ECC constant time scalar multiplication support. First step in overhauling

the EC module.

From Billy Brumley and his team, via
https://github.com/libressl-portable/openbsd/pull/94

With tweaks from jsing and me.

ok jsing

5 files changed, 337 insertions, 46 deletions

diff --git a/lib/libcrypto/ec/ec2_smpl.c b/lib/libcrypto/ec/ec2_smpl.c
index 61575999904..358664afc14 100644
--- a/lib/libcrypto/ec/ec2_smpl.c
+++ b/lib/libcrypto/ec/ec2_smpl.c
@@ -1,4 +1,4 @@
-/* $OpenBSD: ec2_smpl.c,v 1.15 2017/01/29 17:49:23 beck Exp $ */
+/* $OpenBSD: ec2_smpl.c,v 1.16 2018/07/10 21:55:49 tb Exp $ */
 /* ====================================================================
  * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
  *
@@ -107,15 +107,11 @@ EC_GF2m_simple_method(void)
 		.point_cmp = ec_GF2m_simple_cmp,
 		.make_affine = ec_GF2m_simple_make_affine,
 		.points_make_affine = ec_GF2m_simple_points_make_affine,
-
-		/*
-		 * the following three method functions are defined in
-		 * ec2_mult.c
-		 */
-		.mul = ec_GF2m_simple_mul,
+		.mul_generator_ct = ec_GFp_simple_mul_generator_ct,
+		.mul_single_ct = ec_GFp_simple_mul_single_ct,
+		.mul_double_nonct = ec_GFp_simple_mul_double_nonct,
 		.precompute_mult = ec_GF2m_precompute_mult,
 		.have_precompute_mult = ec_GF2m_have_precompute_mult,
-
 		.field_mul = ec_GF2m_simple_field_mul,
 		.field_sqr = ec_GF2m_simple_field_sqr,
 		.field_div = ec_GF2m_simple_field_div,
diff --git a/lib/libcrypto/ec/ec_lcl.h b/lib/libcrypto/ec/ec_lcl.h
index e1c91e67ab9..4916d3a14a2 100644
--- a/lib/libcrypto/ec/ec_lcl.h
+++ b/lib/libcrypto/ec/ec_lcl.h
@@ -1,4 +1,4 @@
-/* $OpenBSD: ec_lcl.h,v 1.7 2016/12/21 15:49:29 jsing Exp $ */
+/* $OpenBSD: ec_lcl.h,v 1.8 2018/07/10 21:55:49 tb Exp $ */
 /*
  * Originally written by Bodo Moeller for the OpenSSL project.
  */
@@ -160,10 +160,12 @@ struct ec_method_st {
 	int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
 	int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 
-	/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
-	 * (default implementations are used if the 'mul' pointer is 0): */
-	int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
-		size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
+	/* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult */
+	int (*mul_generator_ct)(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar, BN_CTX *);
+	int (*mul_single_ct)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+		const EC_POINT *point, BN_CTX *);
+	int (*mul_double_nonct)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
+		const BIGNUM *p_scalar, const EC_POINT *point, BN_CTX *);
 	int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
 	int (*have_precompute_mult)(const EC_GROUP *group);
 
@@ -337,6 +339,11 @@ int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
 int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
 int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+int ec_GFp_simple_mul_generator_ct(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar, BN_CTX *);
+int ec_GFp_simple_mul_single_ct(const EC_GROUP *, EC_POINT *r, const BIGNUM *scalar,
+	const EC_POINT *point, BN_CTX *);
+int ec_GFp_simple_mul_double_nonct(const EC_GROUP *, EC_POINT *r, const BIGNUM *g_scalar,
+	const BIGNUM *p_scalar, const EC_POINT *point, BN_CTX *);
 
