diff --git a/nettle/ChangeLog b/nettle/ChangeLog
index bb169e86..4787cff6 100644
--- a/nettle/ChangeLog
+++ b/nettle/ChangeLog
@@ -1,3 +1,39 @@
+2021-05-22  Niels Möller  <nisse@lysator.liu.se>
+
+	* configure.ac: Bump package version, to 3.7.3.
+	(LIBNETTLE_MINOR): Bump minor number, to 8.4.
+	(LIBHOGWEED_MINOR): Bump minor number, to 6.4.
+
+2021-05-17  Niels Möller  <nisse@lysator.liu.se>
+
+	* rsa-decrypt-tr.c (rsa_decrypt_tr): Check up-front that input is
+	in range.
+	* rsa-sec-decrypt.c (rsa_sec_decrypt): Likewise.
+	* rsa-decrypt.c (rsa_decrypt): Likewise.
+	* testsuite/rsa-encrypt-test.c (test_main): Add tests with input > n.
+
+2021-05-14  Niels Möller  <nisse@lysator.liu.se>
+
+	* rsa-sign-tr.c (rsa_sec_blind): Delete mn argument.
+	(_rsa_sec_compute_root_tr): Delete mn argument, instead require
+	that input size matches key size. Rearrange use of temporary
+	storage, to support in-place operation, x == m. Update all
+	callers.
+
+	* rsa-decrypt-tr.c (rsa_decrypt_tr): Make zero-padded copy of
+	input, for calling _rsa_sec_compute_root_tr.
+	* rsa-sec-decrypt.c (rsa_sec_decrypt): Likewise.
+
+	* testsuite/rsa-encrypt-test.c (test_main): Test calling all of
+	rsa_decrypt, rsa_decrypt_tr, and rsa_sec_decrypt with zero input.
+
+2021-05-06  Niels Möller  <nisse@lysator.liu.se>
+
+	* pkcs1-sec-decrypt.c (_pkcs1_sec_decrypt): Check that message
+	length is valid, for given key size.
+	* testsuite/rsa-sec-decrypt-test.c (test_main): Add test cases for
+	calls to rsa_sec_decrypt specifying a too large message length.
+
 2021-03-21  Niels Möller  <nisse@lysator.liu.se>
 
 	* NEWS: NEWS entries for 3.7.2.
diff --git a/nettle/NEWS b/nettle/NEWS
index 897527c9..277ef383 100644
--- a/nettle/NEWS
+++ b/nettle/NEWS
@@ -1,3 +1,40 @@
+NEWS for the Nettle 3.7.3 release
+
+	This is bugfix release, fixing bugs that could make the RSA
+	decryption functions crash on invalid inputs.
+
+	Upgrading to the new version is strongly recommended. For
+	applications that want to support older versions of Nettle,
+	the bug can be worked around by adding a check that the RSA
+	ciphertext is in the range 0 < ciphertext < n, before
+	attempting to decrypt it.
+
+	Thanks to Justus Winter for reporting these problems.
+
+	The new version is intended to be fully source and binary
+	compatible with Nettle-3.6. The shared library names are
+	libnettle.so.8.4 and libhogweed.so.6.4, with sonames
+	libnettle.so.8 and libhogweed.so.6.
+
+	Bug fixes:
+
+	* Fix crash for zero input to rsa_sec_decrypt and
+	  rsa_decrypt_tr. Potential denial of service vector.
+
+	* Ensure that all of rsa_decrypt_tr and rsa_sec_decrypt return
+	  failure for out of range inputs, instead of either crashing,
+	  or silently reducing input modulo n. Potential denial of
+	  service vector.
+
+	* Ensure that all of rsa_decrypt returns failure for out of
+	  range inputs, instead of silently reducing input modulo n.
+
+	* Ensure that rsa_sec_decrypt returns failure if the message
+	  size is too large for the given key. Unlike the other bugs,
+	  this would typically be triggered by invalid local
+	  configuration, rather than by processing untrusted remote
+	  data.
+
 NEWS for the Nettle 3.7.2 release
 
 	This is a bugfix release, fixing a bug in ECDSA signature
diff --git a/nettle/configure.ac b/nettle/configure.ac
index 9b2c153b..f4d9e905 100644
--- a/nettle/configure.ac
+++ b/nettle/configure.ac
@@ -2,7 +2,7 @@ dnl -*- mode: shell-script; sh-indentation: 2; -*-
 
 dnl Process this file with autoconf to produce a configure script.
 
