diff --git a/apps/s_apps.h b/apps/s_apps.h
index c47932bfb6..4c24b2eb28 100644
--- a/apps/s_apps.h
+++ b/apps/s_apps.h
@@ -59,7 +59,7 @@ int set_cert_key_stuff(SSL_CTX *ctx, X509 *cert, EVP_PKEY *key,
                        STACK_OF(X509) *chain, int build_chain);
 int ssl_print_sigalgs(BIO *out, SSL *s);
 int ssl_print_point_formats(BIO *out, SSL *s);
-int ssl_print_curves(BIO *out, SSL *s, int noshared);
+int ssl_print_groups(BIO *out, SSL *s, int noshared);
 #endif
 int ssl_print_tmp_key(BIO *out, SSL *s);
 int init_client(int *sock, const char *host, const char *port,
diff --git a/apps/s_cb.c b/apps/s_cb.c
index c37b9a1cda..d5c308ee13 100644
--- a/apps/s_cb.c
+++ b/apps/s_cb.c
@@ -307,50 +307,52 @@ int ssl_print_point_formats(BIO *out, SSL *s)
     return 1;
 }
 
-int ssl_print_curves(BIO *out, SSL *s, int noshared)
+int ssl_print_groups(BIO *out, SSL *s, int noshared)
 {
-    int i, ncurves, *curves, nid;
-    const char *cname;
+    int i, ngroups, *groups, nid;
+    const char *gname;
 
-    ncurves = SSL_get1_curves(s, NULL);
-    if (ncurves <= 0)
+    ngroups = SSL_get1_groups(s, NULL);
+    if (ngroups <= 0)
         return 1;
-    curves = app_malloc(ncurves * sizeof(int), "curves to print");
-    SSL_get1_curves(s, curves);
+    groups = app_malloc(ngroups * sizeof(int), "groups to print");
+    SSL_get1_groups(s, groups);
 
-    BIO_puts(out, "Supported Elliptic Curves: ");
-    for (i = 0; i < ncurves; i++) {
+    BIO_puts(out, "Supported Elliptic Groups: ");
+    for (i = 0; i < ngroups; i++) {
         if (i)
             BIO_puts(out, ":");
-        nid = curves[i];
+        nid = groups[i];
         /* If unrecognised print out hex version */
         if (nid & TLSEXT_nid_unknown)
             BIO_printf(out, "0x%04X", nid & 0xFFFF);
         else {
+            /* TODO(TLS1.3): Get group name here */
             /* Use NIST name for curve if it exists */
-            cname = EC_curve_nid2nist(nid);
-            if (!cname)
-                cname = OBJ_nid2sn(nid);
-            BIO_printf(out, "%s", cname);
+            gname = EC_curve_nid2nist(nid);
+            if (!gname)
+                gname = OBJ_nid2sn(nid);
+            BIO_printf(out, "%s", gname);
         }
     }
-    OPENSSL_free(curves);
+    OPENSSL_free(groups);
     if (noshared) {
         BIO_puts(out, "\n");
         return 1;
     }
-    BIO_puts(out, "\nShared Elliptic curves: ");
-    ncurves = SSL_get_shared_curve(s, -1);
-    for (i = 0; i < ncurves; i++) {
+    BIO_puts(out, "\nShared Elliptic groups: ");
+    ngroups = SSL_get_shared_group(s, -1);
+    for (i = 0; i < ngroups; i++) {
         if (i)
             BIO_puts(out, ":");
-        nid = SSL_get_shared_curve(s, i);
-        cname = EC_curve_nid2nist(nid);
-        if (!cname)
-            cname = OBJ_nid2sn(nid);
-        BIO_printf(out, "%s", cname);
+        nid = SSL_get_shared_group(s, i);
+        /* TODO(TLS1.3): Convert for DH groups */
+        gname = EC_curve_nid2nist(nid);
+        if (!gname)
+            gname = OBJ_nid2sn(nid);
+        BIO_printf(out, "%s", gname);
     }
-    if (ncurves == 0)
+    if (ngroups == 0)
         BIO_puts(out, "NONE");
     BIO_puts(out, "\n");
     return 1;
@@ -604,7 +606,7 @@ static STRINT_PAIR tlsext_types[] = {
     {"client authz", TLSEXT_TYPE_client_authz},
     {"server authz", TLSEXT_TYPE_server_authz},
     {"cert type", TLSEXT_TYPE_cert_type},
-    {"elliptic curves", TLSEXT_TYPE_elliptic_curves},
+    {"supported_groups", TLSEXT_TYPE_supported_groups},
     {"EC point formats", TLSEXT_TYPE_ec_point_formats},
     {"SRP", TLSEXT_TYPE_srp},
     {"signature algorithms", TLSEXT_TYPE_signature_algorithms},
@@ -1093,7 +1095,7 @@ void print_ssl_summary(SSL *s)
 #ifndef OPENSSL_NO_EC
     ssl_print_point_formats(bio_err, s);
     if (SSL_is_server(s))
-        ssl_print_curves(bio_err, s, 1);
+        ssl_print_groups(bio_err, s, 1);
     else
         ssl_print_tmp_key(bio_err, s);
 #else
diff --git a/apps/s_server.c b/apps/s_server.c
index 24841c528e..985841352d 100644
--- a/apps/s_server.c
+++ b/apps/s_server.c
@@ -2560,7 +2560,7 @@ static int init_ssl_connection(SSL *con)
     ssl_print_sigalgs(bio_s_out, con);
 #ifndef OPENSSL_NO_EC
     ssl_print_point_formats(bio_s_out, con);
-    ssl_print_curves(bio_s_out, con, 0);
+    ssl_print_groups(bio_s_out, con, 0);
 #endif
     BIO_printf(bio_s_out, "CIPHER is %s\n", (str != NULL) ? str : "(NONE)");
 
