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@@ -8,113 +8,7 @@
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*/
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#include "internal/cryptlib.h"
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-#include "bn_lcl.h"
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-
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-static BIGNUM *euclid(BIGNUM *a, BIGNUM *b);
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-
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-int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
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-{
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- BIGNUM *a, *b, *t;
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- int ret = 0;
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-
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- bn_check_top(in_a);
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- bn_check_top(in_b);
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-
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- BN_CTX_start(ctx);
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- a = BN_CTX_get(ctx);
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- b = BN_CTX_get(ctx);
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- if (b == NULL)
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- goto err;
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-
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- if (BN_copy(a, in_a) == NULL)
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- goto err;
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- if (BN_copy(b, in_b) == NULL)
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- goto err;
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- a->neg = 0;
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- b->neg = 0;
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-
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- if (BN_cmp(a, b) < 0) {
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- t = a;
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- a = b;
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- b = t;
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- }
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- t = euclid(a, b);
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- if (t == NULL)
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- goto err;
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-
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- if (BN_copy(r, t) == NULL)
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- goto err;
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- ret = 1;
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- err:
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- BN_CTX_end(ctx);
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- bn_check_top(r);
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- return ret;
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-}
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-
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-static BIGNUM *euclid(BIGNUM *a, BIGNUM *b)
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-{
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- BIGNUM *t;
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- int shifts = 0;
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-
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- bn_check_top(a);
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- bn_check_top(b);
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-
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- /* 0 <= b <= a */
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- while (!BN_is_zero(b)) {
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- /* 0 < b <= a */
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-
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- if (BN_is_odd(a)) {
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- if (BN_is_odd(b)) {
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- if (!BN_sub(a, a, b))
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- goto err;
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- if (!BN_rshift1(a, a))
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- goto err;
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- if (BN_cmp(a, b) < 0) {
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- t = a;
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- a = b;
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- b = t;
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- }
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- } else { /* a odd - b even */
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-
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- if (!BN_rshift1(b, b))
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- goto err;
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- if (BN_cmp(a, b) < 0) {
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- t = a;
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- a = b;
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- b = t;
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- }
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- }
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- } else { /* a is even */
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-
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- if (BN_is_odd(b)) {
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- if (!BN_rshift1(a, a))
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- goto err;
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- if (BN_cmp(a, b) < 0) {
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- t = a;
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- a = b;
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- b = t;
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- }
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- } else { /* a even - b even */
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-
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- if (!BN_rshift1(a, a))
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- goto err;
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- if (!BN_rshift1(b, b))
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- goto err;
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- shifts++;
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- }
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- }
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- /* 0 <= b <= a */
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- }
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-
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- if (shifts) {
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- if (!BN_lshift(a, a, shifts))
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- goto err;
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- }
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- bn_check_top(a);
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- return a;
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- err:
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- return NULL;
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-}
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+#include "bn_local.h"
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/* solves ax == 1 (mod n) */
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static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
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@@ -621,3 +515,115 @@ static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
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bn_check_top(ret);
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return ret;
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}
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+
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+/*-
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+ * This function is based on the constant-time GCD work by Bernstein and Yang:
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+ * https://eprint.iacr.org/2019/266
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+ * Generalized fast GCD function to allow even inputs.
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+ * The algorithm first finds the shared powers of 2 between
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+ * the inputs, and removes them, reducing at least one of the
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+ * inputs to an odd value. Then it proceeds to calculate the GCD.
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+ * Before returning the resulting GCD, we take care of adding
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+ * back the powers of two removed at the beginning.
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+ * Note 1: we assume the bit length of both inputs is public information,
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+ * since access to top potentially leaks this information.