 
 /* method functions in ecp_mont.c */
diff --git a/lib/libcrypto/ec/ec_lib.c b/lib/libcrypto/ec/ec_lib.c
index 0d062111b59..5580375321b 100644
--- a/lib/libcrypto/ec/ec_lib.c
+++ b/lib/libcrypto/ec/ec_lib.c
@@ -1,4 +1,4 @@
-/* $OpenBSD: ec_lib.c,v 1.24 2017/05/02 03:59:44 deraadt Exp $ */
+/* $OpenBSD: ec_lib.c,v 1.25 2018/07/10 21:55:49 tb Exp $ */
 /*
  * Originally written by Bodo Moeller for the OpenSSL project.
  */
@@ -1026,47 +1026,88 @@ EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[],
 }
 
 
-/* Functions for point multiplication.
- *
- * If group->meth->mul is 0, we use the wNAF-based implementations in ec_mult.c;
- * otherwise we dispatch through methods.
- */
-
+/* Functions for point multiplication */
 int 
 EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
     size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
 {
-	if (group->meth->mul == 0)
-		/* use default */
-		return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
-
-	return group->meth->mul(group, r, scalar, num, points, scalars, ctx);
+	/*
+	 * The function pointers must be set, and only support num == 0 and
+	 * num == 1.
+	 */
+	if (group->meth->mul_generator_ct == NULL ||
+	    group->meth->mul_single_ct == NULL ||
+	    group->meth->mul_double_nonct == NULL ||
+	    num > 1) {
+		ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+		return 0;
+	}
+	
+	/* Either bP or aG + bP, this is sane. */
+	if (num == 1 && points != NULL && scalars != NULL)
+		return EC_POINT_mul(group, r, scalar, points[0], scalars[0],
+		    ctx);
+	
+	/* aG, this is sane */
+	if (scalar != NULL && points == NULL && scalars == NULL)
+		return EC_POINT_mul(group, r, scalar, NULL, NULL, ctx);
+	
+	/* anything else is an error */
+	ECerror(ERR_R_EC_LIB);
+	return 0;
 }
 
 int 
 EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
     const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
 {
-	/* just a convenient interface to EC_POINTs_mul() */
-
-	const EC_POINT *points[1];
-	const BIGNUM *scalars[1];
-
-	points[0] = point;
-	scalars[0] = p_scalar;
-
-	return EC_POINTs_mul(group, r, g_scalar,
-	    (point != NULL && p_scalar != NULL),
-	    points, scalars, ctx);
+	if (group->meth->mul_generator_ct == NULL ||
+	    group->meth->mul_single_ct == NULL ||
+	    group->meth->mul_double_nonct == NULL) {
+		ECerror(ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+		return 0;
+	}
+	if (g_scalar != NULL && point == NULL && p_scalar == NULL) {
+		/*
+		 * In this case we want to compute g_scalar * GeneratorPoint:
+		 * this codepath is reached most prominently by (ephemeral) key
+		 * generation of EC cryptosystems (i.e. ECDSA keygen and sign
+		 * setup, ECDH keygen/first half), where the scalar is always
+		 * secret. This is why we ignore if BN_FLG_CONSTTIME is actually
+		 * set and we always call the constant time version.
+		 */
+		return group->meth->mul_generator_ct(group, r, g_scalar, ctx);
+	}
+	if (g_scalar == NULL && point != NULL && p_scalar != NULL) {
+		/* In this case we want to compute p_scalar * GenericPoint:
+		 * this codepath is reached most prominently by the second half
+		 * of ECDH, where the secret scalar is multiplied by the peer's
+		 * public point. To protect the secret scalar, we ignore if
+		 * BN_FLG_CONSTTIME is actually set and we always call the
+		 * constant time version.
+		 */
+		return group->meth->mul_single_ct(group, r, p_scalar, point,
+		    ctx);
+	}
+	if (g_scalar != NULL && point != NULL && p_scalar != NULL) {
+		/*
+		 * In this case we want to compute
+		 *   g_scalar * GeneratorPoint + p_scalar * GenericPoint:
+		 * this codepath is reached most prominently by ECDSA signature
+		 * verification. So we call the non-ct version.
+		 */
+		return group->meth->mul_double_nonct(group, r, g_scalar,
+		    p_scalar, point, ctx);
+	}
+		
+	/* Anything else is an error. */
+	ECerror(ERR_R_EC_LIB);
+	return 0;
 }
 
