs(fb_t rhs, const eb_t p) {
	fb_t t0, t1;

	fb_null(t0);
	fb_null(t1);

	TRY {
		fb_new(t0);
		fb_new(t1);

		/* t0 = x1^2. */
		fb_sqr(t0, p->x);
		/* t1 = x1^3. */
		fb_mul(t1, t0, p->x);

		/* t1 = x1^3 + a * x1^2 + b. */
		switch (eb_curve_opt_a()) {
			case OPT_ZERO:
				break;
			case OPT_ONE:
				fb_add(t1, t1, t0);
				break;
			case OPT_DIGIT:
				fb_mul_dig(t0, t0, eb_curve_get_a()[0]);
				fb_add(t1, t1, t0);
				break;
			default:
				fb_mul(t0, t0, eb_curve_get_a());
				fb_add(t1, t1, t0);
				break;
		}

		switch (eb_curve_opt_b()) {
			case OPT_ZERO:
				break;
			case OPT_ONE:
				fb_add_dig(t1, t1, 1);
				break;
			case OPT_DIGIT:
				fb_add_dig(t1, t1, eb_curve_get_b()[0]);
				break;
			default:
				fb_add(t1, t1, eb_curve_get_b());
				break;
		}

		fb_copy(rhs, t1);
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
	}
}
예제 #9
0
/**
 * Find non-zero bits for fast trace computation.
 *
 * @throw ERR_NO_MEMORY if there is no available memory.
 * @throw ERR_NO_VALID if the polynomial is invalid.
 */
static void find_trace() {
	fb_t t0, t1;
	int counter;
	ctx_t *ctx = core_get();

	fb_null(t0);
	fb_null(t1);

	ctx->fb_ta = ctx->fb_tb = ctx->fb_tc = -1;

	TRY {
		fb_new(t0);
		fb_new(t1);

		counter = 0;
		for (int i = 0; i < FB_BITS; i++) {
			fb_zero(t0);
			fb_set_bit(t0, i, 1);
			fb_copy(t1, t0);
			for (int j = 1; j < FB_BITS; j++) {
				fb_sqr(t1, t1);
				fb_add(t0, t0, t1);
			}
			if (!fb_is_zero(t0)) {
				switch (counter) {
					case 0:
						ctx->fb_ta = i;
						ctx->fb_tb = ctx->fb_tc = -1;
						break;
					case 1:
						ctx->fb_tb = i;
						ctx->fb_tc = -1;
						break;
					case 2:
						ctx->fb_tc = i;
						break;
					default:
						THROW(ERR_NO_VALID);
						break;
				}
				counter++;
			}
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
	}
}
예제 #10
0
/**
 * Find non-zero bits for fast trace computation.
 *
 * @throw ERR_NO_MEMORY if there is no available memory.
 * @throw ERR_INVALID if the polynomial is invalid.
 */
static void find_trace() {
	fb_t t0, t1;
	int i, j, counter;

	fb_null(t0);
	fb_null(t1);

	trc_a = trc_b = trc_c = -1;

	TRY {
		fb_new(t0);
		fb_new(t1);

		counter = 0;
		for (i = 0; i < FB_BITS; i++) {
			fb_zero(t0);
			fb_set_bit(t0, i, 1);
			fb_copy(t1, t0);
			for (j = 1; j < FB_BITS; j++) {
				fb_sqr(t1, t1);
				fb_add(t0, t0, t1);
			}
			if (!fb_is_zero(t0)) {
				switch (counter) {
					case 0:
						trc_a = i;
						trc_b = trc_c = -1;
						break;
					case 1:
						trc_b = i;
						trc_c = -1;
						break;
					case 2:
						trc_c = i;
						break;
					default:
						THROW(ERR_INVALID);
						break;
				}
				counter++;
			}
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
	}
}
예제 #11
0
/**
 * Normalizes a point represented in projective coordinates.
 *
 * @param[out] r		- the result.
 * @param[in] p			- the point to normalize.
 * @param[in] flag		- if the Z coordinate is already inverted.
 */
static void eb_norm_ordin(eb_t r, const eb_t p, int flag) {
	if (!p->norm) {
		if (flag) {
			fb_copy(r->z, p->z);
		} else {
			fb_inv(r->z, p->z);
		}
		fb_mul(r->x, p->x, r->z);
		fb_sqr(r->z, r->z);
		fb_mul(r->y, p->y, r->z);
		fb_set_dig(r->z, 1);
	}

