diff --git a/library/ssl_misc.h b/library/ssl_misc.h
index 997a38d5d5..b40f3355c8 100644
--- a/library/ssl_misc.h
+++ b/library/ssl_misc.h
@@ -1673,6 +1673,38 @@ static inline mbedtls_x509_crt *mbedtls_ssl_own_cert(mbedtls_ssl_context *ssl)
     return key_cert == NULL ? NULL : key_cert->cert;
 }
 
+/*
+ * Verify a certificate.
+ *
+ * [in/out] ssl: misc. things read
+ *               ssl->session_negotiate->verify_result updated
+ * [in] authmode: one of MBEDTLS_SSL_VERIFY_{NONE,OPTIONAL,REQUIRED}
+ * [in] chain: the certificate chain to verify (ie the peer's chain)
+ * [in] ciphersuite_info: For TLS 1.2, this session's ciphersuite;
+ *                        for TLS 1.3, may be left NULL.
+ * [in] rs_ctx: restart context if restartable ECC is in use;
+ *              leave NULL for no restartable behaviour.
+ *
+ * Return:
+ * - 0 if the certificate is the handshake should continue. Depending on the
+ *   authmode it means:
+ *   - REQUIRED: the certificate was found to be valid, trusted & acceptable.
+ *     ssl->session_negotiate->verify_result is 0.
+ *   - OPTIONAL: the certificate may or may not be acceptable, but
+ *     ssl->session_negotiate->verify_result was updated with the result.
+ *   - NONE: the certificate wasn't even checked.
+ * - MBEDTLS_ERR_X509_CERT_VERIFY_FAILED or MBEDTLS_ERR_SSL_BAD_CERTIFICATE if
+ *   the certificate was found to be invalid/untrusted/unacceptable and the
+ *   handshake should be aborted (can only happen with REQUIRED).
+ * - another error code if another error happened (out-of-memory, etc.)
+ */
+MBEDTLS_CHECK_RETURN_CRITICAL
+int mbedtls_ssl_verify_certificate(mbedtls_ssl_context *ssl,
+                                   int authmode,
+                                   mbedtls_x509_crt *chain,
+                                   const mbedtls_ssl_ciphersuite_t *ciphersuite_info,
+                                   void *rs_ctx);
+
 /*
  * Check usage of a certificate wrt usage extensions:
  * keyUsage and extendedKeyUsage.
diff --git a/library/ssl_tls.c b/library/ssl_tls.c
index e87f985e51..fb48b95c14 100644
--- a/library/ssl_tls.c
+++ b/library/ssl_tls.c
@@ -7938,12 +7938,11 @@ static int ssl_parse_certificate_coordinate(mbedtls_ssl_context *ssl,
     return SSL_CERTIFICATE_EXPECTED;
 }
 
-MBEDTLS_CHECK_RETURN_CRITICAL
-static int ssl_verify_certificate(mbedtls_ssl_context *ssl,
-                                  int authmode,
-                                  mbedtls_x509_crt *chain,
-                                  const mbedtls_ssl_ciphersuite_t *ciphersuite_info,
-                                  void *rs_ctx)
+int mbedtls_ssl_verify_certificate(mbedtls_ssl_context *ssl,
+                                   int authmode,
+                                   mbedtls_x509_crt *chain,
+                                   const mbedtls_ssl_ciphersuite_t *ciphersuite_info,
+                                   void *rs_ctx)
 {
     int ret = 0;
     int have_ca_chain_or_callback = 0;
@@ -8025,23 +8024,32 @@ static int ssl_verify_certificate(mbedtls_ssl_context *ssl,
      * Secondary checks: always done, but change 'ret' only if it was 0
      */
 
-    /* Check curve for ECC certs */
-#if defined(PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY)
-    if (mbedtls_pk_can_do(&chain->pk, MBEDTLS_PK_ECKEY) &&
-        mbedtls_ssl_check_curve(ssl, mbedtls_pk_get_ec_group_id(&chain->pk)) != 0) {
-        MBEDTLS_SSL_DEBUG_MSG(1, ("bad certificate (EC key curve)"));
-        ssl->session_negotiate->verify_result |= MBEDTLS_X509_BADCERT_BAD_KEY;
-        if (ret == 0) {
-            ret = MBEDTLS_ERR_SSL_BAD_CERTIFICATE;
+    /* With TLS 1.2 and ECC certs, check that the curve used by the
+     * certificate is on our list of acceptable curves.
+     *
+     * With TLS 1.3 this is not needed because the curve is part of the
+     * signature algorithm (eg ecdsa_secp256r1_sha256) which is checked when
+     * we validate the signature made with the key associated to this cert.
+     */
+#if defined(MBEDTLS_SSL_PROTO_TLS1_2) && \
+    defined(PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY)
+    if (ssl->tls_version == MBEDTLS_SSL_VERSION_TLS1_2 &&
+        mbedtls_pk_can_do(&chain->pk, MBEDTLS_PK_ECKEY)) {
+        if (mbedtls_ssl_check_curve(ssl, mbedtls_pk_get_ec_group_id(&chain->pk)) != 0) {
+            MBEDTLS_SSL_DEBUG_MSG(1, ("bad certificate (EC key curve)"));
+            ssl->session_negotiate->verify_result |= MBEDTLS_X509_BADCERT_BAD_KEY;
+            if (ret == 0) {
+                ret = MBEDTLS_ERR_SSL_BAD_CERTIFICATE;
+            }
         }
     }
-#endif /* PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY */
+#endif /* MBEDTLS_SSL_PROTO_TLS1_2 && PSA_WANT_KEY_TYPE_ECC_PUBLIC_KEY */
 
