diff --git a/library/ssl_misc.h b/library/ssl_misc.h
index ce41a45f9..6f9100bd9 100644
--- a/library/ssl_misc.h
+++ b/library/ssl_misc.h
@@ -243,6 +243,18 @@
 
 #define MBEDTLS_RECEIVED_SIG_ALGS_SIZE         20
 
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+
+#define MBEDTLS_TLS_SIG_NONE MBEDTLS_TLS1_3_SIG_NONE
+
+#if defined(MBEDTLS_SSL_PROTO_TLS1_2)
+#define MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( sig, hash ) (( hash << 8 ) | sig)
+#define MBEDTLS_SSL_TLS12_SIG_ALG_FROM_SIG_AND_HASH_ALG(alg) (alg & 0xFF)
+#define MBEDTLS_SSL_TLS12_HASH_ALG_FROM_SIG_AND_HASH_ALG(alg) (alg >> 8)
+#endif /* MBEDTLS_SSL_PROTO_TLS1_2 */
+
+#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
+
 /*
  * Check that we obey the standard's message size bounds
  */
@@ -423,24 +435,6 @@ static inline int mbedtls_ssl_chk_buf_ptr( const uint8_t *cur,
 extern "C" {
 #endif
 
-#if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
-    defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-/*
- * Abstraction for a grid of allowed signature-hash-algorithm pairs.
- */
-struct mbedtls_ssl_sig_hash_set_t
-{
-    /* At the moment, we only need to remember a single suitable
-     * hash algorithm per signature algorithm. As long as that's
-     * the case - and we don't need a general lookup function -
-     * we can implement the sig-hash-set as a map from signatures
-     * to hash algorithms. */
-    mbedtls_md_type_t rsa;
-    mbedtls_md_type_t ecdsa;
-};
-#endif /* MBEDTLS_SSL_PROTO_TLS1_2 &&
-          MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
-
 typedef int  mbedtls_ssl_tls_prf_cb( const unsigned char *secret, size_t slen,
                                      const char *label,
                                      const unsigned char *random, size_t rlen,
@@ -594,13 +588,7 @@ struct mbedtls_ssl_handshake_params
 #endif /* MBEDTLS_SSL_SRV_C */
 #endif /* MBEDTLS_SSL_PROTO_TLS1_3 */
 
-#if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
-    defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-    mbedtls_ssl_sig_hash_set_t hash_algs;             /*!<  Set of suitable sig-hash pairs */
-#endif
-
-#if defined(MBEDTLS_SSL_PROTO_TLS1_3) && \
-    defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
     uint16_t received_sig_algs[MBEDTLS_RECEIVED_SIG_ALGS_SIZE];
 #endif
 
@@ -1115,24 +1103,21 @@ int mbedtls_ssl_tls12_write_client_hello_exts( mbedtls_ssl_context *ssl,
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
     defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
 
-/* Find an entry in a signature-hash set matching a given hash algorithm. */
-mbedtls_md_type_t mbedtls_ssl_sig_hash_set_find( mbedtls_ssl_sig_hash_set_t *set,
-                                                 mbedtls_pk_type_t sig_alg );
-/* Add a signature-hash-pair to a signature-hash set */
-void mbedtls_ssl_sig_hash_set_add( mbedtls_ssl_sig_hash_set_t *set,
-                                   mbedtls_pk_type_t sig_alg,
-                                   mbedtls_md_type_t md_alg );
-/* Allow exactly one hash algorithm for each signature. */
-void mbedtls_ssl_sig_hash_set_const_hash( mbedtls_ssl_sig_hash_set_t *set,
-                                          mbedtls_md_type_t md_alg );
+/**
+ * \brief Find the preferred hash for a given signature algorithm.
+ *
+ * \param[in]   ssl     SSL context
+ * \param[in]   sig_alg A signature algorithm identifier as defined in the
+ *                      TLS 1.2 SignatureAlgorithm enumeration.
+ *
+ * \return  The preferred hash algorithm for \p sig_alg. It is a hash algorithm
+ *          identifier as defined in the TLS 1.2 HashAlgorithm enumeration.
+ */
+unsigned int mbedtls_ssl_tls12_get_preferred_hash_for_sig_alg(
+                mbedtls_ssl_context *ssl,
+                unsigned int sig_alg );
 
