Use tls_choose_sigalg for client auth.

For client auth call tls_choose_sigalg to select the certificate
and signature algorithm. Use the selected algorithm in
tls_construct_cert_verify.

Remove obsolete tls12_get_sigandhash.

Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/2643)
diff --git a/ssl/statem/statem_clnt.c b/ssl/statem/statem_clnt.c
index 8ca3c4c..4923e24 100644
--- a/ssl/statem/statem_clnt.c
+++ b/ssl/statem/statem_clnt.c
@@ -3090,10 +3090,8 @@
  */
 static int ssl3_check_client_certificate(SSL *s)
 {
-    if (!s->cert || !s->cert->key->x509 || !s->cert->key->privatekey)
-        return 0;
     /* If no suitable signature algorithm can't use certificate */
-    if (SSL_USE_SIGALGS(s) && !s->s3->tmp.md[s->cert->key - s->cert->pkeys])
+    if (!tls_choose_sigalg(s, NULL) || s->s3->tmp.sigalg == NULL)
         return 0;
     /*
      * If strict mode check suitability of chain before using it. This also
diff --git a/ssl/statem/statem_lib.c b/ssl/statem/statem_lib.c
index 31156fd..ed07266 100644
--- a/ssl/statem/statem_lib.c
+++ b/ssl/statem/statem_lib.c
@@ -171,17 +171,27 @@
 
 int tls_construct_cert_verify(SSL *s, WPACKET *pkt)
 {
-    EVP_PKEY *pkey = s->cert->key->privatekey;
-    const EVP_MD *md = s->s3->tmp.md[s->cert->key - s->cert->pkeys];
+    EVP_PKEY *pkey = NULL;
+    const EVP_MD *md = NULL;
     EVP_MD_CTX *mctx = NULL;
     EVP_PKEY_CTX *pctx = NULL;
     size_t hdatalen = 0, siglen = 0;
     void *hdata;
     unsigned char *sig = NULL;
     unsigned char tls13tbs[TLS13_TBS_PREAMBLE_SIZE + EVP_MAX_MD_SIZE];
-    int pktype, ispss = 0;
+    const SIGALG_LOOKUP *lu = s->s3->tmp.sigalg;
 
-    pktype = EVP_PKEY_id(pkey);
+    if (lu == NULL || s->s3->tmp.cert == NULL) {
+        SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
+        goto err;
+    }
+    pkey = s->s3->tmp.cert->privatekey;
+    md = ssl_md(lu->hash_idx);
+
+    if (pkey == NULL || md == NULL) {
+        SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
+        goto err;
+    }
 
     mctx = EVP_MD_CTX_new();
     if (mctx == NULL) {
@@ -195,13 +205,10 @@
         goto err;
     }
 
-    if (SSL_USE_SIGALGS(s) && !tls12_get_sigandhash(s, pkt, pkey, md, &ispss)) {
+    if (SSL_USE_SIGALGS(s) && !WPACKET_put_bytes_u16(pkt, lu->sigalg)) {
         SSLerr(SSL_F_TLS_CONSTRUCT_CERT_VERIFY, ERR_R_INTERNAL_ERROR);
         goto err;
     }
-#ifdef SSL_DEBUG
-    fprintf(stderr, "Using client alg %s\n", EVP_MD_name(md));
-#endif
     siglen = EVP_PKEY_size(pkey);
     sig = OPENSSL_malloc(siglen);
     if (sig == NULL) {
@@ -215,7 +222,7 @@
         goto err;
     }
 
-    if (ispss) {
+    if (lu->sig == EVP_PKEY_RSA_PSS) {
         if (EVP_PKEY_CTX_set_rsa_padding(pctx, RSA_PKCS1_PSS_PADDING) <= 0
             || EVP_PKEY_CTX_set_rsa_pss_saltlen(pctx,
                                                 RSA_PSS_SALTLEN_DIGEST) <= 0) {
@@ -238,6 +245,8 @@
 
 #ifndef OPENSSL_NO_GOST
     {
+        int pktype = lu->sig;
+
         if (pktype == NID_id_GostR3410_2001
             || pktype == NID_id_GostR3410_2012_256
             || pktype == NID_id_GostR3410_2012_512)