diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index 1ff23bc..79ecfff 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -107,11 +107,60 @@
                                          unsigned char *end,
                                          size_t *olen )
 {
-    ((void) ssl);
-    ((void) buf);
-    ((void) end);
+    unsigned char *p = buf;
+    unsigned char *sig_alg_ptr; /* Start of supported_signature_algorithms */
+    size_t sig_alg_len = 0;     /* Length of supported_signature_algorithms */
+
     *olen = 0;
-    MBEDTLS_SSL_DEBUG_MSG( 3, ( "signature_algorithm extension is not available" ) );
+
+    /* Skip the extension on the client if all allowed key exchanges
+     * are PSK-based. */
+#if defined(MBEDTLS_SSL_CLI_C)
+    if( ssl->conf->endpoint == MBEDTLS_SSL_IS_CLIENT &&
+        !mbedtls_ssl_conf_tls13_some_ephemeral_enabled( ssl ) )
+    {
+        return( 0 );
+    }
+#endif /* MBEDTLS_SSL_CLI_C */
+
+    MBEDTLS_SSL_DEBUG_MSG( 3, ( "adding signature_algorithms extension" ) );
+
+    /* Check there is space for extension header */
+    MBEDTLS_SSL_CHK_BUF_PTR( p, end, 6 );
+    p += 6;
+
+    /*
+     * Write supported_signature_algorithms
+     */
+    sig_alg_ptr = p;
+    for( const uint16_t *sig_alg = ssl->conf->tls13_sig_algs;
+         *sig_alg != MBEDTLS_TLS13_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*/
+    sig_alg_len = p - sig_alg_ptr;
+    if( 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( sig_alg_len + 2, buf, 2 );
+    /* Write length of supported_signature_algorithms */
+    MBEDTLS_PUT_UINT16_BE( sig_alg_len, buf, 4 );
+
+    /* Output the total length of signature algorithms extension. */
+    *olen = p - buf;
+
+    ssl->handshake->extensions_present |= MBEDTLS_SSL_EXT_SIG_ALG;
     return( 0 );
 }