-/* Setup an empty signature-hash set */
-static inline void mbedtls_ssl_sig_hash_set_init( mbedtls_ssl_sig_hash_set_t *set )
-{
-    mbedtls_ssl_sig_hash_set_const_hash( set, MBEDTLS_MD_NONE );
-}
-
-#endif /* MBEDTLS_SSL_PROTO_TLS1_2) &&
+#endif /* MBEDTLS_SSL_PROTO_TLS1_2 &&
           MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
 
 /**
@@ -1804,11 +1789,11 @@ int mbedtls_ssl_tls13_generate_and_write_ecdh_key_exchange(
 
 #if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
 /*
- * Parse TLS 1.3 Signature Algorithm extension
+ * Parse TLS Signature Algorithm extension
  */
-int mbedtls_ssl_tls13_parse_sig_alg_ext( mbedtls_ssl_context *ssl,
-                                         const unsigned char *buf,
-                                         const unsigned char *end );
+int mbedtls_ssl_parse_sig_alg_ext( mbedtls_ssl_context *ssl,
+                                   const unsigned char *buf,
+                                   const unsigned char *end );
 #endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
 
 /* Get handshake transcript */
@@ -1954,7 +1939,7 @@ static inline int mbedtls_ssl_sig_alg_is_received( const mbedtls_ssl_context *ss
     if( sig_alg == NULL )
         return( 0 );
 
-    for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE; sig_alg++ )
+    for( ; *sig_alg != MBEDTLS_TLS_SIG_NONE; sig_alg++ )
     {
         if( *sig_alg == own_sig_alg )
             return( 1 );
@@ -1970,7 +1955,7 @@ static inline int mbedtls_ssl_sig_alg_is_offered( const mbedtls_ssl_context *ssl
     if( sig_alg == NULL )
         return( 0 );
 
-    for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE; sig_alg++ )
+    for( ; *sig_alg != MBEDTLS_TLS_SIG_NONE; sig_alg++ )
     {
         if( *sig_alg == proposed_sig_alg )
             return( 1 );
@@ -2152,19 +2137,6 @@ static inline int mbedtls_ssl_sig_alg_is_supported(
 }
 #endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
 
-#if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
-    defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-#if defined(MBEDTLS_ECDSA_C) && defined(MBEDTLS_RSA_C)
-#define MBEDTLS_SSL_SIG_ALG( hash ) (( hash << 8 ) | MBEDTLS_SSL_SIG_ECDSA), \
-                                    (( hash << 8 ) | MBEDTLS_SSL_SIG_RSA),
-#elif defined(MBEDTLS_ECDSA_C)
-#define MBEDTLS_SSL_SIG_ALG( hash ) (( hash << 8 ) | MBEDTLS_SSL_SIG_ECDSA),
-#elif defined(MBEDTLS_RSA_C)
-#define MBEDTLS_SSL_SIG_ALG( hash ) (( hash << 8 ) | MBEDTLS_SSL_SIG_RSA),
-#else
-#define MBEDTLS_SSL_SIG_ALG( hash )
-#endif /* MBEDTLS_ECDSA_C && MBEDTLS_RSA_C */
-#endif /* MBEDTLS_SSL_PROTO_TLS1_2 && MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
 /* Corresponding PSA algorithm for MBEDTLS_CIPHER_NULL.
  * Same value is used for PSA_ALG_CATEGORY_CIPHER, hence it is
diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index a1a0003c6..8d6d379b5 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -616,11 +616,6 @@ static void ssl_handshake_params_init( mbedtls_ssl_handshake_params *handshake )
 
     handshake->update_checksum = ssl_update_checksum_start;
 
-#if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
-    defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-    mbedtls_ssl_sig_hash_set_init( &handshake->hash_algs );
-#endif
-
 #if defined(MBEDTLS_DHM_C)
     mbedtls_dhm_init( &handshake->dhm_ctx );
 #endif
@@ -852,7 +847,7 @@ static int ssl_handshake_init( mbedtls_ssl_context *ssl )
             p++;
 #endif
         }
-        *p = MBEDTLS_TLS1_3_SIG_NONE;
+        *p = MBEDTLS_TLS_SIG_NONE;
         ssl->handshake->sig_algs_heap_allocated = 1;
     }
     else
@@ -4143,22 +4138,37 @@ static uint16_t ssl_preset_default_sig_algs[] = {
     MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256,
 #endif /* MBEDTLS_RSA_C && MBEDTLS_SHA256_C */
 
-    MBEDTLS_TLS1_3_SIG_NONE
+    MBEDTLS_TLS_SIG_NONE
 };
 