-AC_INIT([nettle], [3.7.2], [nettle-bugs@lists.lysator.liu.se])
+AC_INIT([nettle], [3.7.3], [nettle-bugs@lists.lysator.liu.se])
 AC_PREREQ(2.61)
 AC_CONFIG_SRCDIR([arcfour.c])
 # Needed to stop autoconf from looking for files in parent directories.
@@ -11,10 +11,10 @@ AC_CONFIG_AUX_DIR([.])
 AC_CONFIG_HEADER([config.h])
 
 LIBNETTLE_MAJOR=8
-LIBNETTLE_MINOR=3
+LIBNETTLE_MINOR=4
 
 LIBHOGWEED_MAJOR=6
-LIBHOGWEED_MINOR=3
+LIBHOGWEED_MINOR=4
 
 dnl Note double square brackets, for extra m4 quoting.
 MAJOR_VERSION=`echo $PACKAGE_VERSION | sed 's/^\([[^.]]*\)\..*/\1/'`
diff --git a/nettle/pkcs1-sec-decrypt.c b/nettle/pkcs1-sec-decrypt.c
index 4f13080e..942a2bd3 100644
--- a/nettle/pkcs1-sec-decrypt.c
+++ b/nettle/pkcs1-sec-decrypt.c
@@ -63,7 +63,9 @@ _pkcs1_sec_decrypt (size_t length, uint8_t *message,
   volatile int ok;
   size_t i, t;
 
-  assert (padded_message_length >= length);
+  /* Message independent branch */
+  if (length + 11 > padded_message_length)
+    return 0;
 
   t = padded_message_length - length - 1;
 
@@ -99,8 +101,8 @@ _pkcs1_sec_decrypt_variable(size_t *length, uint8_t *message,
 
   /* length is discovered in a side-channel silent way.
    * not_found goes to 0 when the terminator is found.
-   * offset strts at 3 as it includes the terminator and
-   * the fomat bytes already */
+   * offset starts at 3 as it includes the terminator and
+   * the format bytes already */
   offset = 3;
   for (i = 2; i < padded_message_length; i++)
     {
diff --git a/nettle/rsa-decrypt-tr.c b/nettle/rsa-decrypt-tr.c
index 0224c0b7..4a9e9d74 100644
--- a/nettle/rsa-decrypt-tr.c
+++ b/nettle/rsa-decrypt-tr.c
@@ -52,14 +52,17 @@ rsa_decrypt_tr(const struct rsa_public_key *pub,
   mp_size_t key_limb_size;
   int res;
 
-  key_limb_size = NETTLE_OCTET_SIZE_TO_LIMB_SIZE(key->size);
+  /* First check that input is in range. */
+  if (mpz_sgn (gibberish) < 0 || mpz_cmp (gibberish, pub->n) >= 0)
+    return 0;
+
+  key_limb_size = mpz_size(pub->n);
 
   TMP_GMP_ALLOC (m, key_limb_size);
   TMP_GMP_ALLOC (em, key->size);
+  mpz_limbs_copy(m, gibberish, key_limb_size);
 
