diff --git a/dirmngr/crlcache.c b/dirmngr/crlcache.c
index c9e5ca68f..73944667d 100644
--- a/dirmngr/crlcache.c
+++ b/dirmngr/crlcache.c
@@ -1531,17 +1531,104 @@ crl_cache_cert_isvalid (ctrl_t ctrl, ksba_cert_t cert,
 }
 
 
+/* Return the hash algorithm's algo id from its name given in the
+ * non-null termnated string in (buffer,buflen).  Returns 0 on failure
+ * or if the algo is not known.  */
+static int
+hash_algo_from_buffer (const void *buffer, size_t buflen)
+{
+  char *string;
+  int algo;
+
+  string = xtrymalloc (buflen + 1);
+  if (!string)
+    {
+      log_error (_("out of core\n"));
+      return 0;
+    }
+  memcpy (string, buffer, buflen);
+  string[buflen] = 0;
+  algo = gcry_md_map_name (string);
+  if (!algo)
+    log_error ("unknown digest algorithm '%s' used in certificate\n", string);
+  xfree (string);
+  return algo;
+}
+
+
+/* Return an unsigned integer from the non-null termnated string
+ * (buffer,buflen).  Returns 0 on failure.  */
+static unsigned int
+uint_from_buffer (const void *buffer, size_t buflen)
+{
+  char *string;
+  unsigned int val;
+
+  string = xtrymalloc (buflen + 1);
+  if (!string)
+    {
+      log_error (_("out of core\n"));
+      return 0;
+    }
+  memcpy (string, buffer, buflen);
+  string[buflen] = 0;
+  val = strtoul (string, NULL, 10);
+  xfree (string);
+  return val;
+}
+
+
 /* Prepare a hash context for the signature verification.  Input is
    the CRL and the output is the hash context MD as well as the uses
    algorithm identifier ALGO. */
 static gpg_error_t
-start_sig_check (ksba_crl_t crl, gcry_md_hd_t *md, int *algo)
+start_sig_check (ksba_crl_t crl, gcry_md_hd_t *md, int *algo, int *use_pss)
 {
   gpg_error_t err;
   const char *algoid;
 
+  *use_pss = 0;
   algoid = ksba_crl_get_digest_algo (crl);
-  *algo = gcry_md_map_name (algoid);
+  if (algoid && !strcmp (algoid, "1.2.840.113549.1.1.10"))
+    {
+      /* Parse rsaPSS parameter.  */
+      gcry_buffer_t ioarray[1] = { {0} };
+      ksba_sexp_t pssparam;
+      size_t n;
+      gcry_sexp_t psssexp;
+
+      pssparam = ksba_crl_get_sig_val (crl);
+      n = gcry_sexp_canon_len (pssparam, 0, NULL, NULL);
+      if (!n)
+        {
+          ksba_free (pssparam);
+          log_error (_("got an invalid S-expression from libksba\n"));
+          return gpg_error (GPG_ERR_INV_SEXP);
+        }
+      err = gcry_sexp_sscan (&psssexp, NULL, pssparam, n);
+      ksba_free (pssparam);
+      if (err)
+        {
+          log_error (_("converting S-expression failed: %s\n"),
+                     gcry_strerror (err));
+          return err;
+        }
+
+      err = gcry_sexp_extract_param (psssexp, "sig-val",
+                                    "&'hash-algo'", ioarray, NULL);
+      gcry_sexp_release (psssexp);
+      if (err)
+        {
+          log_error ("extracting params from PSS failed: %s\n",
+                     gpg_strerror (err));
+          return err;
+        }
+      *algo = hash_algo_from_buffer (ioarray[0].data, ioarray[0].len);
+      xfree (ioarray[0].data);
+      *use_pss = 1;
+    }
+  else
+    *algo = gcry_md_map_name (algoid);
   if (!*algo)
     {
       log_error (_("unknown hash algorithm '%s'\n"), algoid? algoid:"?");
@@ -1570,15 +1657,13 @@ start_sig_check (ksba_crl_t crl, gcry_md_hd_t *md, int *algo)
    certificate of the CRL issuer.  This function takes ownership of MD.  */
 static gpg_error_t
 finish_sig_check (ksba_crl_t crl, gcry_md_hd_t md, int algo,
-                  ksba_cert_t issuer_cert)
+                  ksba_cert_t issuer_cert, int use_pss)
 {
   gpg_error_t err;
   ksba_sexp_t sigval = NULL, pubkey = NULL;
-  const char *s;
-  char algoname[50];
   size_t n;
   gcry_sexp_t s_sig = NULL, s_hash = NULL, s_pkey = NULL;
-  unsigned int i;
+  unsigned int saltlen = 0;  /* (used only with use_pss)  */
 