 /* NOTICE: see above */
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2)
 static uint16_t ssl_tls12_preset_default_sig_algs[] = {
 #if defined(MBEDTLS_SHA512_C)
-    MBEDTLS_SSL_SIG_ALG( MBEDTLS_SSL_HASH_SHA512 )
+#if defined(MBEDTLS_ECDSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA, MBEDTLS_SSL_HASH_SHA512 ),
 #endif
+#if defined(MBEDTLS_RSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA, MBEDTLS_SSL_HASH_SHA512 ),
+#endif
+#endif /* MBEDTLS_SHA512_C */
 #if defined(MBEDTLS_SHA384_C)
-    MBEDTLS_SSL_SIG_ALG( MBEDTLS_SSL_HASH_SHA384 )
+#if defined(MBEDTLS_ECDSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA, MBEDTLS_SSL_HASH_SHA384 ),
 #endif
+#if defined(MBEDTLS_RSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA, MBEDTLS_SSL_HASH_SHA384 ),
+#endif
+#endif /* MBEDTLS_SHA384_C */
 #if defined(MBEDTLS_SHA256_C)
-    MBEDTLS_SSL_SIG_ALG( MBEDTLS_SSL_HASH_SHA256 )
+#if defined(MBEDTLS_ECDSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA, MBEDTLS_SSL_HASH_SHA256 ),
 #endif
-    MBEDTLS_TLS1_3_SIG_NONE
+#if defined(MBEDTLS_RSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA, MBEDTLS_SSL_HASH_SHA256 ),
+#endif
+#endif /* MBEDTLS_SHA256_C */
+    MBEDTLS_TLS_SIG_NONE
 };
 #endif /* MBEDTLS_SSL_PROTO_TLS1_2 */
 /* NOTICE: see above */
@@ -4184,19 +4194,29 @@ static uint16_t ssl_preset_suiteb_sig_algs[] = {
     MBEDTLS_TLS1_3_SIG_RSA_PKCS1_SHA256,
 #endif /* MBEDTLS_RSA_C && MBEDTLS_SHA256_C */
 
-    MBEDTLS_TLS1_3_SIG_NONE
+    MBEDTLS_TLS_SIG_NONE
 };
 
 /* NOTICE: see above */
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2)
 static uint16_t ssl_tls12_preset_suiteb_sig_algs[] = {
 #if defined(MBEDTLS_SHA256_C)
-    MBEDTLS_SSL_SIG_ALG( MBEDTLS_SSL_HASH_SHA256 )
+#if defined(MBEDTLS_ECDSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA, MBEDTLS_SSL_HASH_SHA256 ),
 #endif
+#if defined(MBEDTLS_RSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA, MBEDTLS_SSL_HASH_SHA256 ),
+#endif
+#endif /* MBEDTLS_SHA256_C */
 #if defined(MBEDTLS_SHA384_C)
-    MBEDTLS_SSL_SIG_ALG( MBEDTLS_SSL_HASH_SHA384 )
+#if defined(MBEDTLS_ECDSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA, MBEDTLS_SSL_HASH_SHA384 ),
 #endif
-    MBEDTLS_TLS1_3_SIG_NONE
+#if defined(MBEDTLS_RSA_C)
+    MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA, MBEDTLS_SSL_HASH_SHA384 ),
+#endif
+#endif /* MBEDTLS_SHA256_C */
+    MBEDTLS_TLS_SIG_NONE
 };
 #endif /* MBEDTLS_SSL_PROTO_TLS1_2 */
 
@@ -4220,7 +4240,7 @@ static int ssl_check_no_sig_alg_duplication( uint16_t * sig_algs )
     size_t i, j;
     int ret = 0;
 
-    for( i = 0; sig_algs[i] != MBEDTLS_TLS1_3_SIG_NONE; i++ )
+    for( i = 0; sig_algs[i] != MBEDTLS_TLS_SIG_NONE; i++ )
     {
         for( j = 0; j < i; j++ )
         {
@@ -4852,6 +4872,109 @@ int mbedtls_ssl_get_handshake_transcript( mbedtls_ssl_context *ssl,
 