 int 
 EC_GROUP_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
 {
-	if (group->meth->mul == 0)
-		/* use default */
-		return ec_wNAF_precompute_mult(group, ctx);
-
 	if (group->meth->precompute_mult != 0)
 		return group->meth->precompute_mult(group, ctx);
 	else
@@ -1076,10 +1117,6 @@ EC_GROUP_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
 int 
 EC_GROUP_have_precompute_mult(const EC_GROUP * group)
 {
-	if (group->meth->mul == 0)
-		/* use default */
-		return ec_wNAF_have_precompute_mult(group);
-
 	if (group->meth->have_precompute_mult != 0)
 		return group->meth->have_precompute_mult(group);
 	else
diff --git a/lib/libcrypto/ec/ecp_mont.c b/lib/libcrypto/ec/ecp_mont.c
index 68fc26de1ec..8b4c529222e 100644
--- a/lib/libcrypto/ec/ecp_mont.c
+++ b/lib/libcrypto/ec/ecp_mont.c
@@ -1,4 +1,4 @@
-/* $OpenBSD: ecp_mont.c,v 1.11 2017/01/29 17:49:23 beck Exp $ */
+/* $OpenBSD: ecp_mont.c,v 1.12 2018/07/10 21:55:49 tb Exp $ */
 /*
  * Originally written by Bodo Moeller for the OpenSSL project.
  */
@@ -102,6 +102,9 @@ EC_GFp_mont_method(void)
 		.point_cmp = ec_GFp_simple_cmp,
 		.make_affine = ec_GFp_simple_make_affine,
 		.points_make_affine = ec_GFp_simple_points_make_affine,
+		.mul_generator_ct = ec_GFp_simple_mul_generator_ct,
+		.mul_single_ct = ec_GFp_simple_mul_single_ct,
+		.mul_double_nonct = ec_GFp_simple_mul_double_nonct,
 		.field_mul = ec_GFp_mont_field_mul,
 		.field_sqr = ec_GFp_mont_field_sqr,
 		.field_encode = ec_GFp_mont_field_encode,
diff --git a/lib/libcrypto/ec/ecp_smpl.c b/lib/libcrypto/ec/ecp_smpl.c
index ddba49c693d..402ee2294d9 100644
--- a/lib/libcrypto/ec/ecp_smpl.c
+++ b/lib/libcrypto/ec/ecp_smpl.c
@@ -1,4 +1,4 @@
-/* $OpenBSD: ecp_smpl.c,v 1.17 2017/01/29 17:49:23 beck Exp $ */
+/* $OpenBSD: ecp_smpl.c,v 1.18 2018/07/10 21:55:49 tb Exp $ */
 /* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de>
  * for the OpenSSL project.
  * Includes code written by Bodo Moeller for the OpenSSL project.
@@ -103,6 +103,9 @@ EC_GFp_simple_method(void)
 		.point_cmp = ec_GFp_simple_cmp,
 		.make_affine = ec_GFp_simple_make_affine,
 		.points_make_affine = ec_GFp_simple_points_make_affine,
+		.mul_generator_ct = ec_GFp_simple_mul_generator_ct,
+		.mul_single_ct = ec_GFp_simple_mul_single_ct,
+		.mul_double_nonct = ec_GFp_simple_mul_double_nonct,
 		.field_mul = ec_GFp_simple_field_mul,
 		.field_sqr = ec_GFp_simple_field_sqr
 	};
@@ -1409,3 +1412,248 @@ ec_GFp_simple_field_sqr(const EC_GROUP * group, BIGNUM * r, const BIGNUM * a, BN
 {
 	return BN_mod_sqr(r, a, &group->field, ctx);
 }
+
+#define EC_POINT_BN_set_flags(P, flags) do {				\
+	BN_set_flags(&(P)->X, (flags));         			\
+	BN_set_flags(&(P)->Y, (flags));         			\
+	BN_set_flags(&(P)->Z, (flags));         			\
+} while(0)
+
+#define EC_POINT_CSWAP(c, a, b, w, t) do {      			\
+	if (!BN_swap_ct(c, &(a)->X, &(b)->X, w)	||			\
+	    !BN_swap_ct(c, &(a)->Y, &(b)->Y, w)	|| 			\
+	    !BN_swap_ct(c, &(a)->Z, &(b)->Z, w))			\
+		goto err;						\