-  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, m,
-				  mpz_limbs_read(gibberish),
-				  mpz_size(gibberish));
+  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, m, m);
 
   mpn_get_base256 (em, key->size, m, key_limb_size);
 
diff --git a/nettle/rsa-decrypt.c b/nettle/rsa-decrypt.c
index 7681439d..540d8baa 100644
--- a/nettle/rsa-decrypt.c
+++ b/nettle/rsa-decrypt.c
@@ -48,6 +48,16 @@ rsa_decrypt(const struct rsa_private_key *key,
   int res;
 
   mpz_init(m);
+
+  /* First check that input is in range. Since we don't have the
+     public key available here, we need to reconstruct n. */
+  mpz_mul (m, key->p, key->q);
+  if (mpz_sgn (gibberish) < 0 || mpz_cmp (gibberish, m) >= 0)
+    {
+      mpz_clear (m);
+      return 0;
+    }
+
   rsa_compute_root(key, m, gibberish);
 
   res = pkcs1_decrypt (key->size, m, length, message);
diff --git a/nettle/rsa-internal.h b/nettle/rsa-internal.h
index b828e451..f66a7df0 100644
--- a/nettle/rsa-internal.h
+++ b/nettle/rsa-internal.h
@@ -78,11 +78,11 @@ _rsa_sec_compute_root(const struct rsa_private_key *key,
                       mp_limb_t *scratch);
 
 /* Safe side-channel silent variant, using RSA blinding, and checking the
- * result after CRT. */
+ * result after CRT. In-place calls, with x == m, is allowed. */
 int
 _rsa_sec_compute_root_tr(const struct rsa_public_key *pub,
 			 const struct rsa_private_key *key,
 			 void *random_ctx, nettle_random_func *random,
-			 mp_limb_t *x, const mp_limb_t *m, size_t mn);
+			 mp_limb_t *x, const mp_limb_t *m);
 
 #endif /* NETTLE_RSA_INTERNAL_H_INCLUDED */
diff --git a/nettle/rsa-sec-decrypt.c b/nettle/rsa-sec-decrypt.c
index 6866e7c8..4c98958d 100644
--- a/nettle/rsa-sec-decrypt.c
+++ b/nettle/rsa-sec-decrypt.c
@@ -55,12 +55,19 @@ rsa_sec_decrypt(const struct rsa_public_key *pub,
   TMP_GMP_DECL (em, uint8_t);
   int res;
 
+  /* First check that input is in range. */
+  if (mpz_sgn (gibberish) < 0 || mpz_cmp (gibberish, pub->n) >= 0)
+    return 0;
+
   TMP_GMP_ALLOC (m, mpz_size(pub->n));
   TMP_GMP_ALLOC (em, key->size);
 
-  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, m,
-				  mpz_limbs_read(gibberish),
-				  mpz_size(gibberish));
+  /* We need a copy because m can be shorter than key_size,
+   * but _rsa_sec_compute_root_tr expect all inputs to be
+   * normalized to a key_size long buffer length */
+  mpz_limbs_copy(m, gibberish, mpz_size(pub->n));
+
+  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, m, m);
 
   mpn_get_base256 (em, key->size, m, mpz_size(pub->n));
 
diff --git a/nettle/rsa-sign-tr.c b/nettle/rsa-sign-tr.c
index f824c4ca..9e137c7a 100644
--- a/nettle/rsa-sign-tr.c
+++ b/nettle/rsa-sign-tr.c
@@ -131,35 +131,34 @@ int
 _rsa_sec_compute_root_tr(const struct rsa_public_key *pub,
 			 const struct rsa_private_key *key,
 			 void *random_ctx, nettle_random_func *random,
-			 mp_limb_t *x, const mp_limb_t *m, size_t mn)
+			 mp_limb_t *x, const mp_limb_t *m)
 {
+  mp_size_t nn;
   mpz_t mz;
   mpz_t xz;
   int res;
 
-  mpz_init(mz);
   mpz_init(xz);
 
-  mpn_copyi(mpz_limbs_write(mz, mn), m, mn);
-  mpz_limbs_finish(mz, mn);
+  nn = mpz_size (pub->n);
 
-  res = rsa_compute_root_tr(pub, key, random_ctx, random, xz, mz);
+  res = rsa_compute_root_tr(pub, key, random_ctx, random, xz,
+			    mpz_roinit_n(mz, m, nn));
 
   if (res)
-    mpz_limbs_copy(x, xz, mpz_size(pub->n));
+    mpz_limbs_copy(x, xz, nn);
 