 #endif /* !MBEDTLS_USE_PSA_CRYPTO */
 
+#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+/* mbedtls_ssl_parse_sig_alg_ext()
+ *
+ * The `extension_data` field of signature algorithm contains  a `SignatureSchemeList`
+ * value (TLS 1.3 RFC8446):
+ *      enum {
+ *         ....
+ *        ecdsa_secp256r1_sha256( 0x0403 ),
+ *        ecdsa_secp384r1_sha384( 0x0503 ),
+ *        ecdsa_secp521r1_sha512( 0x0603 ),
+ *         ....
+ *      } SignatureScheme;
+ *
+ *      struct {
+ *         SignatureScheme supported_signature_algorithms<2..2^16-2>;
+ *      } SignatureSchemeList;
+ *
+ * The `extension_data` field of signature algorithm contains a `SignatureAndHashAlgorithm`
+ * value (TLS 1.2 RFC5246):
+ *      enum {
+ *          none(0), md5(1), sha1(2), sha224(3), sha256(4), sha384(5),
+ *          sha512(6), (255)
+ *      } HashAlgorithm;
+ *
+ *      enum { anonymous(0), rsa(1), dsa(2), ecdsa(3), (255) }
+ *        SignatureAlgorithm;
+ *
+ *      struct {
+ *          HashAlgorithm hash;
+ *          SignatureAlgorithm signature;
+ *      } SignatureAndHashAlgorithm;
+ *
+ *      SignatureAndHashAlgorithm
+ *        supported_signature_algorithms<2..2^16-2>;
+ *
+ * The TLS 1.3 signature algorithm extension was defined to be a compatible
+ * generalization of the TLS 1.2 signature algorithm extension.
+ * `SignatureAndHashAlgorithm` field of TLS 1.2 can be represented by
+ * `SignatureScheme` field of TLS 1.3
+ *
+ */
+int mbedtls_ssl_parse_sig_alg_ext( mbedtls_ssl_context *ssl,
+                                   const unsigned char *buf,
+                                   const unsigned char *end )
+{
+    const unsigned char *p = buf;
+    size_t supported_sig_algs_len = 0;
+    const unsigned char *supported_sig_algs_end;
+    uint16_t sig_alg;
+    uint32_t common_idx = 0;
+
+    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
+    supported_sig_algs_len = MBEDTLS_GET_UINT16_BE( p, 0 );
+    p += 2;
+
+    memset( ssl->handshake->received_sig_algs, 0,
+            sizeof(ssl->handshake->received_sig_algs) );
+
+    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, supported_sig_algs_len );
+    supported_sig_algs_end = p + supported_sig_algs_len;
+    while( p < supported_sig_algs_end )
+    {
+        MBEDTLS_SSL_CHK_BUF_READ_PTR( p, supported_sig_algs_end, 2 );
+        sig_alg = MBEDTLS_GET_UINT16_BE( p, 0 );
+        p += 2;
+
+        MBEDTLS_SSL_DEBUG_MSG( 4, ( "received signature algorithm: 0x%x",
+                                    sig_alg ) );
+
+        if( ! mbedtls_ssl_sig_alg_is_supported( ssl, sig_alg ) ||
+            ! mbedtls_ssl_sig_alg_is_offered( ssl, sig_alg ) )
+            continue;
+
+        if( common_idx + 1 < MBEDTLS_RECEIVED_SIG_ALGS_SIZE )
+        {
+            ssl->handshake->received_sig_algs[common_idx] = sig_alg;
+            common_idx += 1;
+        }
+    }
+    /* Check that we consumed all the message. */
+    if( p != end )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1,
+            ( "Signature algorithms extension length misaligned" ) );
+        MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_DECODE_ERROR,
+                                      MBEDTLS_ERR_SSL_DECODE_ERROR );
+        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
+    }
+
+    if( common_idx == 0 )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 3, ( "no signature algorithm in common" ) );
+        MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_HANDSHAKE_FAILURE,
+                                      MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
+    }
+
+    ssl->handshake->received_sig_algs[common_idx] = MBEDTLS_TLS_SIG_NONE;
+    return( 0 );
+}
+
+#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
+
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2)
 
 #if defined(MBEDTLS_USE_PSA_CRYPTO)
@@ -7555,49 +7678,26 @@ exit:
 