+	t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c);			\
+	(a)->Z_is_one ^= (t);						\
+	(b)->Z_is_one ^= (t);						\
+} while(0)
+
+/*
+ * This function computes (in constant time) a point multiplication over the
+ * EC group.
+ *
+ * At a high level, it is Montgomery ladder with conditional swaps.
+ *
+ * It performs either a fixed point multiplication
+ *          (scalar * generator)
+ * when point is NULL, or a variable point multiplication
+ *          (scalar * point)
+ * when point is not NULL.
+ *
+ * scalar should be in the range [0,n) otherwise all constant time bets are off.
+ *
+ * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
+ * which of course are not constant time themselves.
+ *
+ * The product is stored in r.
+ *
+ * Returns 1 on success, 0 otherwise.
+ */
+static int
+ec_GFp_simple_mul_ct(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+    const EC_POINT *point, BN_CTX *ctx)
+{
+	int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
+	EC_POINT *s = NULL;
+	BIGNUM *k = NULL;
+	BIGNUM *lambda = NULL;
+	BIGNUM *cardinality = NULL;
+	BN_CTX *new_ctx = NULL;
+	int ret = 0;
+
+	if (ctx == NULL && (ctx = new_ctx = BN_CTX_new()) == NULL)
+		return 0;
+
+	BN_CTX_start(ctx);
+
+	if ((s = EC_POINT_new(group)) == NULL)
+		goto err;
+
+	if (point == NULL) {
+		if (!EC_POINT_copy(s, group->generator))
+			goto err;
+	} else {
+		if (!EC_POINT_copy(s, point))
+			goto err;
+	}
+
+	EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
+
+	if ((cardinality = BN_CTX_get(ctx)) == NULL)
+		goto err;
+	if ((lambda = BN_CTX_get(ctx)) == NULL)
+		goto err;
+	if ((k = BN_CTX_get(ctx)) == NULL)
+		goto err;
+	if (!BN_mul(cardinality, &group->order, &group->cofactor, ctx))
+		goto err;
+
+	/*
+	 * Group cardinalities are often on a word boundary.
+	 * So when we pad the scalar, some timing diff might
+	 * pop if it needs to be expanded due to carries.
+	 * So expand ahead of time.
+	 */
+	cardinality_bits = BN_num_bits(cardinality);
+	group_top = cardinality->top;
+	if ((bn_wexpand(k, group_top + 1) == NULL) ||
+	    (bn_wexpand(lambda, group_top + 1) == NULL))
+		goto err;
+
+	if (!BN_copy(k, scalar))
+		goto err;
+
+	BN_set_flags(k, BN_FLG_CONSTTIME);
+
+	if (BN_num_bits(k) > cardinality_bits || BN_is_negative(k)) {
+		/*
+		 * This is an unusual input, and we don't guarantee
+		 * constant-timeness
+		 */
+		if (!BN_nnmod(k, k, cardinality, ctx))
+			goto err;
+	}
+
+	if (!BN_add(lambda, k, cardinality))
+		goto err;
+	BN_set_flags(lambda, BN_FLG_CONSTTIME);
+	if (!BN_add(k, lambda, cardinality))
+		goto err;
+	/*
+	 * lambda := scalar + cardinality
+	 * k := scalar + 2*cardinality
+	 */
+	kbit = BN_is_bit_set(lambda, cardinality_bits);
+	if (!BN_swap_ct(kbit, k, lambda, group_top + 1))
+		goto err;
+
+	group_top = group->field.top;
+	if ((bn_wexpand(&s->X, group_top) == NULL) ||
+	    (bn_wexpand(&s->Y, group_top) == NULL) ||
+	    (bn_wexpand(&s->Z, group_top) == NULL) ||
+	    (bn_wexpand(&r->X, group_top) == NULL) ||
