Fix timing leak in BN_from_montgomery_word.

BN_from_montgomery_word doesn't have a constant memory access pattern.
Replace the pointer trick with a constant-time select. There is, of
course, still the bn_correct_top leak pervasive in BIGNUM itself.

See also https://boringssl-review.googlesource.com/22904 from BoringSSL.

Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Kurt Roeckx <kurt@roeckx.be>
(Merged from https://github.com/openssl/openssl/pull/5228)

1 files changed, 20 insertions, 37 deletions

diff --git a/crypto/bn/bn_mont.c b/crypto/bn/bn_mont.c
index 2119bfa331..6357c60c77 100644
--- a/crypto/bn/bn_mont.c
+++ b/crypto/bn/bn_mont.c
@@ -101,6 +101,11 @@ static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
     r->top = max;
     n0 = mont->n0[0];
 
+    /*
+     * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
+     * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
+     * includes |carry| which is stored separately.
+     */
     for (carry = 0, i = 0; i < nl; i++, rp++) {
         v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
         v = (v + carry + rp[nl]) & BN_MASK2;
@@ -115,46 +120,24 @@ static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
     ret->neg = r->neg;
 
     rp = ret->d;
-    ap = &(r->d[nl]);
 
-# define BRANCH_FREE 1
-# if BRANCH_FREE
-    {
-        BN_ULONG *nrp;
-        size_t m;
+    /*
+     * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
+     * includes |carry| which is stored separately.
+     */
+    ap = &(r->d[nl]);
 
-        v = bn_sub_words(rp, ap, np, nl) - carry;
-        /*
-         * if subtraction result is real, then trick unconditional memcpy
-         * below to perform in-place "refresh" instead of actual copy.
-         */
-        m = (0 - (size_t)v);
-        nrp =
-            (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
-
-        for (i = 0, nl -= 4; i < nl; i += 4) {
-            BN_ULONG t1, t2, t3, t4;
-
-            t1 = nrp[i + 0];
-            t2 = nrp[i + 1];
-            t3 = nrp[i + 2];
-            ap[i + 0] = 0;
-            t4 = nrp[i + 3];
-            ap[i + 1] = 0;
-            rp[i + 0] = t1;
-            ap[i + 2] = 0;
-            rp[i + 1] = t2;
-            ap[i + 3] = 0;
-            rp[i + 2] = t3;
-            rp[i + 3] = t4;
-        }
-        for (nl += 4; i < nl; i++)
-            rp[i] = nrp[i], ap[i] = 0;
+    /*
+     * |v| is one if |ap| - |np| underflowed or zero if it did not. Note |v|
+     * cannot be -1. That would imply the subtraction did not fit in |nl| words,
+     * and we know at most one subtraction is needed.
+     */
+    v = bn_sub_words(rp, ap, np, nl) - carry;
+    v = 0 - v;
+    for (i = 0; i < nl; i++) {
+        rp[i] = (v & ap[i]) | (~v & rp[i]);
+        ap[i] = 0;
     }
-# else
-    if (bn_sub_words(rp, ap, np, nl) - carry)
-        memcpy(rp, ap, nl * sizeof(BN_ULONG));
-# endif
     bn_correct_top(r);
     bn_correct_top(ret);
     bn_check_top(ret);