void fb2_mul(fb2_t c, fb2_t a, fb2_t b) {
fb_t t0, t1, t2;
fb_null(t0);
fb_null(t1);
fb_null(t2);
TRY {
fb_new(t0);
fb_new(t1);
fb_new(t2);
fb_add(t0, a[0], a[1]);
fb_add(t1, b[0], b[1]);
fb_mul(t0, t0, t1);
fb_mul(t1, a[0], b[0]);
fb_mul(t2, a[1], b[1]);
fb_add(c[0], t1, t2);
fb_add(c[1], t0, t1);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fb_free(t0);
fb_free(t1);
fb_free(t2);
}
}
void eb_hlv(eb_t r, const eb_t p) {
fb_t l, t;
fb_null(l);
fb_null(t);
TRY {
fb_new(l);
fb_new(t);
/* Solve l^2 + l = u + a. */
switch (eb_curve_opt_a()) {
case RLC_ZERO:
fb_copy(t, p->x);
break;
case RLC_ONE:
fb_add_dig(t, p->x, (dig_t)1);
break;
case RLC_TINY:
fb_add_dig(t, p->x, eb_curve_get_a()[0]);
break;
default:
fb_add(t, p->x, eb_curve_get_a());
break;
}
fb_slv(l, t);
if (p->norm == 1) {
/* Compute t = v + u * lambda. */
fb_mul(t, l, p->x);
fb_add(t, t, p->y);
} else {
/* Compute t = u * (u + lambda_P + lambda). */
fb_add(t, l, p->y);
fb_add(t, t, p->x);
fb_mul(t, t, p->x);
}
/* If Tr(t) = 0 then lambda_P = lambda, u = sqrt(t + u). */
if (fb_trc(t) == 0) {
fb_copy(r->y, l);
fb_add(t, t, p->x);
fb_srt(r->x, t);
} else {
/* Else lambda_P = lambda + 1, u = sqrt(t). */
fb_add_dig(r->y, l, 1);
fb_srt(r->x, t);
}
fb_set_dig(r->z, 1);
r->norm = 2;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(l);
fb_free(t);
}
}
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);
}
}
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);
}
}
void fb_poly_add(fb_t c, const fb_t a) {
ctx_t *ctx = core_get();
if (c != a) {
fb_copy(c, a);
}
if (ctx->fb_pa != 0) {
c[FB_DIGS - 1] ^= ctx->fb_poly[FB_DIGS - 1];
if (ctx->fb_na != FB_DIGS - 1) {
c[ctx->fb_na] ^= ctx->fb_poly[ctx->fb_na];
}
if (ctx->fb_pb != 0 && ctx->fb_pc != 0) {
if (ctx->fb_nb != ctx->fb_na) {
c[ctx->fb_nb] ^= ctx->fb_poly[ctx->fb_nb];
}
if (ctx->fb_nc != ctx->fb_na && ctx->fb_nc != ctx->fb_nb) {
c[ctx->fb_nc] ^= ctx->fb_poly[ctx->fb_nc];
}
}
if (ctx->fb_na != 0 && ctx->fb_nb != 0 && ctx->fb_nc != 0) {
c[0] ^= 1;
}
} else {
fb_add(c, a, ctx->fb_poly);
}
}
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;
}
void fb4_inv(fb4_t c, fb4_t a) {
fb2_t a0, a1, m0, m1;
fb2_null(a0);
fb2_null(a1);
fb2_null(m0);
fb2_null(m1);
TRY {
fb2_new(a0);
fb2_new(a1);
fb2_new(m0);
fb2_new(m1);
fb2_add(a0, a, (a + 2));
fb2_mul(m1, a0, a);
fb2_sqr(m0, a + 2);
fb2_copy(a1, m0);
fb_add(m0[1], a1[0], a1[1]);
fb_copy(m0[0], a1[1]);
fb2_add(m1, m0, m1);
fb2_inv(m1, m1);
fb2_mul(c, a0, m1);
fb2_mul(c + 2, a + 2, m1);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fb2_free(a0);
fb2_free(a1);
fb2_free(m0);
fb2_free(m1);
}
}
/**
* Multiplies two binary field elements using shift-and-add multiplication.
*
* @param c - the result.
* @param a - the first binary field element.
* @param b - the second binary field element.
* @param size - the number of digits to multiply.