 #if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
 
-/* Find an entry in a signature-hash set matching a given hash algorithm. */
-mbedtls_md_type_t mbedtls_ssl_sig_hash_set_find( mbedtls_ssl_sig_hash_set_t *set,
-                                                 mbedtls_pk_type_t sig_alg )
+/* Find the preferred hash for a given signature algorithm. */
+unsigned int mbedtls_ssl_tls12_get_preferred_hash_for_sig_alg(
+                mbedtls_ssl_context *ssl,
+                unsigned int sig_alg )
 {
-    switch( sig_alg )
+    unsigned int i;
+    uint16_t *received_sig_algs = ssl->handshake->received_sig_algs;
+
+    if( sig_alg == MBEDTLS_SSL_SIG_ANON )
+        return( MBEDTLS_SSL_HASH_NONE );
+
+    for( i = 0; received_sig_algs[i] != MBEDTLS_TLS_SIG_NONE; i++ )
     {
-        case MBEDTLS_PK_RSA:
-            return( set->rsa );
-        case MBEDTLS_PK_ECDSA:
-            return( set->ecdsa );
-        default:
-            return( MBEDTLS_MD_NONE );
+        if( sig_alg == MBEDTLS_SSL_TLS12_SIG_ALG_FROM_SIG_AND_HASH_ALG(
+                            received_sig_algs[i] ) )
+            return( MBEDTLS_SSL_TLS12_HASH_ALG_FROM_SIG_AND_HASH_ALG(
+                        received_sig_algs[i] ) );
     }
-}
 
-/* Add a signature-hash-pair to a signature-hash set */
-void mbedtls_ssl_sig_hash_set_add( mbedtls_ssl_sig_hash_set_t *set,
-                                   mbedtls_pk_type_t sig_alg,
-                                   mbedtls_md_type_t md_alg )
-{
-    switch( sig_alg )
-    {
-        case MBEDTLS_PK_RSA:
-            if( set->rsa == MBEDTLS_MD_NONE )
-                set->rsa = md_alg;
-            break;
-
-        case MBEDTLS_PK_ECDSA:
-            if( set->ecdsa == MBEDTLS_MD_NONE )
-                set->ecdsa = md_alg;
-            break;
-
-        default:
-            break;
-    }
-}
-
-/* Allow exactly one hash algorithm for each signature. */
-void mbedtls_ssl_sig_hash_set_const_hash( mbedtls_ssl_sig_hash_set_t *set,
-                                          mbedtls_md_type_t md_alg )
-{
-    set->rsa   = md_alg;
-    set->ecdsa = md_alg;
+    return( MBEDTLS_SSL_HASH_NONE );
 }
 
 #endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
diff --git a/library/ssl_tls12_server.c b/library/ssl_tls12_server.c
index 590c874d6..d09263344 100644
--- a/library/ssl_tls12_server.c
+++ b/library/ssl_tls12_server.c
@@ -209,96 +209,6 @@ static int ssl_parse_renegotiation_info( mbedtls_ssl_context *ssl,
     return( 0 );
 }
 
