ret=1;
err:
BN_CTX_end(ctx);
+ bn_check_top(r);
return(ret);
}
{
if (!BN_lshift(a,a,shifts)) goto err;
}
+ bn_check_top(a);
return(a);
err:
return(NULL);
/* solves ax == 1 (mod n) */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx);
BIGNUM *BN_mod_inverse(BIGNUM *in,
const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
{
BIGNUM *ret=NULL;
int sign;
+ if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
+ {
+ return BN_mod_inverse_no_branch(in, a, n, ctx);
+ }
+
bn_check_top(a);
bn_check_top(n);
if (!BN_nnmod(B, B, A, ctx)) goto err;
}
sign = -1;
- /* From B = a mod |n|, A = |n| it follows that
+ /*-
+ * From B = a mod |n|, A = |n| it follows that
*
* 0 <= B < A,
* -sign*X*a == B (mod |n|),
* sign*Y*a == A (mod |n|).
*/
- if (BN_is_odd(n) && (BN_num_bits(n) <= 400))
+ if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))
{
/* Binary inversion algorithm; requires odd modulus.
* This is faster than the general algorithm if the modulus
- * is sufficiently small. */
+ * is sufficiently small (about 400 .. 500 bits on 32-bit
+ * sytems, but much more on 64-bit systems) */
int shift;
while (!BN_is_zero(B))
{
- /*
+ /*-
* 0 < B < |n|,
* 0 < A <= |n|,
* (1) -sign*X*a == B (mod |n|),
}
- /* We still have (1) and (2).
+ /*-
+ * We still have (1) and (2).
* Both A and B are odd.
* The following computations ensure that
*
{
BIGNUM *tmp;
- /*
+ /*-
* 0 < B < A,
* (*) -sign*X*a == B (mod |n|),
* sign*Y*a == A (mod |n|)
if (!BN_div(D,M,A,B,ctx)) goto err;
}
- /* Now
+ /*-
+ * Now
* A = D*B + M;
* thus we have
* (**) sign*Y*a == D*B + M (mod |n|).
B=M;
/* ... so we have 0 <= B < A again */
- /* Since the former M is now B and the former B is now A,
+ /*-
+ * Since the former M is now B and the former B is now A,
* (**) translates into
* sign*Y*a == D*A + B (mod |n|),
* i.e.
}
}
- /*
+ /*-
* The while loop (Euclid's algorithm) ends when
* A == gcd(a,n);
* we have
err:
if ((ret == NULL) && (in == NULL)) BN_free(R);
BN_CTX_end(ctx);
+ bn_check_top(ret);
+ return(ret);
+ }
+
+
+/* BN_mod_inverse_no_branch is a special version of BN_mod_inverse.
+ * It does not contain branches that may leak sensitive information.
+ */
+static BIGNUM *BN_mod_inverse_no_branch(BIGNUM *in,
+ const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
+ {
+ BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
+ BIGNUM local_A, local_B;
+ BIGNUM *pA, *pB;
+ BIGNUM *ret=NULL;
+ int sign;
+
+ bn_check_top(a);
+ bn_check_top(n);
+
+ BN_CTX_start(ctx);
+ A = BN_CTX_get(ctx);
+ B = BN_CTX_get(ctx);
+ X = BN_CTX_get(ctx);
+ D = BN_CTX_get(ctx);
+ M = BN_CTX_get(ctx);
+ Y = BN_CTX_get(ctx);
+ T = BN_CTX_get(ctx);
+ if (T == NULL) goto err;
+
+ if (in == NULL)
+ R=BN_new();
+ else
+ R=in;
+ if (R == NULL) goto err;
+
+ BN_one(X);
+ BN_zero(Y);
+ if (BN_copy(B,a) == NULL) goto err;
+ if (BN_copy(A,n) == NULL) goto err;
+ A->neg = 0;
+
+ if (B->neg || (BN_ucmp(B, A) >= 0))
+ {
+ /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ pB = &local_B;
+ BN_with_flags(pB, B, BN_FLG_CONSTTIME);
+ if (!BN_nnmod(B, pB, A, ctx)) goto err;
+ }
+ sign = -1;
+ /*-
+ * From B = a mod |n|, A = |n| it follows that
+ *
+ * 0 <= B < A,
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ */
+
+ while (!BN_is_zero(B))
+ {
+ BIGNUM *tmp;
+
+ /*-
+ * 0 < B < A,
+ * (*) -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|)
+ */
+
+ /* Turn BN_FLG_CONSTTIME flag on, so that when BN_div is invoked,
+ * BN_div_no_branch will be called eventually.
+ */
+ pA = &local_A;
+ BN_with_flags(pA, A, BN_FLG_CONSTTIME);
+
+ /* (D, M) := (A/B, A%B) ... */
+ if (!BN_div(D,M,pA,B,ctx)) goto err;
+
+ /*-
+ * Now
+ * A = D*B + M;
+ * thus we have
+ * (**) sign*Y*a == D*B + M (mod |n|).
+ */
+
+ tmp=A; /* keep the BIGNUM object, the value does not matter */
+
+ /* (A, B) := (B, A mod B) ... */
+ A=B;
+ B=M;
+ /* ... so we have 0 <= B < A again */
+
+ /*-
+ * Since the former M is now B and the former B is now A,
+ * (**) translates into
+ * sign*Y*a == D*A + B (mod |n|),
+ * i.e.
+ * sign*Y*a - D*A == B (mod |n|).
+ * Similarly, (*) translates into
+ * -sign*X*a == A (mod |n|).
+ *
+ * Thus,
+ * sign*Y*a + D*sign*X*a == B (mod |n|),
+ * i.e.
+ * sign*(Y + D*X)*a == B (mod |n|).
+ *
+ * So if we set (X, Y, sign) := (Y + D*X, X, -sign), we arrive back at
+ * -sign*X*a == B (mod |n|),
+ * sign*Y*a == A (mod |n|).
+ * Note that X and Y stay non-negative all the time.
+ */
+
+ if (!BN_mul(tmp,D,X,ctx)) goto err;
+ if (!BN_add(tmp,tmp,Y)) goto err;
+
+ M=Y; /* keep the BIGNUM object, the value does not matter */
+ Y=X;
+ X=tmp;
+ sign = -sign;
+ }
+
+ /*-
+ * The while loop (Euclid's algorithm) ends when
+ * A == gcd(a,n);
+ * we have
+ * sign*Y*a == A (mod |n|),
+ * where Y is non-negative.
+ */
+
+ if (sign < 0)
+ {
+ if (!BN_sub(Y,n,Y)) goto err;
+ }
+ /* Now Y*a == A (mod |n|). */
+
+ if (BN_is_one(A))
+ {
+ /* Y*a == 1 (mod |n|) */
+ if (!Y->neg && BN_ucmp(Y,n) < 0)
+ {
+ if (!BN_copy(R,Y)) goto err;
+ }
+ else
+ {
+ if (!BN_nnmod(R,Y,n,ctx)) goto err;
+ }
+ }
+ else
+ {
+ BNerr(BN_F_BN_MOD_INVERSE_NO_BRANCH,BN_R_NO_INVERSE);
+ goto err;
+ }
+ ret=R;
+err:
+ if ((ret == NULL) && (in == NULL)) BN_free(R);
+ BN_CTX_end(ctx);
+ bn_check_top(ret);
return(ret);
}
projects / openssl.git / blobdiff