     /* Check X.509 usage extensions (keyUsage, extKeyUsage) */
     if (mbedtls_ssl_check_cert_usage(chain,
                                      ciphersuite_info,
                                      ssl->conf->endpoint,
-                                     MBEDTLS_SSL_VERSION_TLS1_2,
+                                     ssl->tls_version,
                                      &ssl->session_negotiate->verify_result) != 0) {
         MBEDTLS_SSL_DEBUG_MSG(1, ("bad certificate (usage extensions)"));
         if (ret == 0) {
@@ -8245,8 +8253,9 @@ crt_verify:
     }
 #endif
 
-    ret = ssl_verify_certificate(ssl, authmode, chain,
-                                 ssl->handshake->ciphersuite_info, rs_ctx);
+    ret = mbedtls_ssl_verify_certificate(ssl, authmode, chain,
+                                         ssl->handshake->ciphersuite_info,
+                                         rs_ctx);
     if (ret != 0) {
         goto exit;
     }
diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index fb57aa4a75..3f1f551dd1 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -628,10 +628,6 @@ int mbedtls_ssl_tls13_parse_certificate(mbedtls_ssl_context *ssl,
 MBEDTLS_CHECK_RETURN_CRITICAL
 static int ssl_tls13_validate_certificate(mbedtls_ssl_context *ssl)
 {
-    int ret = 0;
-    int have_ca_chain_or_callback = 0;
-    uint32_t verify_result = 0;
-
     /* Authmode: precedence order is SNI if used else configuration */
 #if defined(MBEDTLS_SSL_SRV_C) && defined(MBEDTLS_SSL_SERVER_NAME_INDICATION)
     const int authmode = ssl->handshake->sni_authmode != MBEDTLS_SSL_VERIFY_UNSET
@@ -683,152 +679,9 @@ static int ssl_tls13_validate_certificate(mbedtls_ssl_context *ssl)
 #endif /* MBEDTLS_SSL_CLI_C */
     }
 