*/
static void fb_mul_basic_imp(dig_t *c, const dig_t *a, const dig_t *b, int size) {
int i;
dv_t s;
dv_null(s);
TRY {
/* We need a temporary variable so that c can be a or b. */
dv_new(s);
dv_zero(s, 2 * FB_DIGS);
dv_copy(s, b, size);
dv_zero(c, 2 * size);
if (a[0] & 1) {
dv_copy(c, b, size);
}
for (i = 1; i <= (FB_DIGIT * size) - 1; i++) {
fb_lsh1_low(s, s);
fb_rdc(s, s);
if (fb_get_bit(a, i)) {
fb_add(c, c, s);
}
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
dv_free(s);
}
}
/**
* 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);
}
}
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);
}
}
void fb_poly_add(fb_t c, fb_t a) {
if (c != a) {
fb_copy(c, a);
}
if (poly_a != 0) {
c[FB_DIGS - 1] ^= fb_poly[FB_DIGS - 1];
if (pos_a != FB_DIGS - 1) {
c[pos_a] ^= fb_poly[pos_a];
}
if (poly_b != 0 && poly_c != 0) {
if (pos_b != pos_a) {
c[pos_b] ^= fb_poly[pos_b];
}
if (pos_c != pos_a && pos_c != pos_b) {
c[pos_c] ^= fb_poly[pos_c];
}
}
if (pos_a != 0 && pos_b != 0 && pos_c != 0) {
c[0] ^= 1;
}
} else {
fb_add(c, a, fb_poly);
}
}
void eb_neg_projc(eb_t r, const eb_t p) {
fb_t t;
fb_null(t);
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (p->norm) {
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
fb_add(r->y, p->x, p->y);
r->norm = 1;
return;
}
TRY {
fb_new(t);
fb_mul(t, p->x, p->z);
fb_add(r->y, p->y, t);
if (r != p) {
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t);
}
}
/**
* 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);
}
}
/**
* 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);
}
}
void eb_neg_basic(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
fb_add(r->y, p->x, p->y);
r->norm = 1;
}
void eb_neg_basic(eb_t r, const eb_t p) {
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
switch (eb_curve_opt_c()) {
case OPT_ZERO:
fb_copy(r->y, p->y);
break;
case OPT_ONE:
fb_add_dig(r->y, p->y, (dig_t)1);
break;
case OPT_DIGIT:
fb_add_dig(r->y, p->y, eb_curve_get_c()[0]);
break;
default:
fb_add(r->y, p->y, eb_curve_get_c());
break;
}
r->norm = 1;
return;
}
#endif
fb_add(r->y, p->x, p->y);
r->norm = 1;
}
void fb2_mul_nor(fb2_t c, fb2_t a) {
fb_t t;
fb_null(t);
TRY {
fb_new(t);
fb_copy(t, a[1]);
fb_add(c[1], a[0], a[1]);
fb_copy(c[0], t);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fb_free(t);
}
}
void fb_mul_basic(fb_t c, const fb_t a, const fb_t b) {
int i;
dv_t s;
fb_t t;
dv_null(s);
fb_null(t);
TRY {
/* We need a temporary variable so that c can be a or b. */
fb_new(t);
dv_new(s);
fb_zero(t);
dv_zero(s + FB_DIGS, FB_DIGS);
fb_copy(s, b);
if (a[0] & 1) {
fb_copy(t, b);
}
for (i = 1; i < FB_BITS; i++) {
/* We are already shifting a temporary value, so this is more efficient
* than calling fb_lsh(). */
s[FB_DIGS] = fb_lsh1_low(s, s);
fb_rdc(s, s);
if (fb_get_bit(a, i)) {
fb_add(t, t, s);
}
}
if (fb_bits(t) > FB_BITS) {
fb_poly_add(c, t);
} else {
fb_copy(c, t);
}
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t);
fb_free(s);
}
}
/**
* 向编辑器当前位置插入字符串
* @param editor 编辑器
* @param str 字符串起始指针
* @param len 字符串长度
* @return 操作成功与否
*/
static bool raw_insert(editor_t *editor, const char *str,
text_line_size_t len)
{
text_line_t *tl = editor_current_line(editor);
if (fb_overflow(text_line_size_t, TEXT_LINE_SIZE_MAX, tl->size, len))
return false;
if (!text_line_allocate(editor, tl,
fb_add(text_line_size_t, tl->size, len), false)) {
return false;
}
text_line_size_t pos = editor->buffer_pos;
memmove(tl->buf + pos + len, tl->buf + pos, tl->size - pos);
memcpy(tl->buf + pos, str, len);
tl->size += len;
editor->buffer_pos += len;
return true;
}
void fb4_frb(fb4_t c, fb4_t a) {
int alpha;
if (FB_BITS % 4 == 3) {
alpha = 0;
} else {
alpha = 1;
}
if (alpha == 1) {
fb_add(c[0], a[0], a[1]);
fb_add(c[0], c[0], a[3]);
} else {
fb_add(c[0], a[0], a[1]);
fb_add(c[0], c[0], a[2]);
}
fb_add(c[1], a[1], a[2]);
if (alpha == 0) {
fb_add(c[1], c[1], a[3]);
}
fb_add(c[2], a[2], a[3]);
fb_copy(c[3], a[3]);
}
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]);
}
/**
* 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);
}
}
/**
* 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);
}
}
/**
* 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);
}
}
void eb_neg_projc(eb_t r, const eb_t p) {
fb_t t;
fb_null(t);
if (eb_is_infty(p)) {
eb_set_infty(r);
return;
}
if (p->norm) {
if (r != p) {
fb_copy(r->x, p->x);
fb_copy(r->z, p->z);
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
switch (eb_curve_opt_c()) {
case OPT_ZERO:
fb_copy(r->y, p->y);
break;
case OPT_ONE:
fb_add_dig(r->y, p->y, (dig_t)1);
break;
case OPT_DIGIT:
fb_add_dig(r->y, p->y, eb_curve_get_c()[0]);
break;
default:
fb_add(r->y, p->y, eb_curve_get_c());
break;
}
r->norm = 1;
return;
}
#endif
fb_add(r->y, p->x, p->y);
r->norm = 1;
return;
}
#if defined(EB_SUPER)
if (eb_curve_is_super()) {
fb_add(r->y, p->y, p->z);
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
r->norm = 0;
return;
}
#endif
TRY {
fb_new(t);
fb_mul(t, p->x, p->z);
fb_add(r->y, p->y, t);
if (r != p) {
fb_copy(r->z, p->z);
fb_copy(r->x, p->x);
}
r->norm = 0;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t);
}
}
/**
* Normalizes a point represented in lambda-coordinates.
*
* @param[out] r - the result.
* @param[in] p - the point to normalize.
*/
static void eb_norm_halve(eb_t r, const eb_t p) {
fb_add(r->y, p->x, p->y);
fb_mul(r->y, r->y, p->x);
fb_copy(r->x, p->x);
r->norm = 1;
}
/**
* 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);
}
}
/**
* 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);
}
}
/**
* 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
}
