crypto: dh - implement private key generation primitive for ffdheXYZ(dh)

The support for NVME in-band authentication currently in the works ([1])
needs to generate ephemeral DH keys for use with the RFC 7919 safe-prime
FFDHE groups.

In analogy to ECDH and its ecc_gen_privkey(), implement a
dh_safe_prime_gen_privkey() and invoke it from the ffdheXYZ(dh) templates'
common ->set_secret(), i.e. dh_safe_prime_set_secret(), in case the input
->key_size is zero.

As the RFC 7919 FFDHE groups are classified as approved safe-prime groups
by SP800-56Arev3, it's worthwhile to make the new
dh_safe_prime_gen_privkey() to follow the approach specified in
SP800-56Arev3, sec. 5.6.1.1.3 ("Key-Pair Generation Using Extra Random
Bits") in order to achieve conformance.

SP800-56Arev3 specifies a lower as well as an upper bound on the generated
key's length:
- it must be >= two times the maximum supported security strength of
  the group in question and
- it must be <= the length of the domain parameter Q.

For any safe-prime group Q = (P - 1)/2 by definition and the individual
maximum supported security strengths as specified by SP800-56Arev3 have
been made available as part of the FFDHE dh_safe_prime definitions
introduced with a previous patch. Make dh_safe_prime_gen_privkey() pick
twice the maximum supported strength rounded up to the next power of two
for the output key size. This choice respects both, the lower and upper
bounds given by SP800-90Arev3 for any of the approved safe-prime groups and
is also in line with the NVME base spec 2.0, which requires the key size to
be >= 256bits.

[1] https://lore.kernel.org/r/[email protected]

Signed-off-by: Nicolai Stange <[email protected]>
Reviewed-by: Hannes Reinecke <[email protected]>
Signed-off-by: Herbert Xu <[email protected]>

crypto/Kconfig

@@ -234,6 +234,7 @@ config CRYPTO_DH
 config CRYPTO_DH_RFC7919_GROUPS
 	bool "Support for RFC 7919 FFDHE group parameters"
 	depends on CRYPTO_DH
+	select CRYPTO_RNG_DEFAULT
 	help
 	  Provide support for RFC 7919 FFDHE group parameters. If unsure, say N.
 

crypto/dh.c

@@ -10,6 +10,7 @@
 #include <crypto/internal/kpp.h>
 #include <crypto/kpp.h>
 #include <crypto/dh.h>
+#include <crypto/rng.h>
 #include <linux/mpi.h>
 
 struct dh_ctx {
@@ -315,14 +316,136 @@ static void dh_safe_prime_exit_tfm(struct crypto_kpp *tfm)
 	crypto_free_kpp(tfm_ctx->dh_tfm);
 }
 
