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From:   Ard Biesheuvel <ardb@kernel.org>
To:     linux-crypto@vger.kernel.org
Cc:     herbert@gondor.apana.org.au, ebiggers@kernel.org,
        keescook@chromium.org, jason@zx2c4.com, nikunj@amd.com,
        Ard Biesheuvel <ardb@kernel.org>
Subject: [PATCH v4 2/3] crypto: gf128mul - make gf128mul_lle time invariant
Date:   Mon, 24 Oct 2022 08:30:51 +0200
Message-Id: <20221024063052.109148-3-ardb@kernel.org>
In-Reply-To: <20221024063052.109148-1-ardb@kernel.org>
References: <20221024063052.109148-1-ardb@kernel.org>
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The gf128mul library has different variants with different
memory/performance tradeoffs, where the faster ones use 4k or 64k lookup
tables precomputed at runtime, which are based on one of the
multiplication factors, which is commonly the key for keyed hash
algorithms such as GHASH.

The slowest variant is gf128_mul_lle() [and its bbe/ble counterparts],
which does not use precomputed lookup tables, but it still relies on a
single u16[256] lookup table which is input independent. The use of such
a table may cause the execution time of gf128_mul_lle() to correlate
with the value of the inputs, which is generally something that must be
avoided for cryptographic algorithms. On top of that, the function uses
a sequence of if () statements that conditionally invoke be128_xor()
based on which bits are set in the second argument of the function,
which is usually a pointer to the multiplication factor that represents
the key.

In order to remove the correlation between the execution time of
gf128_mul_lle() and the value of its inputs, let's address the
identified shortcomings:
- add a time invariant version of gf128mul_x8_lle() that replaces the
  table lookup with the expression that is used at compile time to
  populate the lookup table;
- make the invocations of be128_xor() unconditional, but pass a zero
  vector as the third argument if the associated bit in the key is
  cleared.

The resulting code is likely to be significantly slower. However, given
that this is the slowest version already, making it even slower in order
to make it more secure is assumed to be justified.

The bbe and ble counterparts could receive the same treatment, but the
former is never used anywhere in the kernel, and the latter is only
used in the driver for a asynchronous crypto h/w accelerator (Chelsio),
where timing variances are unlikely to matter.

Signed-off-by: Ard Biesheuvel <ardb@kernel.org>
---
 lib/crypto/gf128mul.c | 58 +++++++++++++-------
 1 file changed, 39 insertions(+), 19 deletions(-)

diff --git a/lib/crypto/gf128mul.c b/lib/crypto/gf128mul.c
index a69ae3e6c16c..cd0cb1d3bf36 100644
--- a/lib/crypto/gf128mul.c
+++ b/lib/crypto/gf128mul.c
@@ -146,6 +146,17 @@ static void gf128mul_x8_lle(be128 *x)
 	x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
 }
 
+/* time invariant version of gf128mul_x8_lle */
+static void gf128mul_x8_lle_ti(be128 *x)
+{
+	u64 a = be64_to_cpu(x->a);
+	u64 b = be64_to_cpu(x->b);
+	u64 _tt = xda_le(b & 0xff); /* avoid table lookup */
+
+	x->b = cpu_to_be64((b >> 8) | (a << 56));
+	x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
+}
+
 static void gf128mul_x8_bbe(be128 *x)
 {
 	u64 a = be64_to_cpu(x->a);
@@ -169,38 +180,47 @@ EXPORT_SYMBOL(gf128mul_x8_ble);
 
 void gf128mul_lle(be128 *r, const be128 *b)
 {
-	be128 p[8];
+	/*
+	 * The p array should be aligned to twice the size of its element type,
+	 * so that every even/odd pair is guaranteed to share a cacheline
+	 * (assuming a cacheline size of 32 bytes or more, which is by far the
+	 * most common). This ensures that each be128_xor() call in the loop
+	 * takes the same amount of time regardless of the value of 'ch', which
+	 * is derived from function parameter 'b', which is commonly used as a
+	 * key, e.g., for GHASH. The odd array elements are all set to zero,
+	 * making each be128_xor() a NOP if its associated bit in 'ch' is not
+	 * set, and this is equivalent to calling be128_xor() conditionally.
+	 * This approach aims to avoid leaking information about such keys
+	 * through execution time invariances.
+	 *
+	 * Unfortunately, __aligned(16) or higher does not work on x86 for
+	 * variables on the stack so we need to perform the alignment by hand.
+	 */
+	be128 array[16 + 3] = {};
+	be128 *p = PTR_ALIGN(&array[0], 2 * sizeof(be128));
 	int i;
 
 	p[0] = *r;
 	for (i = 0; i < 7; ++i)
-		gf128mul_x_lle(&p[i + 1], &p[i]);
+		gf128mul_x_lle(&p[2 * i + 2], &p[2 * i]);
 
 	memset(r, 0, sizeof(*r));
 	for (i = 0;;) {
 		u8 ch = ((u8 *)b)[15 - i];
 
-		if (ch & 0x80)
-			be128_xor(r, r, &p[0]);
-		if (ch & 0x40)
-			be128_xor(r, r, &p[1]);
-		if (ch & 0x20)
-			be128_xor(r, r, &p[2]);
-		if (ch & 0x10)
-			be128_xor(r, r, &p[3]);
-		if (ch & 0x08)
-			be128_xor(r, r, &p[4]);
-		if (ch & 0x04)
-			be128_xor(r, r, &p[5]);
-		if (ch & 0x02)
-			be128_xor(r, r, &p[6]);
-		if (ch & 0x01)
-			be128_xor(r, r, &p[7]);
+		be128_xor(r, r, &p[ 0 + !(ch & 0x80)]);
+		be128_xor(r, r, &p[ 2 + !(ch & 0x40)]);
+		be128_xor(r, r, &p[ 4 + !(ch & 0x20)]);
+		be128_xor(r, r, &p[ 6 + !(ch & 0x10)]);
+		be128_xor(r, r, &p[ 8 + !(ch & 0x08)]);
+		be128_xor(r, r, &p[10 + !(ch & 0x04)]);
+		be128_xor(r, r, &p[12 + !(ch & 0x02)]);
+		be128_xor(r, r, &p[14 + !(ch & 0x01)]);
 
 		if (++i >= 16)
 			break;
 
-		gf128mul_x8_lle(r);
+		gf128mul_x8_lle_ti(r); /* use the time invariant version */
 	}
 }
 EXPORT_SYMBOL(gf128mul_lle);
-- 
2.35.1