-#if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-
-/*
- * Status of the implementation of signature-algorithms extension:
- *
- * Currently, we are only considering the signature-algorithm extension
- * to pick a ciphersuite which allows us to send the ServerKeyExchange
- * message with a signature-hash combination that the user allows.
- *
- * We do *not* check whether all certificates in our certificate
- * chain are signed with an allowed signature-hash pair.
- * This needs to be done at a later stage.
- *
- */
-static int ssl_parse_sig_alg_ext( mbedtls_ssl_context *ssl,
-                                  const unsigned char *buf,
-                                  size_t len )
-{
-    size_t sig_alg_list_size;
-
-    const unsigned char *p;
-    const unsigned char *end = buf + len;
-
-    mbedtls_md_type_t md_cur;
-    mbedtls_pk_type_t sig_cur;
-
-    if ( len < 2 ) {
-        MBEDTLS_SSL_DEBUG_MSG( 1, ( "bad client hello message" ) );
-        mbedtls_ssl_send_alert_message( ssl, MBEDTLS_SSL_ALERT_LEVEL_FATAL,
-                                       MBEDTLS_SSL_ALERT_MSG_DECODE_ERROR );
-        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
-    }
-    sig_alg_list_size = ( ( buf[0] << 8 ) | ( buf[1] ) );
-    if( sig_alg_list_size + 2 != len ||
-        sig_alg_list_size % 2 != 0 )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 1, ( "bad client hello message" ) );
-        mbedtls_ssl_send_alert_message( ssl, MBEDTLS_SSL_ALERT_LEVEL_FATAL,
-                                        MBEDTLS_SSL_ALERT_MSG_DECODE_ERROR );
-        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
-    }
-
-    /* Currently we only guarantee signing the ServerKeyExchange message according
-     * to the constraints specified in this extension (see above), so it suffices
-     * to remember only one suitable hash for each possible signature algorithm.
-     *
-     * This will change when we also consider certificate signatures,
-     * in which case we will need to remember the whole signature-hash
-     * pair list from the extension.
-     */
-
-    for( p = buf + 2; p < end; p += 2 )
-    {
-        /* Silently ignore unknown signature or hash algorithms. */
-
-        if( ( sig_cur = mbedtls_ssl_pk_alg_from_sig( p[1] ) ) == MBEDTLS_PK_NONE )
-        {
-            MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext"
-                                        " unknown sig alg encoding %d", p[1] ) );
-            continue;
-        }
-
-        /* Check if we support the hash the user proposes */
-        md_cur = mbedtls_ssl_md_alg_from_hash( p[0] );
-        if( md_cur == MBEDTLS_MD_NONE )
-        {
-            MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext:"
-                                        " unknown hash alg encoding %d", p[0] ) );
-            continue;
-        }
-
-        if( mbedtls_ssl_sig_alg_is_offered(
-                ssl, MBEDTLS_GET_UINT16_BE( p, 0 ) ) )
-        {
-            mbedtls_ssl_sig_hash_set_add( &ssl->handshake->hash_algs, sig_cur, md_cur );
-            MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext:"
-                                        " match sig %u and hash %u",
-                                        (unsigned) sig_cur, (unsigned) md_cur ) );
-        }
-        else
-        {
-            MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext: "
-                                        "hash alg %u not supported", (unsigned) md_cur ) );
-        }
-    }
-
-    return( 0 );
-}
-#endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
-
 #if defined(MBEDTLS_ECDH_C) || defined(MBEDTLS_ECDSA_C) || \
     defined(MBEDTLS_KEY_EXCHANGE_ECJPAKE_ENABLED)
 /*
@@ -1078,7 +988,8 @@ static int ssl_ciphersuite_match( mbedtls_ssl_context *ssl, int suite_id,
      * a suitable hash algorithm is present. */
     sig_type = mbedtls_ssl_get_ciphersuite_sig_alg( suite_info );
     if( sig_type != MBEDTLS_PK_NONE &&
-        mbedtls_ssl_sig_hash_set_find( &ssl->handshake->hash_algs, sig_type ) == MBEDTLS_MD_NONE )
+        mbedtls_ssl_tls12_get_preferred_hash_for_sig_alg(
+            ssl, mbedtls_ssl_sig_from_pk_alg( sig_type ) ) == MBEDTLS_SSL_HASH_NONE )
     {
         MBEDTLS_SSL_DEBUG_MSG( 3, ( "ciphersuite mismatch: no suitable hash algorithm "
                                     "for signature algorithm %u", (unsigned) sig_type ) );
@@ -1593,7 +1504,7 @@ read_record_header:
             case MBEDTLS_TLS_EXT_SIG_ALG:
                 MBEDTLS_SSL_DEBUG_MSG( 3, ( "found signature_algorithms extension" ) );
 
-                ret = ssl_parse_sig_alg_ext( ssl, ext + 4, ext_size );
+                ret = mbedtls_ssl_parse_sig_alg_ext( ssl, ext + 4, ext + 4 + ext_size );
                 if( ret != 0 )
                     return( ret );
 
@@ -1717,18 +1628,27 @@ read_record_header:
      * Try to fall back to default hash SHA1 if the client
      * hasn't provided any preferred signature-hash combinations.
      */
-    if( sig_hash_alg_ext_present == 0 )
+    if( ! sig_hash_alg_ext_present )
     {
-        uint16_t sig_algs[] = { MBEDTLS_SSL_SIG_ALG(MBEDTLS_SSL_HASH_SHA1) };
-        mbedtls_md_type_t md_default = MBEDTLS_MD_NONE;
-        for( i = 0; i < sizeof( sig_algs ) / sizeof( sig_algs[0] ) ; i++ )
-        {
-            if( mbedtls_ssl_sig_alg_is_offered( ssl, sig_algs[ i ] ) )
-                md_default = MBEDTLS_MD_SHA1;
-        }
+        uint16_t *received_sig_algs = ssl->handshake->received_sig_algs;
+        const uint16_t default_sig_algs[] = {
+#if defined(MBEDTLS_ECDSA_C)
+            MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_ECDSA,
+                                                MBEDTLS_SSL_HASH_SHA1 ),
+#endif
+#if defined(MBEDTLS_RSA_C)
+            MBEDTLS_SSL_TLS12_SIG_AND_HASH_ALG( MBEDTLS_SSL_SIG_RSA,
+                                                MBEDTLS_SSL_HASH_SHA1 ),
+#endif
+            MBEDTLS_TLS_SIG_NONE
+        };
 