	r->norm = 1;
}
예제 #12
0
/**
 * Precomputes the square root of z.
 */
static void find_srz() {
	int i;

	fb_set_dig(fb_srz, 2);

	for (i = 1; i < FB_BITS; i++) {
		fb_sqr(fb_srz, fb_srz);
	}

#ifdef FB_PRECO
	for (i = 0; i <= 255; i++) {
		fb_mul_dig(fb_tab_srz[i], fb_srz, i);
	}
#endif
}
예제 #13
0
/**
 * Precomputes the square root of z.
 */
static void find_srz() {
	ctx_t *ctx = core_get();

	fb_set_dig(ctx->fb_srz, 2);

	for (int i = 1; i < FB_BITS; i++) {
		fb_sqr(ctx->fb_srz, ctx->fb_srz);
	}

#ifdef FB_PRECO
	for (int i = 0; i <= 255; i++) {
		fb_mul_dig(ctx->fb_tab_srz[i], ctx->fb_srz, i);
	}
#endif
}
예제 #14
0
void fb2_sqr(fb2_t c, fb2_t a) {
	fb_sqr(c[1], a[1]);
	fb_sqr(c[0], a[0]);
	fb_add(c[0], c[0], c[1]);
}
예제 #15
0
파일: relic_eb_add.c 프로젝트: Gesine/relic
/**
 * Adds two points represented in affine coordinates on an ordinary binary
 * elliptic curve.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the first point to add.
 * @param[in] q					- the second point to add.
 */
static void eb_add_basic_imp(eb_t r, const eb_t p, const eb_t q) {
	fb_t t0, t1, t2;

	fb_null(t0);
	fb_null(t1);
	fb_null(t2);

	TRY {
		fb_new(t0);
		fb_new(t1);
		fb_new(t2);

		/* t0 = (y1 + y2). */
		fb_add(t0, p->y, q->y);
		/* t1 = (x1 + x2). */
		fb_add(t1, p->x, q->x);

		if (fb_is_zero(t1)) {
			if (fb_is_zero(t0)) {
				/* If t1 is zero and t0 is zero, p = q, should have doubled. */
				eb_dbl_basic(r, p);
			} else {
				/* If t0 is not zero and t1 is zero, q = -p and r = infinity. */
				eb_set_infty(r);
			}
		} else {
			/* t2 = 1/(x1 + x2). */
			fb_inv(t2, t1);
			/* t0 = lambda = (y1 + y2)/(x1 + x2). */
			fb_mul(t0, t0, t2);
			/* t2 = lambda^2. */
			fb_sqr(t2, t0);

			/* t2 = lambda^2 + lambda + x1 + x2 + a. */
			fb_add(t2, t2, t0);
			fb_add(t2, t2, t1);

			switch (eb_curve_opt_a()) {
				case OPT_ZERO:
					break;
				case OPT_ONE:
					fb_add_dig(t2, t2, (dig_t)1);
					break;
				case OPT_DIGIT:
					fb_add_dig(t2, t2, eb_curve_get_a()[0]);
					break;
				default:
					fb_add(t2, t2, eb_curve_get_a());
					break;
			}

			/* y3 = lambda*(x3 + x1) + x3 + y1. */
			fb_add(t1, t2, p->x);
			fb_mul(t1, t1, t0);
			fb_add(t1, t1, t2);
			fb_add(r->y, p->y, t1);