-    /*
-     * NONE means we skip all checks
-     *
-     * Note: we still check above that the server did send a certificate,
-     * because only a non-compliant server would fail to do so. NONE means we
-     * don't care about the server certificate being valid, but we still care
-     * about the server otherwise following the TLS standard.
-     */
-    if (authmode == MBEDTLS_SSL_VERIFY_NONE) {
-        return 0;
-    }
-
-    /* Verify callback: precedence order is SSL context, else conf struct. */
-    int (*f_vrfy)(void *, mbedtls_x509_crt *, int, uint32_t *);
-    void *p_vrfy;
-    if (ssl->f_vrfy != NULL) {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("Use context-specific verification callback"));
-        f_vrfy = ssl->f_vrfy;
-        p_vrfy = ssl->p_vrfy;
-    } else {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("Use configuration-specific verification callback"));
-        f_vrfy = ssl->conf->f_vrfy;
-        p_vrfy = ssl->conf->p_vrfy;
-    }
-
-    /*
-     * Main check: verify certificate
-     */
-#if defined(MBEDTLS_X509_TRUSTED_CERTIFICATE_CALLBACK)
-    if (ssl->conf->f_ca_cb != NULL) {
-        have_ca_chain_or_callback = 1;
-
-        MBEDTLS_SSL_DEBUG_MSG(3, ("use CA callback for X.509 CRT verification"));
-        ret = mbedtls_x509_crt_verify_with_ca_cb(
-            ssl->session_negotiate->peer_cert,
-            ssl->conf->f_ca_cb,
-            ssl->conf->p_ca_cb,
-            ssl->conf->cert_profile,
-            ssl->hostname,
-            &verify_result,
-            f_vrfy, p_vrfy);
-    } else
-#endif /* MBEDTLS_X509_TRUSTED_CERTIFICATE_CALLBACK */
-    {
-        mbedtls_x509_crt *ca_chain;
-        mbedtls_x509_crl *ca_crl;
-#if defined(MBEDTLS_SSL_SERVER_NAME_INDICATION)
-        if (ssl->handshake->sni_ca_chain != NULL) {
-            ca_chain = ssl->handshake->sni_ca_chain;
-            ca_crl = ssl->handshake->sni_ca_crl;
-        } else
-#endif /* MBEDTLS_SSL_SERVER_NAME_INDICATION */
-        {
-            ca_chain = ssl->conf->ca_chain;
-            ca_crl = ssl->conf->ca_crl;
-        }
-
-        if (ca_chain != NULL) {
-            have_ca_chain_or_callback = 1;
-        }
-
-        ret = mbedtls_x509_crt_verify_with_profile(
-            ssl->session_negotiate->peer_cert,
-            ca_chain, ca_crl,
-            ssl->conf->cert_profile,
-            ssl->hostname,
-            &verify_result,
-            f_vrfy, p_vrfy);
-    }
-
-    if (ret != 0) {
-        MBEDTLS_SSL_DEBUG_RET(1, "x509_verify_cert", ret);
-    }
-
-    /*
-     * Secondary checks: always done, but change 'ret' only if it was 0
-     */
-    if (mbedtls_ssl_check_cert_usage(ssl->session_negotiate->peer_cert,
-                                     NULL,
-                                     ssl->conf->endpoint,
-                                     MBEDTLS_SSL_VERSION_TLS1_3,
-                                     &verify_result) != 0) {
-        MBEDTLS_SSL_DEBUG_MSG(1, ("bad certificate (usage extensions)"));
-        if (ret == 0) {
-            ret = MBEDTLS_ERR_SSL_BAD_CERTIFICATE;
-        }
-    }
-
-    /* mbedtls_x509_crt_verify_with_profile is supposed to report a
-     * verification failure through MBEDTLS_ERR_X509_CERT_VERIFY_FAILED,
-     * with details encoded in the verification flags. All other kinds
-     * of error codes, including those from the user provided f_vrfy
-     * functions, are treated as fatal and lead to a failure of
-     * mbedtls_ssl_tls13_parse_certificate even if verification was optional.
-     */
-    if (authmode == MBEDTLS_SSL_VERIFY_OPTIONAL &&
-        (ret == MBEDTLS_ERR_X509_CERT_VERIFY_FAILED ||
-         ret == MBEDTLS_ERR_SSL_BAD_CERTIFICATE)) {
-        ret = 0;
-    }
-
-    if (!have_ca_chain_or_callback && authmode == MBEDTLS_SSL_VERIFY_REQUIRED) {
-        MBEDTLS_SSL_DEBUG_MSG(1, ("got no CA chain"));
-        ret = MBEDTLS_ERR_SSL_CA_CHAIN_REQUIRED;
-    }
-
-    if (ret != 0) {
-        /* The certificate may have been rejected for several reasons.
-           Pick one and send the corresponding alert. Which alert to send
-           may be a subject of debate in some cases. */
-        if (verify_result & MBEDTLS_X509_BADCERT_OTHER) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(
-                MBEDTLS_SSL_ALERT_MSG_ACCESS_DENIED, ret);
-        } else if (verify_result & MBEDTLS_X509_BADCERT_CN_MISMATCH) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(MBEDTLS_SSL_ALERT_MSG_BAD_CERT, ret);
-        } else if (verify_result & (MBEDTLS_X509_BADCERT_KEY_USAGE |
-                                    MBEDTLS_X509_BADCERT_EXT_KEY_USAGE |
-                                    MBEDTLS_X509_BADCERT_BAD_PK |
-                                    MBEDTLS_X509_BADCERT_BAD_KEY)) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(
-                MBEDTLS_SSL_ALERT_MSG_UNSUPPORTED_CERT, ret);
-        } else if (verify_result & MBEDTLS_X509_BADCERT_EXPIRED) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(
-                MBEDTLS_SSL_ALERT_MSG_CERT_EXPIRED, ret);
-        } else if (verify_result & MBEDTLS_X509_BADCERT_REVOKED) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(
-                MBEDTLS_SSL_ALERT_MSG_CERT_REVOKED, ret);
-        } else if (verify_result & MBEDTLS_X509_BADCERT_NOT_TRUSTED) {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(MBEDTLS_SSL_ALERT_MSG_UNKNOWN_CA, ret);
-        } else {
-            MBEDTLS_SSL_PEND_FATAL_ALERT(
-                MBEDTLS_SSL_ALERT_MSG_CERT_UNKNOWN, ret);
-        }
-    }
-
-#if defined(MBEDTLS_DEBUG_C)
-    if (verify_result != 0) {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("! Certificate verification flags %08x",
-                                  (unsigned int) verify_result));
-    } else {
-        MBEDTLS_SSL_DEBUG_MSG(3, ("Certificate verification flags clear"));
-    }
-#endif /* MBEDTLS_DEBUG_C */
-
-    ssl->session_negotiate->verify_result = verify_result;
-    return ret;
+    return mbedtls_ssl_verify_certificate(ssl, authmode,
+                                          ssl->session_negotiate->peer_cert,
+                                          NULL, NULL);
 }
 #else /* MBEDTLS_SSL_KEEP_PEER_CERTIFICATE */
 MBEDTLS_CHECK_RETURN_CRITICAL