-        mbedtls_ssl_sig_hash_set_const_hash( &ssl->handshake->hash_algs,
-                                             md_default );
+#if defined(static_assert)
+        static_assert( sizeof( default_sig_algs ) / sizeof( default_sig_algs[0] ) <=
+                       MBEDTLS_RECEIVED_SIG_ALGS_SIZE, "default_sig_algs is too big" );
+#endif
+
+        memcpy( received_sig_algs, default_sig_algs, sizeof( default_sig_algs ) );
     }
 
 #endif /* MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED */
@@ -1889,10 +1809,10 @@ have_ciphersuite:
     mbedtls_pk_type_t sig_alg = mbedtls_ssl_get_ciphersuite_sig_alg( ciphersuite_info );
     if( sig_alg != MBEDTLS_PK_NONE )
     {
-        mbedtls_md_type_t md_alg = mbedtls_ssl_sig_hash_set_find( &ssl->handshake->hash_algs,
-                                                              sig_alg );
-        MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext: %d",
-                                    mbedtls_ssl_hash_from_md_alg( md_alg ) ) );
+        unsigned int sig_hash = mbedtls_ssl_tls12_get_preferred_hash_for_sig_alg(
+                                    ssl, mbedtls_ssl_sig_from_pk_alg( sig_alg ) );
+        MBEDTLS_SSL_DEBUG_MSG( 3, ( "client hello v3, signature_algorithm ext: %u",
+                                    sig_hash ) );
     }
     else
     {
@@ -2728,7 +2648,7 @@ static int ssl_write_certificate_request( mbedtls_ssl_context *ssl )
     if( sig_alg == NULL )
         return( MBEDTLS_ERR_SSL_BAD_CONFIG );
 
-    for( ; *sig_alg != MBEDTLS_TLS1_3_SIG_NONE; sig_alg++ )
+    for( ; *sig_alg != MBEDTLS_TLS_SIG_NONE; sig_alg++ )
     {
         unsigned char hash = MBEDTLS_BYTE_1( *sig_alg );
 
@@ -3255,15 +3175,18 @@ curve_matching_done:
          *      to choose appropriate hash.
          */
 
-        mbedtls_md_type_t md_alg;
         mbedtls_pk_type_t sig_alg =
             mbedtls_ssl_get_ciphersuite_sig_pk_alg( ciphersuite_info );
 
+        unsigned int sig_hash =
+            mbedtls_ssl_tls12_get_preferred_hash_for_sig_alg(
+                ssl, mbedtls_ssl_sig_from_pk_alg( sig_alg ) );
+
+        mbedtls_md_type_t md_alg = mbedtls_ssl_md_alg_from_hash( sig_hash );
+
         /*    For TLS 1.2, obey signature-hash-algorithm extension
          *    (RFC 5246, Sec. 7.4.1.4.1). */
-        if( sig_alg == MBEDTLS_PK_NONE ||
-            ( md_alg = mbedtls_ssl_sig_hash_set_find( &ssl->handshake->hash_algs,
-                                                      sig_alg ) ) == MBEDTLS_MD_NONE )
+        if( sig_alg == MBEDTLS_PK_NONE || md_alg == MBEDTLS_MD_NONE )
         {
             MBEDTLS_SSL_DEBUG_MSG( 1, ( "should never happen" ) );
             /* (... because we choose a cipher suite
diff --git a/library/ssl_tls13_client.c b/library/ssl_tls13_client.c
index 320c5b4b2..305ac0050 100644
--- a/library/ssl_tls13_client.c
+++ b/library/ssl_tls13_client.c
@@ -1612,8 +1612,8 @@ static int ssl_tls13_parse_certificate_request( mbedtls_ssl_context *ssl,
             case MBEDTLS_TLS_EXT_SIG_ALG:
                 MBEDTLS_SSL_DEBUG_MSG( 3,
                         ( "found signature algorithms extension" ) );
-                ret = mbedtls_ssl_tls13_parse_sig_alg_ext( ssl, p,
-                              p + extension_data_len );
+                ret = mbedtls_ssl_parse_sig_alg_ext( ssl, p,
+                                                     p + extension_data_len );
                 if( ret != 0 )
                     return( ret );
                 if( ! sig_alg_ext_found )
diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index 9de9d6d9c..f5e38abf5 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -80,80 +80,6 @@ cleanup:
 }
 