			/* x3 = lambda^2 + lambda + x1 + x2 + a. */
			fb_copy(r->x, t2);
			fb_copy(r->z, p->z);

			r->norm = 1;
		}
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
		fb_free(t2);
	}
}
예제 #16
0
파일: relic_eb_dbl.c 프로젝트: Gesine/relic
/**
 * Doubles a point represented in projective coordinates on an ordinary binary
 * elliptic curve.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the point to double.
 */
static void eb_dbl_projc_imp(eb_t r, const eb_t p) {
	fb_t t0, t1;

	fb_null(t0);
	fb_null(t1);

	TRY {
		fb_new(t0);
		fb_new(t1);

		/* t0 = B = x1^2. */
		fb_sqr(t0, p->x);
		/* C = B + y1. */
		fb_add(r->y, t0, p->y);

		if (!p->norm) {
			/* A = x1 * z1. */
			fb_mul(t1, p->x, p->z);
			/* z3 = A^2. */
			fb_sqr(r->z, t1);
		} else {
			/* if z1 = 1, A = x1. */
			fb_copy(t1, p->x);
			/* if z1 = 1, z3 = x1^2. */
			fb_copy(r->z, t0);
		}

		/* t1 = D = A * C. */
		fb_mul(t1, t1, r->y);

		/* C^2 + D. */
		fb_sqr(r->y, r->y);
		fb_add(r->x, t1, r->y);

		/* C^2 + D + a2 * z3. */
		switch (eb_curve_opt_a()) {
			case OPT_ZERO:
				break;
			case OPT_ONE:
				fb_add(r->x, r->z, r->x);
				break;
			case OPT_DIGIT:
				fb_mul_dig(r->y, r->z, eb_curve_get_a()[0]);
				fb_add(r->x, r->y, r->x);
				break;
			default:
				fb_mul(r->y, r->z, eb_curve_get_a());
				fb_add(r->x, r->y, r->x);
				break;
		}

		/* t1 = (D + z3). */
		fb_add(t1, t1, r->z);
		/* t0 = B^2. */
		fb_sqr(t0, t0);
		/* t0 = B^2 * z3. */
		fb_mul(t0, t0, r->z);
		/* y3 = (D + z3) * r3 + B^2 * z3. */
		fb_mul(r->y, t1, r->x);
		fb_add(r->y, r->y, t0);

		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
	}
}
예제 #17
0
파일: relic_eb_dbl.c 프로젝트: Gesine/relic
/**
 * Doubles a point represented in affine coordinates on an ordinary binary
 * elliptic curve.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the point to double.
 */
static void eb_dbl_basic_imp(eb_t r, const eb_t p) {
	fb_t t0, t1, t2;

	fb_null(t0);
	fb_null(t1);
	fb_null(t2);

	TRY {
		fb_new(t0);
		fb_new(t1);
		fb_new(t2);

		/* t0 = 1/x1. */
		fb_inv(t0, p->x);
		/* t0 = y1/x1. */
		fb_mul(t0, t0, p->y);
		/* t0 = lambda = x1 + y1/x1. */
		fb_add(t0, t0, p->x);
		/* t1 = lambda^2. */
		fb_sqr(t1, t0);
		/* t2 = lambda^2 + lambda. */
		fb_add(t2, t1, t0);

		/* t2 = lambda^2 + lambda + a2. */
		switch (eb_curve_opt_a()) {
			case OPT_ZERO:
				break;
			case OPT_ONE:
				fb_add_dig(t2, t2, (dig_t)1);
				break;
			case OPT_DIGIT:
				fb_add_dig(t2, t2, eb_curve_get_a()[0]);
				break;
			default:
				fb_add(t2, t2, eb_curve_get_a());
				break;
		}

		/* t1 = x1 + x3. */
		fb_add(t1, t2, p->x);