-  mpz_clear(mz);
   mpz_clear(xz);
   return res;
 }
 #else
 /* Blinds m, by computing c = m r^e (mod n), for a random r. Also
-   returns the inverse (ri), for use by rsa_unblind. */
+   returns the inverse (ri), for use by rsa_unblind. Must have c != m,
+   no in-place operation.*/
 static void
 rsa_sec_blind (const struct rsa_public_key *pub,
                void *random_ctx, nettle_random_func *random,
-               mp_limb_t *c, mp_limb_t *ri, const mp_limb_t *m,
-               mp_size_t mn)
+               mp_limb_t *c, mp_limb_t *ri, const mp_limb_t *m)
 {
   const mp_limb_t *ep = mpz_limbs_read (pub->e);
   const mp_limb_t *np = mpz_limbs_read (pub->n);
@@ -177,15 +176,15 @@ rsa_sec_blind (const struct rsa_public_key *pub,
 
   /* c = m*(r^e) mod n */
   itch = mpn_sec_powm_itch(nn, ebn, nn);
-  i2 = mpn_sec_mul_itch(nn, mn);
+  i2 = mpn_sec_mul_itch(nn, nn);
   itch = MAX(itch, i2);
-  i2 = mpn_sec_div_r_itch(nn + mn, nn);
+  i2 = mpn_sec_div_r_itch(2*nn, nn);
   itch = MAX(itch, i2);
   i2 = mpn_sec_invert_itch(nn);
   itch = MAX(itch, i2);
 
-  TMP_GMP_ALLOC (tp, nn + mn + itch);
-  scratch = tp + nn + mn;
+  TMP_GMP_ALLOC (tp, 2*nn  + itch);
+  scratch = tp + 2*nn;
 
   /* ri = r^(-1) */
   do
@@ -198,9 +197,8 @@ rsa_sec_blind (const struct rsa_public_key *pub,
   while (!mpn_sec_invert (ri, tp, np, nn, 2 * nn * GMP_NUMB_BITS, scratch));
 
   mpn_sec_powm (c, rp, nn, ep, ebn, np, nn, scratch);
-  /* normally mn == nn, but m can be smaller in some cases */
-  mpn_sec_mul (tp, c, nn, m, mn, scratch);
-  mpn_sec_div_r (tp, nn + mn, np, nn, scratch);
+  mpn_sec_mul (tp, c, nn, m, nn, scratch);
+  mpn_sec_div_r (tp, 2*nn, np, nn, scratch);
   mpn_copyi(c, tp, nn);
 
   TMP_GMP_FREE (r);
@@ -208,7 +206,7 @@ rsa_sec_blind (const struct rsa_public_key *pub,
   TMP_GMP_FREE (tp);
 }
 
-/* m = c ri mod n */
+/* m = c ri mod n. Allows x == c. */
 static void
 rsa_sec_unblind (const struct rsa_public_key *pub,
                  mp_limb_t *x, mp_limb_t *ri, const mp_limb_t *c)
@@ -299,7 +297,7 @@ int
 _rsa_sec_compute_root_tr(const struct rsa_public_key *pub,
 			 const struct rsa_private_key *key,
 			 void *random_ctx, nettle_random_func *random,
-			 mp_limb_t *x, const mp_limb_t *m, size_t mn)
+			 mp_limb_t *x, const mp_limb_t *m)
 {
   TMP_GMP_DECL (c, mp_limb_t);
   TMP_GMP_DECL (ri, mp_limb_t);
@@ -307,7 +305,7 @@ _rsa_sec_compute_root_tr(const struct rsa_public_key *pub,
   size_t key_limb_size;
   int ret;
 
-  key_limb_size = NETTLE_OCTET_SIZE_TO_LIMB_SIZE(key->size);
+  key_limb_size = mpz_size(pub->n);
 
   /* mpz_powm_sec handles only odd moduli. If p, q or n is even, the
      key is invalid and rejected by rsa_private_key_prepare. However,
@@ -321,19 +319,18 @@ _rsa_sec_compute_root_tr(const struct rsa_public_key *pub,
     }
 
   assert(mpz_size(pub->n) == key_limb_size);
-  assert(mn <= key_limb_size);
 