+	    (bn_wexpand(&r->Y, group_top) == NULL) ||
+	    (bn_wexpand(&r->Z, group_top) == NULL))
+		goto err;
+
+	/* top bit is a 1, in a fixed pos */
+	if (!EC_POINT_copy(r, s))
+		goto err;
+
+	EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
+
+	if (!EC_POINT_dbl(group, s, s, ctx))
+		goto err;
+
+	pbit = 0;
+
+	/*
+	 * The ladder step, with branches, is
+	 *
+	 * k[i] == 0: S = add(R, S), R = dbl(R)
+	 * k[i] == 1: R = add(S, R), S = dbl(S)
+	 *
+	 * Swapping R, S conditionally on k[i] leaves you with state
+	 *
+	 * k[i] == 0: T, U = R, S
+	 * k[i] == 1: T, U = S, R
+	 *
+	 * Then perform the ECC ops.
+	 *
+	 * U = add(T, U)
+	 * T = dbl(T)
+	 *
+	 * Which leaves you with state
+	 *
+	 * k[i] == 0: U = add(R, S), T = dbl(R)
+	 * k[i] == 1: U = add(S, R), T = dbl(S)
+	 *
+	 * Swapping T, U conditionally on k[i] leaves you with state
+	 *
+	 * k[i] == 0: R, S = T, U
+	 * k[i] == 1: R, S = U, T
+	 *
+	 * Which leaves you with state
+	 *
+	 * k[i] == 0: S = add(R, S), R = dbl(R)
+	 * k[i] == 1: R = add(S, R), S = dbl(S)
+	 *
+	 * So we get the same logic, but instead of a branch it's a
+	 * conditional swap, followed by ECC ops, then another conditional swap.
+	 *
+	 * Optimization: The end of iteration i and start of i-1 looks like
+	 *
+	 * ...
+	 * CSWAP(k[i], R, S)
+	 * ECC
+	 * CSWAP(k[i], R, S)
+	 * (next iteration)
+	 * CSWAP(k[i-1], R, S)
+	 * ECC
+	 * CSWAP(k[i-1], R, S)
+	 * ...
+	 *
+	 * So instead of two contiguous swaps, you can merge the condition
+	 * bits and do a single swap.
+	 *
+	 * k[i]   k[i-1]    Outcome
+	 * 0      0         No Swap
+	 * 0      1         Swap
+	 * 1      0         Swap
+	 * 1      1         No Swap
+	 *
+	 * This is XOR. pbit tracks the previous bit of k.
+	 */
+
+	for (i = cardinality_bits - 1; i >= 0; i--) {
+		kbit = BN_is_bit_set(k, i) ^ pbit;
+		EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
+		if (!EC_POINT_add(group, s, r, s, ctx))
+			goto err;
+		if (!EC_POINT_dbl(group, r, r, ctx))
+			goto err;
+		/*
+		 * pbit logic merges this cswap with that of the
+		 * next iteration
+		 */
+		pbit ^= kbit;
+	}
+	/* one final cswap to move the right value into r */
+	EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
+	
+	ret = 1;
+
+ err:
+	EC_POINT_free(s);
+	if (ctx != NULL)
+		BN_CTX_end(ctx);
+	BN_CTX_free(new_ctx);
+
+	return ret;
+}
+
+#undef EC_POINT_BN_set_flags
+#undef EC_POINT_CSWAP
+
+int
+ec_GFp_simple_mul_generator_ct(const EC_GROUP *group, EC_POINT *r,
+    const BIGNUM *scalar, BN_CTX *ctx)
+{
+	return ec_GFp_simple_mul_ct(group, r, scalar, NULL, ctx);
+}
+
+int
+ec_GFp_simple_mul_single_ct(const EC_GROUP *group, EC_POINT *r,
+    const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
+{
+	return ec_GFp_simple_mul_ct(group, r, scalar, point, ctx);
+}
+
+int
+ec_GFp_simple_mul_double_nonct(const EC_GROUP *group, EC_POINT *r,
+    const BIGNUM *g_scalar, const BIGNUM *p_scalar, const EC_POINT *point,
+    BN_CTX *ctx)
+{
+	return ec_wNAF_mul(group, r, g_scalar, 1, &point, &p_scalar, ctx);
+}