@@ -2847,7 +2847,7 @@ static int www_body(int s, int stype, unsigned char *context)
             }
             ssl_print_sigalgs(io, con);
 #ifndef OPENSSL_NO_EC
-            ssl_print_curves(io, con, 0);
+            ssl_print_groups(io, con, 0);
 #endif
             BIO_printf(io, (SSL_session_reused(con)
                             ? "---\nReused, " : "---\nNew, "));
diff --git a/doc/man3/SSL_CTX_set1_curves.pod b/doc/man3/SSL_CTX_set1_curves.pod
index b0276c80f3..a250f20c22 100644
--- a/doc/man3/SSL_CTX_set1_curves.pod
+++ b/doc/man3/SSL_CTX_set1_curves.pod
@@ -2,13 +2,25 @@
 
 =head1 NAME
 
+SSL_CTX_set1_groups, SSL_CTX_set1_groups_list, SSL_set1_groups,
+SSL_set1_groups_list, SSL_get1_groups, SSL_get_shared_group,
 SSL_CTX_set1_curves, SSL_CTX_set1_curves_list, SSL_set1_curves,
-SSL_set1_curves_list, SSL_get1_curves, SSL_get_shared_curve - EC supported curve functions
+SSL_set1_curves_list, SSL_get1_curves, SSL_get_shared_curve
+- EC supported curve functions
 
 =head1 SYNOPSIS
 
  #include <openssl/ssl.h>
 
+ int SSL_CTX_set1_groups(SSL_CTX *ctx, int *glist, int glistlen);
+ int SSL_CTX_set1_groups_list(SSL_CTX *ctx, char *list);
+
+ int SSL_set1_groups(SSL *ssl, int *glist, int glistlen);
+ int SSL_set1_groups_list(SSL *ssl, char *list);
+
+ int SSL_get1_groups(SSL *ssl, int *groups);
+ int SSL_get_shared_group(SSL *s, int n);
+
  int SSL_CTX_set1_curves(SSL_CTX *ctx, int *clist, int clistlen);
  int SSL_CTX_set1_curves_list(SSL_CTX *ctx, char *list);
 
@@ -20,36 +32,42 @@ SSL_set1_curves_list, SSL_get1_curves, SSL_get_shared_curve - EC supported curve
 
 =head1 DESCRIPTION
 
-SSL_CTX_set1_curves() sets the supported curves for B<ctx> to B<clistlen>
-curves in the array B<clist>. The array consist of all NIDs of curves in
-preference order. For a TLS client the curves are used directly in the
-supported curves extension. For a TLS server the curves are used to
-determine the set of shared curves.
+SSL_CTX_set1_groups() sets the supported groups for B<ctx> to B<glistlen>
+groups in the array B<glist>. The array consist of all NIDs of groups in
+preference order. For a TLS client the groups are used directly in the
+supported groups extension. For a TLS server the groups are used to
+determine the set of shared groups.
 
-SSL_CTX_set1_curves_list() sets the supported curves for B<ctx> to
-string B<list>. The string is a colon separated list of curve NIDs or
+SSL_CTX_set1_groups_list() sets the supported groups for B<ctx> to
+string B<list>. The string is a colon separated list of group NIDs or
 names, for example "P-521:P-384:P-256".
 
-SSL_set1_curves() and SSL_set1_curves_list() are similar except they set
-supported curves for the SSL structure B<ssl>.
+SSL_set1_groups() and SSL_set1_groups_list() are similar except they set
+supported groups for the SSL structure B<ssl>.
 