   /* This also stops debugging on the MD.  */
   gcry_md_final (md);
@@ -1600,6 +1685,55 @@ finish_sig_check (ksba_crl_t crl, gcry_md_hd_t md, int algo,
       goto leave;
     }
 
+  if (use_pss)
+    {
+      /* Parse rsaPSS parameter which we should find in S_SIG.  */
+      gcry_buffer_t ioarray[2] = { {0}, {0} };
+      ksba_sexp_t pssparam;
+      gcry_sexp_t psssexp;
+      int hashalgo;
+
+      pssparam = ksba_crl_get_sig_val (crl);
+      n = gcry_sexp_canon_len (pssparam, 0, NULL, NULL);
+      if (!n)
+        {
+          ksba_free (pssparam);
+          log_error (_("got an invalid S-expression from libksba\n"));
+          err = gpg_error (GPG_ERR_INV_SEXP);
+          goto leave;
+        }
+      err = gcry_sexp_sscan (&psssexp, NULL, pssparam, n);
+      ksba_free (pssparam);
+      if (err)
+        {
+          log_error (_("converting S-expression failed: %s\n"),
+                     gcry_strerror (err));
+          goto leave;
+        }
+
+      err = gcry_sexp_extract_param (psssexp, "sig-val",
+                                    "&'hash-algo''salt-length'",
+                                     ioarray+0, ioarray+1, NULL);
+      gcry_sexp_release (psssexp);
+      if (err)
+        {
+          log_error ("extracting params from PSS failed: %s\n",
+                     gpg_strerror (err));
+          goto leave;
+        }
+      hashalgo = hash_algo_from_buffer (ioarray[0].data, ioarray[0].len);
+      saltlen = uint_from_buffer (ioarray[1].data, ioarray[1].len);
+      xfree (ioarray[0].data);
+      xfree (ioarray[1].data);
+      if (hashalgo != algo)
+        {
+          log_error ("hash algo mismatch: %d announced but %d used\n",
+                     algo, hashalgo);
+          return gpg_error (GPG_ERR_INV_CRL);
+        }
+    }
+
+
   /* Get and convert the public key for the issuer certificate. */
   if (DBG_X509)
     dump_cert ("crl_issuer_cert", issuer_cert);
@@ -1620,13 +1754,25 @@ finish_sig_check (ksba_crl_t crl, gcry_md_hd_t md, int algo,
     }
 
   /* Create an S-expression with the actual hash value. */
-  s = gcry_md_algo_name (algo);
-  for (i = 0; *s && i < sizeof(algoname) - 1; s++, i++)
-    algoname[i] = ascii_tolower (*s);
-  algoname[i] = 0;
-  err = gcry_sexp_build (&s_hash, NULL, "(data(flags pkcs1)(hash %s %b))",
-                         algoname,
-                         gcry_md_get_algo_dlen (algo), gcry_md_read (md, algo));
+  if (use_pss)
+    {
+      err = gcry_sexp_build (&s_hash, NULL,
+                             "(data (flags pss)"
+                             "(hash %s %b)"
+                             "(salt-length %u))",
+                             hash_algo_to_string (algo),
+                             (int)gcry_md_get_algo_dlen (algo),
+                             gcry_md_read (md, algo),
+                             saltlen);
+    }
+  else
+    {
+      err = gcry_sexp_build (&s_hash, NULL,
+                             "(data(flags pkcs1)(hash %s %b))",
+                             hash_algo_to_string (algo),
+                             (int)gcry_md_get_algo_dlen (algo),
+                             gcry_md_read (md, algo));
+    }
   if (err)
     {
       log_error (_("creating S-expression failed: %s\n"), gcry_strerror (err));
@@ -1688,6 +1834,7 @@ crl_parse_insert (ctrl_t ctrl, ksba_crl_t crl,
   ksba_cert_t crlissuer_cert = NULL;
   gcry_md_hd_t md = NULL;
   int algo = 0;
+  int use_pss = 0;
   size_t n;
 
   (void)fname;
@@ -1710,7 +1857,7 @@ crl_parse_insert (ctrl_t ctrl, ksba_crl_t crl,
         {
         case KSBA_SR_BEGIN_ITEMS:
           {
-            err = start_sig_check (crl, &md, &algo);
+            err = start_sig_check (crl, &md, &algo, &use_pss);
             if (err)
               goto failure;
 
@@ -1847,7 +1994,7 @@ crl_parse_insert (ctrl_t ctrl, ksba_crl_t crl,
                 goto failure;
               }
 