		/* t1 = lambda * (x1 + x3). */
		fb_mul(t1, t0, t1);

		fb_copy(r->x, t2);
		/* y3 = lambda * (x1 + x3) + x3 + y1. */
		fb_add(t1, t1, r->x);
		fb_add(r->y, t1, p->y);

		fb_copy(r->z, p->z);

		r->norm = 1;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
		fb_free(t2);
	}
}
예제 #18
0
/**
 * Adds a point represented in affine coordinates to a point represented in
 * projective coordinates.
 *
 * @param r					- the result.
 * @param p					- the affine point.
 * @param q					- the projective point.
 */
static void eb_add_projc_ordin_mix(eb_t r, eb_t p, eb_t q) {
	fb_t t0, t1, t2, t3, t4, t5;

	fb_null(t0);
	fb_null(t1);
	fb_null(t2);
	fb_null(t3);
	fb_null(t4);
	fb_null(t5);

	TRY {
		fb_new(t0);
		fb_new(t1);
		fb_new(t2);
		fb_new(t3);
		fb_new(t4);
		fb_new(t5);

		if (!p->norm) {
			/* A = y1 + y2 * z1^2. */
			fb_sqr(t0, p->z);
			fb_mul(t0, t0, q->y);
			fb_add(t0, t0, p->y);
			/* B = x1 + x2 * z1. */
			fb_mul(t1, p->z, q->x);
			fb_add(t1, t1, p->x);
		} else {
			/* t0 = A = y1 + y2. */
			fb_add(t0, p->y, q->y);
			/* t1 = B = x1 + x2. */
			fb_add(t1, p->x, q->x);
		}

		if (fb_is_zero(t1)) {
			if (fb_is_zero(t0)) {
				/* If t0 = 0 and t1 = 0, p = q, should have doubled! */
				eb_dbl_projc(r, p);
			} else {
				/* If t0 = 0, r is infinity. */
				eb_set_infty(r);
			}
		} else {
			if (!p->norm) {
				/* t2 = C = B * z1. */
				fb_mul(t2, p->z, t1);
				/* z3 = C^2. */
				fb_sqr(r->z, t2);
				/* t1 = B^2. */
				fb_sqr(t1, t1);
				/* t1 = A + B^2. */
				fb_add(t1, t0, t1);
			} else {
				/* If z1 = 0, t2 = C = B. */
				fb_copy(t2, t1);
				/* z3 = B^2. */
				fb_sqr(r->z, t1);
				/* t1 = A + z3. */
				fb_add(t1, t0, r->z);
			}

			/* t3 = D = x2 * z3. */
			fb_mul(t3, r->z, q->x);

			/* t4 = (y2 + x2). */
			fb_add(t4, q->x, q->y);

			/* z3 = A^2. */
			fb_sqr(r->x, t0);

			/* t1 = A + B^2 + a2 * C. */
			switch (eb_curve_opt_a()) {
				case OPT_ZERO:
					break;
				case OPT_ONE:
					fb_add(t1, t1, t2);
					break;
				case OPT_DIGIT:
					/* t5 = a2 * C. */
					fb_mul_dig(t5, t2, eb_curve_get_a()[0]);
					fb_add(t1, t1, t5);
					break;
				default:
					/* t5 = a2 * C. */
					fb_mul(t5, eb_curve_get_a(), t2);
					fb_add(t1, t1, t5);
					break;
			}

			/* t1 = C * (A + B^2 + a2 * C). */
			fb_mul(t1, t1, t2);
			/* x3 = A^2 + C * (A + B^2 + a2 * C). */
			fb_add(r->x, r->x, t1);

			/* t3 = D + x3. */
			fb_add(t3, t3, r->x);
			/* t2 = A * B. */
			fb_mul(t2, t0, t2);
			/* y3 = (D + x3) * (A * B + z3). */
			fb_add(r->y, t2, r->z);
			fb_mul(r->y, r->y, t3);
			/* t0 = z3^2. */
			fb_sqr(t0, r->z);
			/* t0 = (y2 + x2) * z3^2. */
			fb_mul(t0, t0, t4);
			/* y3 = (D + x3) * (A * B + z3) + (y2 + x2) * z3^2. */
			fb_add(r->y, r->y, t0);
		}