   TMP_GMP_ALLOC (c, key_limb_size);
   TMP_GMP_ALLOC (ri, key_limb_size);
   TMP_GMP_ALLOC (scratch, _rsa_sec_compute_root_itch(key));
 
-  rsa_sec_blind (pub, random_ctx, random, x, ri, m, mn);
+  rsa_sec_blind (pub, random_ctx, random, c, ri, m);
 
-  _rsa_sec_compute_root(key, c, x, scratch);
+  _rsa_sec_compute_root(key, x, c, scratch);
 
-  ret = rsa_sec_check_root(pub, c, x);
+  ret = rsa_sec_check_root(pub, x, c);
 
-  rsa_sec_unblind(pub, x, ri, c);
+  rsa_sec_unblind(pub, x, ri, x);
 
   cnd_mpn_zero(1 - ret, x, key_limb_size);
 
@@ -357,17 +354,17 @@ rsa_compute_root_tr(const struct rsa_public_key *pub,
 		    mpz_t x, const mpz_t m)
 {
   TMP_GMP_DECL (l, mp_limb_t);
+  mp_size_t nn = mpz_size(pub->n);
   int res;
 
-  mp_size_t l_size = NETTLE_OCTET_SIZE_TO_LIMB_SIZE(key->size);
-  TMP_GMP_ALLOC (l, l_size);
+  TMP_GMP_ALLOC (l, nn);
+  mpz_limbs_copy(l, m, nn);
 
-  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, l,
-				  mpz_limbs_read(m), mpz_size(m));
+  res = _rsa_sec_compute_root_tr (pub, key, random_ctx, random, l, l);
   if (res) {
-    mp_limb_t *xp = mpz_limbs_write (x, l_size);
-    mpn_copyi (xp, l, l_size);
-    mpz_limbs_finish (x, l_size);
+    mp_limb_t *xp = mpz_limbs_write (x, nn);
+    mpn_copyi (xp, l, nn);
+    mpz_limbs_finish (x, nn);
   }
 
   TMP_GMP_FREE (l);
diff --git a/nettle/rsa.h b/nettle/rsa.h
index 3b10155f..2dd35a2d 100644
--- a/nettle/rsa.h
+++ b/nettle/rsa.h
@@ -428,13 +428,14 @@ rsa_sec_decrypt(const struct rsa_public_key *pub,
 	        size_t length, uint8_t *message,
 	        const mpz_t gibberish);
 
-/* Compute x, the e:th root of m. Calling it with x == m is allowed. */
+/* Compute x, the e:th root of m. Calling it with x == m is allowed.
+   It is required that 0 <= m < n. */
 void
 rsa_compute_root(const struct rsa_private_key *key,
 		 mpz_t x, const mpz_t m);
 
 /* Safer variant, using RSA blinding, and checking the result after
-   CRT. */
+   CRT. It is required that 0 <= m < n. */
 int
 rsa_compute_root_tr(const struct rsa_public_key *pub,
 		    const struct rsa_private_key *key,
diff --git a/nettle/testsuite/rsa-encrypt-test.c b/nettle/testsuite/rsa-encrypt-test.c
index 87525f78..d1a440f6 100644
--- a/nettle/testsuite/rsa-encrypt-test.c
+++ b/nettle/testsuite/rsa-encrypt-test.c
@@ -19,10 +19,12 @@ test_main(void)
   uint8_t after;
 
   mpz_t gibberish;
+  mpz_t bad_input;
 
   rsa_private_key_init(&key);
   rsa_public_key_init(&pub);
   mpz_init(gibberish);
+  mpz_init(bad_input);
 
   knuth_lfib_init(&lfib, 17);
   
@@ -101,6 +103,42 @@ test_main(void)
   ASSERT(decrypted[decrypted_length] == after);
   ASSERT(decrypted[0] == 'A');
 