-            err = finish_sig_check (crl, md, algo, crlissuer_cert);
+            err = finish_sig_check (crl, md, algo, crlissuer_cert, use_pss);
             md = NULL; /* Closed.  */
             if (err)
               {
diff --git a/sm/certcheck.c b/sm/certcheck.c
index 51f1a9402..521f775ea 100644
--- a/sm/certcheck.c
+++ b/sm/certcheck.c
@@ -1,5 +1,7 @@
 /* certcheck.c - check one certificate
- *	Copyright (C) 2001, 2003, 2004 Free Software Foundation, Inc.
+ * Copyright (C) 2001, 2003, 2004 Free Software Foundation, Inc.
+ * Copyright (C) 2001-2019 Werner Koch
+ * Copyright (C) 2015-2020 g10 Code GmbH
  *
  * This file is part of GnuPG.
  *
@@ -15,6 +17,7 @@
  *
  * You should have received a copy of the GNU General Public License
  * along with this program; if not, see <https://www.gnu.org/licenses/>.
+ * SPDX-License-Identifier: GPL-3.0-or-later
  */
 
 #include <config.h>
@@ -220,6 +223,53 @@ pk_algo_from_sexp (gcry_sexp_t pkey)
 }
 
 
+/* Return the hash algorithm's algo id from its name given in the
+ * non-null termnated string in (buffer,buflen).  Returns 0 on failure
+ * or if the algo is not known.  */
+static int
+hash_algo_from_buffer (const void *buffer, size_t buflen)
+{
+  char *string;
+  int algo;
+
+  string = xtrymalloc (buflen + 1);
+  if (!string)
+    {
+      log_error (_("out of core\n"));
+      return 0;
+    }
+  memcpy (string, buffer, buflen);
+  string[buflen] = 0;
+  algo = gcry_md_map_name (string);
+  if (!algo)
+    log_error ("unknown digest algorithm '%s' used in certificate\n", string);
+  xfree (string);
+  return algo;
+}
+
+
+/* Return an unsigned integer from the non-null termnated string
+ * (buffer,buflen).  Returns 0 on failure.  */
+static unsigned int
+uint_from_buffer (const void *buffer, size_t buflen)
+{
+  char *string;
+  unsigned int val;
+
+  string = xtrymalloc (buflen + 1);
+  if (!string)
+    {
+      log_error (_("out of core\n"));
+      return 0;
+    }
+  memcpy (string, buffer, buflen);
+  string[buflen] = 0;
+  val = strtoul (string, NULL, 10);
+  xfree (string);
+  return val;
+}
+
+
 /* Check the signature on CERT using the ISSUER-CERT.  This function
    does only test the cryptographic signature and nothing else.  It is
    assumed that the ISSUER_CERT is valid. */
@@ -229,21 +279,76 @@ gpgsm_check_cert_sig (ksba_cert_t issuer_cert, ksba_cert_t cert)
   const char *algoid;
   gcry_md_hd_t md;
   int rc, algo;
-  gcry_mpi_t frame;
   ksba_sexp_t p;
   size_t n;
-  gcry_sexp_t s_sig, s_hash, s_pkey;
+  gcry_sexp_t s_sig, s_data, s_pkey;
+  int use_pss = 0;
+  unsigned int saltlen;
 
   algo = gcry_md_map_name ( (algoid=ksba_cert_get_digest_algo (cert)));
-  if (!algo)
+  if (!algo && algoid && !strcmp (algoid, "1.2.840.113549.1.1.10"))
+    use_pss = 1;
+  else if (!algo)
     {
-      log_error ("unknown hash algorithm '%s'\n", algoid? algoid:"?");
+      log_error ("unknown digest algorithm '%s' used certificate\n",
+                 algoid? algoid:"?");
       if (algoid
           && (  !strcmp (algoid, "1.2.840.113549.1.1.2")
                 ||!strcmp (algoid, "1.2.840.113549.2.2")))
         log_info (_("(this is the MD2 algorithm)\n"));
       return gpg_error (GPG_ERR_GENERAL);
     }
+
+  /* The the signature from the certificate.  */
+  p = ksba_cert_get_sig_val (cert);
+  n = gcry_sexp_canon_len (p, 0, NULL, NULL);
+  if (!n)
+    {
+      log_error ("libksba did not return a proper S-Exp\n");
+      ksba_free (p);
+      return gpg_error (GPG_ERR_BUG);
+    }
+  rc = gcry_sexp_sscan ( &s_sig, NULL, (char*)p, n);
+  ksba_free (p);
+  if (rc)
+    {
+      log_error ("gcry_sexp_scan failed: %s\n", gpg_strerror (rc));
+      return rc;
+    }
+  if (DBG_CRYPTO)
+    gcry_log_debugsxp ("sigval", s_sig);
+
+  if (use_pss)
+    {
+      /* Extract the hash algorithm and the salt length from the sigval.  */
+      gcry_buffer_t ioarray[2] = { {0}, {0} };
+
+      rc = gcry_sexp_extract_param (s_sig, "sig-val",
+                                    "&'hash-algo''salt-length'",
+                                    ioarray+0, ioarray+1, NULL);
+      if (rc)
+        {
+          gcry_sexp_release (s_sig);
+          log_error ("extracting params from PSS failed: %s\n",
+                     gpg_strerror (rc));
+          return rc;
+        }
+      algo = hash_algo_from_buffer (ioarray[0].data, ioarray[0].len);
+      saltlen = uint_from_buffer (ioarray[1].data, ioarray[1].len);
+      xfree (ioarray[0].data);
+      xfree (ioarray[1].data);
+      if (saltlen < 20)
+        {
+          log_error ("length of PSS salt too short\n");
+          return gpg_error (GPG_ERR_DIGEST_ALGO);
+        }
+      if (!algo)
+        return gpg_error (GPG_ERR_DIGEST_ALGO);
+      /* log_debug ("PSS hash=%d saltlen=%u\n", algo, saltlen); */
+    }
+
+
+  /* Hash the to-be-signed parts of the certificate.  */
   rc = gcry_md_open (&md, algo, 0);
   if (rc)
     {
@@ -262,33 +367,7 @@ gpgsm_check_cert_sig (ksba_cert_t issuer_cert, ksba_cert_t cert)
     }
   gcry_md_final (md);
 