		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
		fb_free(t2);
		fb_free(t3);
		fb_free(t4);
		fb_free(t5);
	}
}
예제 #19
0
/**
 * Adds two points represented in projective coordinates on an ordinary binary
 * elliptic curve.
 *
 * @param r					- the result.
 * @param p					- the first point to add.
 * @param q					- the second point to add.
 */
static void eb_add_projc_ordin(eb_t r, eb_t p, eb_t q) {
#if defined(EB_MIXED) && defined(STRIP)
	eb_add_projc_ordin_mix(r, p, q);
#else /* General addition. */
	fb_t t0, t1, t2, t3, t4, t5, t6, t7;

	fb_null(t0);
	fb_null(t1);
	fb_null(t2);
	fb_null(t3);
	fb_null(t4);
	fb_null(t5);
	fb_null(t6);
	fb_null(t7);

	TRY {
		fb_new(t0);
		fb_new(t1);
		fb_new(t2);
		fb_new(t3);
		fb_new(t4);
		fb_new(t5);
		fb_new(t6);
		fb_new(t7);

		if (q->norm) {
			eb_add_projc_ordin_mix(r, p, q);
		} else {
			/* t0 = B = x2 * z1. */
			fb_mul(t0, q->x, p->z);

			/* A = x1 * z2 */
			fb_mul(t1, p->x, q->z);

			/* t2 = E = A + B. */
			fb_add(t2, t1, t0);

			/* t3 = D = B^2. */
			fb_sqr(t3, t0);
			/* t4 = C = A^2. */
			fb_sqr(t4, t1);
			/* t5 = F = C + D. */
			fb_add(t5, t3, t4);

			/* t6 = H = y2 * z1^2. */
			fb_sqr(t6, p->z);
			fb_mul(t6, t6, q->y);

			/* t7 = G = y1 * z2^2. */
			fb_sqr(t7, q->z);
			fb_mul(t7, t7, p->y);

			/* t3 = D + H. */
			fb_add(t3, t3, t6);
			/* t4 = C + G. */
			fb_add(t4, t4, t7);
			/* t6 = I = G + H. */
			fb_add(t6, t7, t6);

			/* If E is zero. */
			if (fb_is_zero(t2)) {
				if (fb_is_zero(t6)) {
					/* If I is zero, p = q, should have doubled. */
					eb_dbl_projc(r, p);
				} else {
					/* If I is not zero, q = -p, r = infinity. */
					eb_set_infty(r);
				}
			} else {
				/* t6 = J = I * E. */
				fb_mul(t6, t6, t2);

				/* z3 = F * z1 * z2. */
				fb_mul(r->z, p->z, q->z);
				fb_mul(r->z, t5, r->z);

				/* t4 = B * (C + G). */
				fb_mul(t4, t0, t4);
				/* t2 = A * J. */
				fb_mul(t2, t1, t6);
				/* x3 = A * (D + H) + B * (C + G). */
				fb_mul(r->x, t1, t3);
				fb_add(r->x, r->x, t4);

				/* t7 = F * G. */
				fb_mul(t7, t7, t5);
				/* Y3 = (A * J + F * G) * F + (J + z3) * x3. */
				fb_add(r->y, t2, t7);
				fb_mul(r->y, r->y, t5);
				/* t7 = (J + z3) * x3. */
				fb_add(t7, t6, r->z);
				fb_mul(t7, t7, r->x);
				fb_add(r->y, r->y, t7);
			}
		}

		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
		fb_free(t2);
		fb_free(t3);
		fb_free(t4);
		fb_free(t5);
		fb_free(t6);
		fb_free(t7);
	}
#endif
}
예제 #20
0
파일: relic_eb_add.c 프로젝트: Gesine/relic
/**
 * Adds a point represented in affine coordinates to a point represented in
 * projective coordinates.
 *
 * @param[out] r				- the result.
 * @param[in] p					- the affine point.
 * @param[in] q					- the projective point.
 */
static void eb_add_projc_mix(eb_t r, const eb_t p, const eb_t q) {
	fb_t t0, t1, t2, t3, t4, t5;

	fb_null(t0);
	fb_null(t1);
	fb_null(t2);
	fb_null(t3);
	fb_null(t4);
	fb_null(t5);