+  /* Test zero input. */
+  mpz_set_ui (bad_input, 0);
+  decrypted_length = msg_length;
+  ASSERT(!rsa_decrypt(&key, &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_decrypt_tr(&pub, &key,
+			 &lfib, (nettle_random_func *) knuth_lfib_random,
+			 &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_sec_decrypt(&pub, &key,
+			  &lfib, (nettle_random_func *) knuth_lfib_random,
+			  decrypted_length, decrypted, bad_input));
+  ASSERT(decrypted_length == msg_length);
+
+  /* Test input that is slightly larger than n */
+  mpz_add(bad_input, gibberish, pub.n);
+  decrypted_length = msg_length;
+  ASSERT(!rsa_decrypt(&key, &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_decrypt_tr(&pub, &key,
+			 &lfib, (nettle_random_func *) knuth_lfib_random,
+			 &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_sec_decrypt(&pub, &key,
+			  &lfib, (nettle_random_func *) knuth_lfib_random,
+			  decrypted_length, decrypted, bad_input));
+  ASSERT(decrypted_length == msg_length);
+
+  /* Test input that is considerably larger than n */
+  mpz_mul_2exp (bad_input, pub.n, 100);
+  mpz_add (bad_input, bad_input, gibberish);
+  decrypted_length = msg_length;
+  ASSERT(!rsa_decrypt(&key, &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_decrypt_tr(&pub, &key,
+			 &lfib, (nettle_random_func *) knuth_lfib_random,
+			 &decrypted_length, decrypted, bad_input));
+  ASSERT(!rsa_sec_decrypt(&pub, &key,
+			  &lfib, (nettle_random_func *) knuth_lfib_random,
+			  decrypted_length, decrypted, bad_input));
+  ASSERT(decrypted_length == msg_length);
 
   /* Test invalid key. */
   mpz_add_ui (key.q, key.q, 2);
@@ -112,6 +150,6 @@ test_main(void)
   rsa_private_key_clear(&key);
   rsa_public_key_clear(&pub);
   mpz_clear(gibberish);
+  mpz_clear(bad_input);
   free(decrypted);
 }
-  
diff --git a/nettle/testsuite/rsa-sec-decrypt-test.c b/nettle/testsuite/rsa-sec-decrypt-test.c
index fb0ed3a1..3419322e 100644
--- a/nettle/testsuite/rsa-sec-decrypt-test.c
+++ b/nettle/testsuite/rsa-sec-decrypt-test.c
@@ -55,6 +55,7 @@ rsa_decrypt_for_test(const struct rsa_public_key *pub,
 #endif
 
 #define PAYLOAD_SIZE 50
+#define DECRYPTED_SIZE 256
 void
 test_main(void)
 {
@@ -63,7 +64,7 @@ test_main(void)
   struct knuth_lfib_ctx random_ctx;
 
   uint8_t plaintext[PAYLOAD_SIZE];
-  uint8_t decrypted[PAYLOAD_SIZE];
+  uint8_t decrypted[DECRYPTED_SIZE];
   uint8_t verifybad[PAYLOAD_SIZE];
   unsigned n_size = 1024;
   mpz_t gibberish;
@@ -99,6 +100,20 @@ test_main(void)
                                     PAYLOAD_SIZE, decrypted, gibberish) == 1);
       ASSERT (MEMEQ (PAYLOAD_SIZE, plaintext, decrypted));
 
+      ASSERT (pub.size > 10);
+      ASSERT (pub.size <= DECRYPTED_SIZE);
+
+      /* Check that too large message length is rejected, largest
+	 valid size is pub.size - 11. */
+      ASSERT (!rsa_decrypt_for_test (&pub, &key, &random_ctx,
+				     (nettle_random_func *) knuth_lfib_random,
+				     pub.size - 10, decrypted, gibberish));
+
+      /* This case used to result in arithmetic underflow and a crash. */
+      ASSERT (!rsa_decrypt_for_test (&pub, &key, &random_ctx,
+				     (nettle_random_func *) knuth_lfib_random,
+				     pub.size, decrypted, gibberish));
+
       /* bad one */
       memcpy(decrypted, verifybad, PAYLOAD_SIZE);
       nettle_mpz_random_size(garbage, &random_ctx,