-  p = ksba_cert_get_sig_val (cert);
-  n = gcry_sexp_canon_len (p, 0, NULL, NULL);
-  if (!n)
-    {
-      log_error ("libksba did not return a proper S-Exp\n");
-      gcry_md_close (md);
-      ksba_free (p);
-      return gpg_error (GPG_ERR_BUG);
-    }
-  if (DBG_CRYPTO)
-    {
-      int j;
-      log_debug ("signature value:");
-      for (j=0; j < n; j++)
-        log_printf (" %02X", p[j]);
-      log_printf ("\n");
-    }
-
-  rc = gcry_sexp_sscan ( &s_sig, NULL, (char*)p, n);
-  ksba_free (p);
-  if (rc)
-    {
-      log_error ("gcry_sexp_scan failed: %s\n", gpg_strerror (rc));
-      gcry_md_close (md);
-      return rc;
-    }
-
+  /* Get the public key from the certificate.  */
   p = ksba_cert_get_public_key (issuer_cert);
   n = gcry_sexp_canon_len (p, 0, NULL, NULL);
   if (!n)
@@ -308,29 +387,50 @@ gpgsm_check_cert_sig (ksba_cert_t issuer_cert, ksba_cert_t cert)
       gcry_sexp_release (s_sig);
       return rc;
     }
+  if (DBG_CRYPTO)
+    gcry_log_debugsxp ("pubkey:", s_pkey);
 
-  rc = do_encode_md (md, algo, pk_algo_from_sexp (s_pkey),
-                     gcry_pk_get_nbits (s_pkey), s_pkey, &frame);
-  if (rc)
+  if (use_pss)
     {
-      gcry_md_close (md);
-      gcry_sexp_release (s_sig);
-      gcry_sexp_release (s_pkey);
-      return rc;
+      rc = gcry_sexp_build (&s_data, NULL,
+                            "(data (flags pss)"
+                            "(hash %s %b)"
+                            "(salt-length %u))",
+                            hash_algo_to_string (algo),
+                            (int)gcry_md_get_algo_dlen (algo),
+                            gcry_md_read (md, algo),
+                            saltlen);
+      if (rc)
+        BUG ();
     }
+  else
+    {
+      /* RSA or DAS: Prepare the hash for verification.  */
+      gcry_mpi_t frame;
 
-  /* put hash into the S-Exp s_hash */
-  if ( gcry_sexp_build (&s_hash, NULL, "%m", frame) )
-    BUG ();
-  gcry_mpi_release (frame);
+      rc = do_encode_md (md, algo, pk_algo_from_sexp (s_pkey),
+                         gcry_pk_get_nbits (s_pkey), s_pkey, &frame);
+      if (rc)
+        {
+          gcry_md_close (md);
+          gcry_sexp_release (s_sig);
+          gcry_sexp_release (s_pkey);
+          return rc;
+        }
+      if ( gcry_sexp_build (&s_data, NULL, "%m", frame) )
+        BUG ();
+      gcry_mpi_release (frame);
+    }
+  if (DBG_CRYPTO)
+    gcry_log_debugsxp ("data:", s_data);
 
-
-  rc = gcry_pk_verify (s_sig, s_hash, s_pkey);
+  /* Verify.  */
+  rc = gcry_pk_verify (s_sig, s_data, s_pkey);
   if (DBG_X509)
       log_debug ("gcry_pk_verify: %s\n", gpg_strerror (rc));
   gcry_md_close (md);
   gcry_sexp_release (s_sig);
-  gcry_sexp_release (s_hash);
+  gcry_sexp_release (s_data);
   gcry_sexp_release (s_pkey);
   return rc;
 }