	TRY {
		fb_new(t0);
		fb_new(t1);
		fb_new(t2);
		fb_new(t3);
		fb_new(t4);
		fb_new(t5);

		/* madd-2005-dl formulas: 7M + 4S + 9add + 1*4 + 3*2. */
		/* http://www.hyperelliptic.org/EFD/g12o/auto-shortw-lopezdahab-1.html#addition-madd-2005-dl */

		if (!p->norm) {
			/* A = y1 + y2 * z1^2. */
			fb_sqr(t0, p->z);
			fb_mul(t0, t0, q->y);
			fb_add(t0, t0, p->y);
			/* B = x1 + x2 * z1. */
			fb_mul(t1, p->z, q->x);
			fb_add(t1, t1, p->x);
		} else {
			/* t0 = A = y1 + y2. */
			fb_add(t0, p->y, q->y);
			/* t1 = B = x1 + x2. */
			fb_add(t1, p->x, q->x);
		}

		if (fb_is_zero(t1)) {
			if (fb_is_zero(t0)) {
				/* If t0 = 0 and t1 = 0, p = q, should have doubled! */
				eb_dbl_projc(r, p);
			} else {
				/* If t0 = 0, r is infinity. */
				eb_set_infty(r);
			}
		} else {
			if (!p->norm) {
				/* t2 = C = B * z1. */
				fb_mul(t2, p->z, t1);
				/* z3 = C^2. */
				fb_sqr(r->z, t2);
				/* t1 = B^2. */
				fb_sqr(t1, t1);
				/* t1 = A + B^2. */
				fb_add(t1, t0, t1);
			} else {
				/* If z1 = 0, t2 = C = B. */
				fb_copy(t2, t1);
				/* z3 = B^2. */
				fb_sqr(r->z, t1);
				/* t1 = A + z3. */
				fb_add(t1, t0, r->z);
			}

			/* t3 = D = x2 * z3. */
			fb_mul(t3, r->z, q->x);

			/* t4 = (y2 + x2). */
			fb_add(t4, q->x, q->y);

			/* z3 = A^2. */
			fb_sqr(r->x, t0);

			/* t1 = A + B^2 + a2 * C. */
			switch (eb_curve_opt_a()) {
				case OPT_ZERO:
					break;
				case OPT_ONE:
					fb_add(t1, t1, t2);
					break;
				case OPT_DIGIT:
					/* t5 = a2 * C. */
					fb_mul_dig(t5, t2, eb_curve_get_a()[0]);
					fb_add(t1, t1, t5);
					break;
				default:
					/* t5 = a2 * C. */
					fb_mul(t5, eb_curve_get_a(), t2);
					fb_add(t1, t1, t5);
					break;
			}

			/* t1 = C * (A + B^2 + a2 * C). */
			fb_mul(t1, t1, t2);
			/* x3 = A^2 + C * (A + B^2 + a2 * C). */
			fb_add(r->x, r->x, t1);

			/* t3 = D + x3. */
			fb_add(t3, t3, r->x);
			/* t2 = A * B. */
			fb_mul(t2, t0, t2);
			/* y3 = (D + x3) * (A * B + z3). */
			fb_add(r->y, t2, r->z);
			fb_mul(r->y, r->y, t3);
			/* t0 = z3^2. */
			fb_sqr(t0, r->z);
			/* t0 = (y2 + x2) * z3^2. */
			fb_mul(t0, t0, t4);
			/* y3 = (D + x3) * (A * B + z3) + (y2 + x2) * z3^2. */
			fb_add(r->y, r->y, t0);
		}

		r->norm = 0;
	}
	CATCH_ANY {
		THROW(ERR_CAUGHT);
	}
	FINALLY {
		fb_free(t0);
		fb_free(t1);
		fb_free(t2);
		fb_free(t3);
		fb_free(t4);
		fb_free(t5);
	}
}