+static u64 __add_u64_to_be(__be64 *dst, unsigned int n, u64 val)
+{
+	unsigned int i;
+
+	for (i = n; val && i > 0; --i) {
+		u64 tmp = be64_to_cpu(dst[i - 1]);
+
+		tmp += val;
+		val = tmp >= val ? 0 : 1;
+		dst[i - 1] = cpu_to_be64(tmp);
+	}
+
+	return val;
+}
+
+static void *dh_safe_prime_gen_privkey(const struct dh_safe_prime *safe_prime,
+				       unsigned int *key_size)
+{
+	unsigned int n, oversampling_size;
+	__be64 *key;
+	int err;
+	u64 h, o;
+
+	/*
+	 * Generate a private key following NIST SP800-56Ar3,
+	 * sec. 5.6.1.1.1 and 5.6.1.1.3 resp..
+	 *
+	 * 5.6.1.1.1: choose key length N such that
+	 * 2 * ->max_strength <= N <= log2(q) + 1 = ->p_size * 8 - 1
+	 * with q = (p - 1) / 2 for the safe-prime groups.
+	 * Choose the lower bound's next power of two for N in order to
+	 * avoid excessively large private keys while still
+	 * maintaining some extra reserve beyond the bare minimum in
+	 * most cases. Note that for each entry in safe_prime_groups[],
+	 * the following holds for such N:
+	 * - N >= 256, in particular it is a multiple of 2^6 = 64
+	 *   bits and
+	 * - N < log2(q) + 1, i.e. N respects the upper bound.
+	 */
+	n = roundup_pow_of_two(2 * safe_prime->max_strength);
+	WARN_ON_ONCE(n & ((1u << 6) - 1));
+	n >>= 6; /* Convert N into units of u64. */
+
+	/*
+	 * Reserve one extra u64 to hold the extra random bits
+	 * required as per 5.6.1.1.3.
+	 */
+	oversampling_size = (n + 1) * sizeof(__be64);
+	key = kmalloc(oversampling_size, GFP_KERNEL);
+	if (!key)
+		return ERR_PTR(-ENOMEM);
+
+	/*
+	 * 5.6.1.1.3, step 3 (and implicitly step 4): obtain N + 64
+	 * random bits and interpret them as a big endian integer.
+	 */
+	err = -EFAULT;
+	if (crypto_get_default_rng())
+		goto out_err;
+
+	err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)key,
+				   oversampling_size);
+	crypto_put_default_rng();
+	if (err)
+		goto out_err;
+
+	/*
+	 * 5.6.1.1.3, step 5 is implicit: 2^N < q and thus,
+	 * M = min(2^N, q) = 2^N.
+	 *
+	 * For step 6, calculate
+	 * key = (key[] mod (M - 1)) + 1 = (key[] mod (2^N - 1)) + 1.
+	 *
+	 * In order to avoid expensive divisions, note that
+	 * 2^N mod (2^N - 1) = 1 and thus, for any integer h,
+	 * 2^N * h mod (2^N - 1) = h mod (2^N - 1) always holds.
+	 * The big endian integer key[] composed of n + 1 64bit words
+	 * may be written as key[] = h * 2^N + l, with h = key[0]
+	 * representing the 64 most significant bits and l
+	 * corresponding to the remaining 2^N bits. With the remark
+	 * from above,
+	 * h * 2^N + l mod (2^N - 1) = l + h mod (2^N - 1).
+	 * As both, l and h are less than 2^N, their sum after
+	 * this first reduction is guaranteed to be <= 2^(N + 1) - 2.
+	 * Or equivalently, that their sum can again be written as
+	 * h' * 2^N + l' with h' now either zero or one and if one,
+	 * then l' <= 2^N - 2. Thus, all bits at positions >= N will
+	 * be zero after a second reduction:
+	 * h' * 2^N + l' mod (2^N - 1) = l' + h' mod (2^N - 1).
+	 * At this point, it is still possible that
+	 * l' + h' = 2^N - 1, i.e. that l' + h' mod (2^N - 1)
+	 * is zero. This condition will be detected below by means of
+	 * the final increment overflowing in this case.
+	 */
+	h = be64_to_cpu(key[0]);
+	h = __add_u64_to_be(key + 1, n, h);
+	h = __add_u64_to_be(key + 1, n, h);
+	WARN_ON_ONCE(h);
+
+	/* Increment to obtain the final result. */
+	o = __add_u64_to_be(key + 1, n, 1);
+	/*
+	 * The overflow bit o from the increment is either zero or
+	 * one. If zero, key[1:n] holds the final result in big-endian
+	 * order. If one, key[1:n] is zero now, but needs to be set to
+	 * one, c.f. above.
+	 */
+	if (o)
+		key[n] = cpu_to_be64(1);
+
+	/* n is in units of u64, convert to bytes. */
+	*key_size = n << 3;
+	/* Strip the leading extra __be64, which is (virtually) zero by now. */
+	memmove(key, &key[1], *key_size);
+
+	return key;
+
+out_err:
+	kfree_sensitive(key);
+	return ERR_PTR(err);
+}
+
 static int dh_safe_prime_set_secret(struct crypto_kpp *tfm, const void *buffer,
 				    unsigned int len)
 {
 	struct dh_safe_prime_instance_ctx *inst_ctx =
 		dh_safe_prime_instance_ctx(tfm);
 	struct dh_safe_prime_tfm_ctx *tfm_ctx = kpp_tfm_ctx(tfm);
 	struct dh params;
-	void *buf;
+	void *buf = NULL, *key = NULL;
 	unsigned int buf_size;
 	int err;
 
@@ -338,10 +461,20 @@ static int dh_safe_prime_set_secret(struct crypto_kpp *tfm, const void *buffer,
 	params.g = safe_prime_g;
 	params.g_size = sizeof(safe_prime_g);
 
+	if (!params.key_size) {
+		key = dh_safe_prime_gen_privkey(inst_ctx->safe_prime,
+						&params.key_size);
+		if (IS_ERR(key))
+			return PTR_ERR(key);
+		params.key = key;
+	}
+
 	buf_size = crypto_dh_key_len(&params);
 	buf = kmalloc(buf_size, GFP_KERNEL);
-	if (!buf)
-		return -ENOMEM;
+	if (!buf) {
+		err = -ENOMEM;
+		goto out;
+	}
 
 	err = crypto_dh_encode_key(buf, buf_size, &params);
 	if (err)
@@ -350,6 +483,7 @@ static int dh_safe_prime_set_secret(struct crypto_kpp *tfm, const void *buffer,
 	err = crypto_kpp_set_secret(tfm_ctx->dh_tfm, buf, buf_size);
 out:
 	kfree_sensitive(buf);
+	kfree_sensitive(key);
 	return err;
 }