 #if defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
-/* mbedtls_ssl_tls13_parse_sig_alg_ext()
- *
- * enum {
- *    ....
- *   ecdsa_secp256r1_sha256( 0x0403 ),
- *   ecdsa_secp384r1_sha384( 0x0503 ),
- *   ecdsa_secp521r1_sha512( 0x0603 ),
- *    ....
- * } SignatureScheme;
- *
- * struct {
- *    SignatureScheme supported_signature_algorithms<2..2^16-2>;
- * } SignatureSchemeList;
- */
-int mbedtls_ssl_tls13_parse_sig_alg_ext( mbedtls_ssl_context *ssl,
-                                         const unsigned char *buf,
-                                         const unsigned char *end )
-{
-    const unsigned char *p = buf;
-    size_t supported_sig_algs_len = 0;
-    const unsigned char *supported_sig_algs_end;
-    uint16_t sig_alg;
-    uint32_t common_idx = 0;
-
-    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, 2 );
-    supported_sig_algs_len = MBEDTLS_GET_UINT16_BE( p, 0 );
-    p += 2;
-
-    memset( ssl->handshake->received_sig_algs, 0,
-            sizeof(ssl->handshake->received_sig_algs) );
-
-    MBEDTLS_SSL_CHK_BUF_READ_PTR( p, end, supported_sig_algs_len );
-    supported_sig_algs_end = p + supported_sig_algs_len;
-    while( p < supported_sig_algs_end )
-    {
-        MBEDTLS_SSL_CHK_BUF_READ_PTR( p, supported_sig_algs_end, 2 );
-        sig_alg = MBEDTLS_GET_UINT16_BE( p, 0 );
-        p += 2;
-
-        MBEDTLS_SSL_DEBUG_MSG( 4, ( "received signature algorithm: 0x%x",
-                                    sig_alg ) );
-
-        if( ! mbedtls_ssl_sig_alg_is_supported( ssl, sig_alg ) ||
-            ! mbedtls_ssl_sig_alg_is_offered( ssl, sig_alg ) )
-            continue;
-
-        if( common_idx + 1 < MBEDTLS_RECEIVED_SIG_ALGS_SIZE )
-        {
-            ssl->handshake->received_sig_algs[common_idx] = sig_alg;
-            common_idx += 1;
-        }
-    }
-    /* Check that we consumed all the message. */
-    if( p != end )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 1,
-            ( "Signature algorithms extension length misaligned" ) );
-        MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_DECODE_ERROR,
-                                      MBEDTLS_ERR_SSL_DECODE_ERROR );
-        return( MBEDTLS_ERR_SSL_DECODE_ERROR );
-    }
-
-    if( common_idx == 0 )
-    {
-        MBEDTLS_SSL_DEBUG_MSG( 3, ( "no signature algorithm in common" ) );
-        MBEDTLS_SSL_PEND_FATAL_ALERT( MBEDTLS_SSL_ALERT_MSG_HANDSHAKE_FAILURE,
-                                      MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
-        return( MBEDTLS_ERR_SSL_HANDSHAKE_FAILURE );
-    }
-
-    ssl->handshake->received_sig_algs[common_idx] = MBEDTLS_TLS1_3_SIG_NONE;
-    return( 0 );
-}
-
 /*
  * STATE HANDLING: Read CertificateVerify
  */
diff --git a/library/ssl_tls13_server.c b/library/ssl_tls13_server.c
index ca1990813..769ed488a 100644
--- a/library/ssl_tls13_server.c
+++ b/library/ssl_tls13_server.c
@@ -651,7 +651,7 @@ static int ssl_tls13_parse_client_hello( mbedtls_ssl_context *ssl,
             case MBEDTLS_TLS_EXT_SIG_ALG:
                 MBEDTLS_SSL_DEBUG_MSG( 3, ( "found signature_algorithms extension" ) );
 
-                ret = mbedtls_ssl_tls13_parse_sig_alg_ext(
+                ret = mbedtls_ssl_parse_sig_alg_ext(
                           ssl, p, extension_data_end );
                 if( ret != 0 )
                 {