Make BN_num_bits_word constant-time.

(This patch was written by Andy Polyakov. I only wrote the commit
message. Mistakes in the analysis are my fault.)

BN_num_bits, by way of BN_num_bits_word, currently leaks the
most-significant word of its argument via branching and memory access
pattern.

BN_num_bits is called on RSA prime factors in various places. These have
public bit lengths, but all bits beyond the high bit are secret. This
fully resolves those cases.

There are a few places where BN_num_bits is called on an input where the
bit length is also secret. This does *not* fully resolve those cases as
we still only look at the top word. Today, that is guaranteed to be
non-zero, but only because of the long-standing bn_correct_top timing
leak. Once that is fixed, a constant-time BN_num_bits on such inputs
must count bits on each word.

Instead, those cases should not call BN_num_bits at all. In particular,
BN_mod_exp_mont_consttime uses the exponent bit width to pick windows,
but it should be using the maximum bit width. The next patch will fix
this.

Thanks to Dinghao Wu, Danfeng Zhang, Shuai Wang, Pei Wang, and Xiao Liu
for reporting this issue.

Reviewed-by: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/5154)

1 files changed, 40 insertions, 67 deletions

diff --git a/crypto/bn/bn_lib.c b/crypto/bn/bn_lib.c
index b9f19d8968..57fe45288b 100644
--- a/crypto/bn/bn_lib.c
+++ b/crypto/bn/bn_lib.c
@@ -88,74 +88,47 @@ const BIGNUM *BN_value_one(void)
 
 int BN_num_bits_word(BN_ULONG l)
 {
-    static const unsigned char bits[256] = {
-        0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
-        5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
-        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
-        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
-        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
-        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
-        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
-        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-        8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
-    };
-
-#if defined(SIXTY_FOUR_BIT_LONG)
-    if (l & 0xffffffff00000000L) {
-        if (l & 0xffff000000000000L) {
-            if (l & 0xff00000000000000L) {
-                return (bits[(int)(l >> 56)] + 56);
-            } else
-                return (bits[(int)(l >> 48)] + 48);
-        } else {
-            if (l & 0x0000ff0000000000L) {
-                return (bits[(int)(l >> 40)] + 40);
-            } else
-                return (bits[(int)(l >> 32)] + 32);
-        }
-    } else
-#else
-# ifdef SIXTY_FOUR_BIT
-    if (l & 0xffffffff00000000LL) {
-        if (l & 0xffff000000000000LL) {
-            if (l & 0xff00000000000000LL) {
-                return (bits[(int)(l >> 56)] + 56);
-            } else
-                return (bits[(int)(l >> 48)] + 48);
-        } else {
-            if (l & 0x0000ff0000000000LL) {
-                return (bits[(int)(l >> 40)] + 40);
-            } else
-                return (bits[(int)(l >> 32)] + 32);
-        }
-    } else
-# endif
-#endif
-    {
-#if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
-        if (l & 0xffff0000L) {
-            if (l & 0xff000000L)
-                return (bits[(int)(l >> 24L)] + 24);
-            else
-                return (bits[(int)(l >> 16L)] + 16);
-        } else
-#endif
-        {
-#if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
-            if (l & 0xff00L)
-                return (bits[(int)(l >> 8)] + 8);
-            else
+    BN_ULONG x, mask;
+    int bits = (l != 0);
+
+#if BN_BITS2 > 32
+    x = l >> 32;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 32 & mask;
+    l ^= (x ^ l) & mask;
 #endif
-                return (bits[(int)(l)]);
-        }
-    }
+
+    x = l >> 16;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 16 & mask;
+    l ^= (x ^ l) & mask;
+
+    x = l >> 8;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 8 & mask;
+    l ^= (x ^ l) & mask;
+
+    x = l >> 4;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 4 & mask;
+    l ^= (x ^ l) & mask;
+
+    x = l >> 2;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 2 & mask;
+    l ^= (x ^ l) & mask;
+
+    x = l >> 1;
+    mask = (0 - x) & BN_MASK2;
+    mask = (0 - (mask >> (BN_BITS2 - 1)));
+    bits += 1 & mask;
+
+    return bits;
 }
 
 int BN_num_bits(const BIGNUM *a)