diff --git a/configure.ac b/configure.ac
index 3c86b79f..5c4f81f4 100644
--- a/configure.ac
+++ b/configure.ac
@@ -276,6 +276,7 @@ AC_DEFUN([CONFIGURE_KERNEL], [
 AC_DEFUN([CONFIGURE_NETTLE], [
 	AC_CHECK_HEADERS(nettle/sha.h,,
 		[AC_MSG_ERROR([You need Nettle cryptographic library.])])
+	AC_CHECK_HEADERS(nettle/version.h)
 
 	saved_LIBS=$LIBS
 	AC_CHECK_LIB(nettle, nettle_pbkdf2_hmac_sha256,,
diff --git a/lib/crypto_backend/crypto_nettle.c b/lib/crypto_backend/crypto_nettle.c
index dfaab1ff..0768d6b6 100644
--- a/lib/crypto_backend/crypto_nettle.c
+++ b/lib/crypto_backend/crypto_nettle.c
@@ -23,11 +23,19 @@
 #include <string.h>
 #include <errno.h>
 #include <nettle/sha.h>
+#include <nettle/sha3.h>
 #include <nettle/hmac.h>
 #include <nettle/pbkdf2.h>
 #include "crypto_backend.h"
 
-static char *version = "Nettle";
+#if HAVE_NETTLE_VERSION_H
+#include <nettle/version.h>
+#define VSTR(s) STR(s)
+#define STR(s) #s
+static const char *version = "Nettle "VSTR(NETTLE_VERSION_MAJOR)"."VSTR(NETTLE_VERSION_MINOR);
+#else
+static const char *version = "Nettle";
+#endif
 
 typedef void (*init_func) (void *);
 typedef void (*update_func) (void *, size_t, const uint8_t *);
@@ -45,6 +53,24 @@ struct hash_alg {
 	set_key_func hmac_set_key;
 };
 
+/* Missing HMAC wrappers in Nettle */
+#define HMAC_FCE(xxx) \
+struct xhmac_##xxx##_ctx HMAC_CTX(struct xxx##_ctx); \
+static void xhmac_##xxx##_set_key(struct xhmac_##xxx##_ctx *ctx, \
+size_t key_length, const uint8_t *key) \
+{HMAC_SET_KEY(ctx, &nettle_##xxx, key_length, key);} \
+static void xhmac_##xxx##_update(struct xhmac_##xxx##_ctx *ctx, \
+size_t length, const uint8_t *data) \
+{xxx##_update(&ctx->state, length, data);} \
+static void xhmac_##xxx##_digest(struct xhmac_##xxx##_ctx *ctx, \
+size_t length, uint8_t *digest) \
+{HMAC_DIGEST(ctx, &nettle_##xxx, length, digest);}
+
+HMAC_FCE(sha3_224);
+HMAC_FCE(sha3_256);
+HMAC_FCE(sha3_384);
+HMAC_FCE(sha3_512);
+
 static struct hash_alg hash_algs[] = {
 	{ "sha1", SHA1_DIGEST_SIZE,
 		(init_func) sha1_init,
@@ -94,6 +120,41 @@ static struct hash_alg hash_algs[] = {
 		(digest_func) hmac_ripemd160_digest,
 		(set_key_func) hmac_ripemd160_set_key,
 	},
+/* Nettle prior to version 3.2 has incompatible SHA3 implementation */
+#if NETTLE_SHA3_FIPS202
+	{ "sha3-224", SHA3_224_DIGEST_SIZE,
+		(init_func) sha3_224_init,
+		(update_func) sha3_224_update,
+		(digest_func) sha3_224_digest,
+		(update_func) xhmac_sha3_224_update,
+		(digest_func) xhmac_sha3_224_digest,
+		(set_key_func) xhmac_sha3_224_set_key,
+	},
+	{ "sha3-256", SHA3_256_DIGEST_SIZE,
+		(init_func) sha3_256_init,
+		(update_func) sha3_256_update,
+		(digest_func) sha3_256_digest,
+		(update_func) xhmac_sha3_256_update,
+		(digest_func) xhmac_sha3_256_digest,
+		(set_key_func) xhmac_sha3_256_set_key,
+	},
+	{ "sha3-384", SHA3_384_DIGEST_SIZE,
+		(init_func) sha3_384_init,
+		(update_func) sha3_384_update,
+		(digest_func) sha3_384_digest,
+		(update_func) xhmac_sha3_384_update,
+		(digest_func) xhmac_sha3_384_digest,
+		(set_key_func) xhmac_sha3_384_set_key,
+	},
+	{ "sha3-512", SHA3_512_DIGEST_SIZE,
+		(init_func) sha3_512_init,
+		(update_func) sha3_512_update,
+		(digest_func) sha3_512_digest,
+		(update_func) xhmac_sha3_512_update,
+		(digest_func) xhmac_sha3_512_digest,
+		(set_key_func) xhmac_sha3_512_set_key,
+	},
+#endif
 	{ NULL, 0, NULL, NULL, NULL, NULL, NULL, NULL, }
 };
 
@@ -106,6 +167,10 @@ struct crypt_hash {
 		struct sha384_ctx sha384;
 		struct sha512_ctx sha512;
 		struct ripemd160_ctx ripemd160;
+		struct sha3_224_ctx sha3_224;
+		struct sha3_256_ctx sha3_256;
+		struct sha3_384_ctx sha3_384;
+		struct sha3_512_ctx sha3_512;
 	} nettle_ctx;
 };
 
@@ -118,6 +183,10 @@ struct crypt_hmac {
 		struct hmac_sha384_ctx sha384;
 		struct hmac_sha512_ctx sha512;
 		struct hmac_ripemd160_ctx ripemd160;
+		struct xhmac_sha3_224_ctx sha3_224;
+		struct xhmac_sha3_256_ctx sha3_256;
+		struct xhmac_sha3_384_ctx sha3_384;
+		struct xhmac_sha3_512_ctx sha3_512;
 	} nettle_ctx;
 	size_t key_length;
 	uint8_t *key;
@@ -301,8 +370,8 @@ int crypt_pbkdf(const char *kdf, const char *hash,
 		if (r < 0)
 			return r;
 
-		nettle_pbkdf2(&h->nettle_ctx, h->hash->nettle_hmac_update,
-			      h->hash->nettle_hmac_digest, h->hash->length, iterations,
+		nettle_pbkdf2(&h->nettle_ctx, h->hash->hmac_update,
+			      h->hash->hmac_digest, h->hash->length, iterations,
 			      salt_length, (const uint8_t *)salt, key_length,
 			      (uint8_t *)key);
 		crypt_hmac_destroy(h);
diff --git a/tests/crypto-vectors.c b/tests/crypto-vectors.c
index 770042bb..9da00695 100644
--- a/tests/crypto-vectors.c
+++ b/tests/crypto-vectors.c
@@ -411,6 +411,10 @@ static int pbkdf_test_vectors(void)
 	for (i = 0; i < (sizeof(kdf_test_vectors) / sizeof(*kdf_test_vectors)); i++) {
 		vec = &kdf_test_vectors[i];
 		printf("PBKDF vector %02d %s ", i, vec->type);
+		if (vec->hash && crypt_hash_size(vec->hash) < 0) {
+			printf("[%s N/A]\n", vec->hash);
+			continue;
+		}
 		if (crypt_pbkdf(vec->type, vec->hash,
 		    vec->password, vec->password_length,
 		    vec->salt, vec->salt_length,