diff --git a/library/ssl_cli.c b/library/ssl_cli.c
index a6f9e7d..023fac6 100644
--- a/library/ssl_cli.c
+++ b/library/ssl_cli.c
@@ -204,67 +204,15 @@
  */
 #if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
     defined(MBEDTLS_KEY_EXCHANGE_WITH_CERT_ENABLED)
+
 static int ssl_write_sig_alg_ext( mbedtls_ssl_context *ssl, unsigned char *buf,
-                                  const unsigned char *end, size_t *olen )
+                                  const unsigned char *end, size_t *out_len )
 {
     unsigned char *p = buf;
-    size_t sig_alg_len = 0;
-    const int *md = mbedtls_ssl_conf_get_sig_algs( ssl->conf );
+    unsigned char *supported_sig_alg; /* Start of supported_signature_algorithms */
+    size_t supported_sig_alg_len = 0; /* Length of supported_signature_algorithms */
 
-#if defined(MBEDTLS_RSA_C) || defined(MBEDTLS_ECDSA_C)
-    unsigned char *sig_alg_list = buf + 6;
-#endif
-
-    *olen = 0;
-
-    if( ssl->conf->max_minor_ver != MBEDTLS_SSL_MINOR_VERSION_3 )
-        return( 0 );
-
-    MBEDTLS_SSL_DEBUG_MSG( 3,
-        ( "client hello, adding signature_algorithms extension" ) );
-
-    if( md == NULL )
-        return( MBEDTLS_ERR_SSL_BAD_CONFIG );
-
-    for( ; *md != MBEDTLS_MD_NONE; md++ )
-    {
-#if defined(MBEDTLS_ECDSA_C)
-        sig_alg_len += 2;
-#endif
-#if defined(MBEDTLS_RSA_C)
-        sig_alg_len += 2;
-#endif
-        if( sig_alg_len > MBEDTLS_SSL_MAX_SIG_HASH_ALG_LIST_LEN )
-        {
-            MBEDTLS_SSL_DEBUG_MSG( 3,
-                ( "length in bytes of sig-hash-alg extension too big" ) );
-            return( MBEDTLS_ERR_SSL_BAD_CONFIG );
-        }
-    }
-
-    /* Empty signature algorithms list, this is a configuration error. */
-    if( sig_alg_len == 0 )
-        return( MBEDTLS_ERR_SSL_BAD_CONFIG );
-
-    MBEDTLS_SSL_CHK_BUF_PTR( p, end, sig_alg_len + 6 );
-
-    /*
-     * Prepare signature_algorithms extension (TLS 1.2)
-     */
-    sig_alg_len = 0;
-
-    for( md = mbedtls_ssl_conf_get_sig_algs( ssl->conf );
-         *md != MBEDTLS_MD_NONE; md++ )
-    {
-#if defined(MBEDTLS_ECDSA_C)
-        sig_alg_list[sig_alg_len++] = mbedtls_ssl_hash_from_md_alg( *md );
-        sig_alg_list[sig_alg_len++] = MBEDTLS_SSL_SIG_ECDSA;
-#endif
-#if defined(MBEDTLS_RSA_C)
-        sig_alg_list[sig_alg_len++] = mbedtls_ssl_hash_from_md_alg( *md );
-        sig_alg_list[sig_alg_len++] = MBEDTLS_SSL_SIG_RSA;
-#endif
-    }
+    *out_len = 0;
 
     /*
      * enum {
@@ -283,16 +231,47 @@
      * SignatureAndHashAlgorithm
      *   supported_signature_algorithms<2..2^16-2>;
      */
-    MBEDTLS_PUT_UINT16_BE( MBEDTLS_TLS_EXT_SIG_ALG, p, 0 );
-    p += 2;
 
-    MBEDTLS_PUT_UINT16_BE( sig_alg_len + 2, p, 0 );
-    p += 2;
+    MBEDTLS_SSL_DEBUG_MSG( 3, ( "adding signature_algorithms extension" ) );
 
-    MBEDTLS_PUT_UINT16_BE( sig_alg_len, p, 0 );
-    p += 2;
+    /* Check if we have space for header and length field:
+     * - extension_type         (2 bytes)
+     * - extension_data_length  (2 bytes)
+     * - supported_signature_algorithms_length   (2 bytes)
+     */
+    MBEDTLS_SSL_CHK_BUF_PTR( p, end, 6 );
+    p += 6;
 
-    *olen = 6 + sig_alg_len;
+    /*
+     * Write supported_signature_algorithms
+     */
+    supported_sig_alg = p;
+    for( const uint16_t *sig_alg = mbedtls_ssl_conf_get_sig_algs( ssl->conf );
+         *sig_alg != MBEDTLS_TLS1_3_SIG_NONE; sig_alg++ )
+    {
+        MBEDTLS_SSL_CHK_BUF_PTR( p, end, 2 );
+        MBEDTLS_PUT_UINT16_BE( *sig_alg, p, 0 );
+        p += 2;
+        MBEDTLS_SSL_DEBUG_MSG( 3, ( "signature scheme [%x]", *sig_alg ) );
+    }
+
+    /* Length of supported_signature_algorithms */
+    supported_sig_alg_len = p - supported_sig_alg;
+    if( supported_sig_alg_len == 0 )
+    {
+        MBEDTLS_SSL_DEBUG_MSG( 1, ( "No signature algorithms defined." ) );
+        return( MBEDTLS_ERR_SSL_INTERNAL_ERROR );
+    }
+
+    /* Write extension_type */
+    MBEDTLS_PUT_UINT16_BE( MBEDTLS_TLS_EXT_SIG_ALG, buf, 0 );
+    /* Write extension_data_length */
+    MBEDTLS_PUT_UINT16_BE( supported_sig_alg_len + 2, buf, 2 );
+    /* Write length of supported_signature_algorithms */
+    MBEDTLS_PUT_UINT16_BE( supported_sig_alg_len, buf, 4 );
+
+    /* Output the total length of signature algorithms extension. */
+    *out_len = p - buf;
 
     return( 0 );
 }