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+ */
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+int BN_gcd(BIGNUM *r, const BIGNUM *in_a, const BIGNUM *in_b, BN_CTX *ctx)
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+{
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+ BIGNUM *g, *temp = NULL;
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+ BN_ULONG mask = 0;
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+ int i, j, top, rlen, glen, m, bit = 1, delta = 1, cond = 0, shifts = 0, ret = 0;
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+
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+ /* Note 2: zero input corner cases are not constant-time since they are
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+ * handled immediately. An attacker can run an attack under this
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+ * assumption without the need of side-channel information. */
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+ if (BN_is_zero(in_b)) {
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+ ret = BN_copy(r, in_a) != NULL;
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+ r->neg = 0;
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+ return ret;
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+ }
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+ if (BN_is_zero(in_a)) {
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+ ret = BN_copy(r, in_b) != NULL;
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+ r->neg = 0;
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+ return ret;
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+ }
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+
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+ bn_check_top(in_a);
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+ bn_check_top(in_b);
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+
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+ BN_CTX_start(ctx);
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+ temp = BN_CTX_get(ctx);
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+ g = BN_CTX_get(ctx);
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+
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+ /* make r != 0, g != 0 even, so BN_rshift is not a potential nop */
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+ if (g == NULL
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+ || !BN_lshift1(g, in_b)
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+ || !BN_lshift1(r, in_a))
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+ goto err;
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+
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+ /* find shared powers of two, i.e. "shifts" >= 1 */
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+ for (i = 0; i < r->dmax && i < g->dmax; i++) {
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+ mask = ~(r->d[i] | g->d[i]);
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+ for (j = 0; j < BN_BITS2; j++) {
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+ bit &= mask;
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+ shifts += bit;
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+ mask >>= 1;
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+ }
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+ }
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+
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+ /* subtract shared powers of two; shifts >= 1 */
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+ if (!BN_rshift(r, r, shifts)
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+ || !BN_rshift(g, g, shifts))
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+ goto err;
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+
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+ /* expand to biggest nword, with room for a possible extra word */
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+ top = 1 + ((r->top >= g->top) ? r->top : g->top);
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+ if (bn_wexpand(r, top) == NULL
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+ || bn_wexpand(g, top) == NULL
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+ || bn_wexpand(temp, top) == NULL)
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+ goto err;
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+
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+ /* re arrange inputs s.t. r is odd */
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+ BN_consttime_swap((~r->d[0]) & 1, r, g, top);
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+
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+ /* compute the number of iterations */
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+ rlen = BN_num_bits(r);
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+ glen = BN_num_bits(g);
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+ m = 4 + 3 * ((rlen >= glen) ? rlen : glen);
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+
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+ for (i = 0; i < m; i++) {
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+ /* conditionally flip signs if delta is positive and g is odd */
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+ cond = (-delta >> (8 * sizeof(delta) - 1)) & g->d[0] & 1
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+ /* make sure g->top > 0 (i.e. if top == 0 then g == 0 always) */
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+ & (~((g->top - 1) >> (sizeof(g->top) * 8 - 1)));
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+ delta = (-cond & -delta) | ((cond - 1) & delta);
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+ r->neg ^= cond;
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+ /* swap */
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+ BN_consttime_swap(cond, r, g, top);
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+
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+ /* elimination step */
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+ delta++;
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+ if (!BN_add(temp, g, r))
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+ goto err;
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+ BN_consttime_swap(g->d[0] & 1 /* g is odd */
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+ /* make sure g->top > 0 (i.e. if top == 0 then g == 0 always) */
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+ & (~((g->top - 1) >> (sizeof(g->top) * 8 - 1))),
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+ g, temp, top);
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+ if (!BN_rshift1(g, g))
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+ goto err;
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+ }
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+
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+ /* remove possible negative sign */
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+ r->neg = 0;
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+ /* add powers of 2 removed, then correct the artificial shift */
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+ if (!BN_lshift(r, r, shifts)
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+ || !BN_rshift1(r, r))
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+ goto err;
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+
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+ ret = 1;
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+
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+ err:
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+ BN_CTX_end(ctx);
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+ bn_check_top(r);
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+ return ret;
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+}
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