-SSL_get1_curves() returns the set of supported curves sent by a client
-in the supported curves extension. It returns the total number of
-supported curves. The B<curves> parameter can be B<NULL> to simply
-return the number of curves for memory allocation purposes. The
-B<curves> array is in the form of a set of curve NIDs in preference
-order. It can return zero if the client did not send a supported curves
+SSL_get1_groups() returns the set of supported groups sent by a client
+in the supported groups extension. It returns the total number of
+supported groups. The B<groups> parameter can be B<NULL> to simply
+return the number of groups for memory allocation purposes. The
+B<groups> array is in the form of a set of group NIDs in preference
+order. It can return zero if the client did not send a supported groups
 extension.
 
-SSL_get_shared_curve() returns shared curve B<n> for a server-side
-SSL B<ssl>. If B<n> is -1 then the total number of shared curves is
+SSL_get_shared_group() returns shared group B<n> for a server-side
+SSL B<ssl>. If B<n> is -1 then the total number of shared groups is
 returned, which may be zero. Other than for diagnostic purposes,
-most applications will only be interested in the first shared curve
+most applications will only be interested in the first shared group
 so B<n> is normally set to zero. If the value B<n> is out of range,
 NID_undef is returned.
 
 All these functions are implemented as macros.
 
+The curve functions are synonyms for the equivalently named group functions and
+are identical in every respect. They exist because, prior to TLS1.3, there was
+only the concept of supported curves. In TLS1.3 this was renamed to supported
+groups, and extended to include Diffie Hellman groups. The group functions
+should be used in preference.
+
 =head1 NOTES
 
 If an application wishes to make use of several of these functions for
@@ -58,16 +76,16 @@ consider using the SSL_CONF interface instead of manually parsing options.
 
 =head1 RETURN VALUES
 
-SSL_CTX_set1_curves(), SSL_CTX_set1_curves_list(), SSL_set1_curves() and
-SSL_set1_curves_list(), return 1 for success and 0 for failure.
+SSL_CTX_set1_groups(), SSL_CTX_set1_groups_list(), SSL_set1_groups() and
+SSL_set1_groups_list(), return 1 for success and 0 for failure.
 
-SSL_get1_curves() returns the number of curves, which may be zero.
+SSL_get1_groups() returns the number of groups, which may be zero.
 
-SSL_get_shared_curve() returns the NID of shared curve B<n> or NID_undef if there
-is no shared curve B<n>; or the total number of shared curves if B<n>
+SSL_get_shared_group() returns the NID of shared group B<n> or NID_undef if there
+is no shared group B<n>; or the total number of shared groups if B<n>
 is -1.
 
-When called on a client B<ssl>, SSL_get_shared_curve() has no meaning and
+When called on a client B<ssl>, SSL_get_shared_group() has no meaning and
 returns -1.
 
 =head1 SEE ALSO
@@ -76,7 +94,8 @@ L<SSL_CTX_add_extra_chain_cert(3)>
 
 =head1 HISTORY
 
-These functions were first added to OpenSSL 1.0.2.
+The curve functions were first added to OpenSSL 1.0.2. The equivalent group
+functions were first added to OpenSSL 1.1.1.
 
 =head1 COPYRIGHT
 
diff --git a/include/openssl/ssl.h b/include/openssl/ssl.h
index 1bb93fef70..b61a992e16 100644
--- a/include/openssl/ssl.h
+++ b/include/openssl/ssl.h
@@ -1109,10 +1109,10 @@ DECLARE_PEM_rw(SSL_SESSION, SSL_SESSION)
 # define SSL_CTRL_CLEAR_EXTRA_CHAIN_CERTS        83
 # define SSL_CTRL_CHAIN                          88
 # define SSL_CTRL_CHAIN_CERT                     89
-# define SSL_CTRL_GET_CURVES                     90
-# define SSL_CTRL_SET_CURVES                     91
-# define SSL_CTRL_SET_CURVES_LIST                92
-# define SSL_CTRL_GET_SHARED_CURVE               93
+# define SSL_CTRL_GET_GROUPS                     90
+# define SSL_CTRL_SET_GROUPS                     91
+# define SSL_CTRL_SET_GROUPS_LIST                92
+# define SSL_CTRL_GET_SHARED_GROUP               93
 # define SSL_CTRL_SET_SIGALGS                    97
 # define SSL_CTRL_SET_SIGALGS_LIST               98
 # define SSL_CTRL_CERT_FLAGS                     99
@@ -1227,18 +1227,30 @@ DECLARE_PEM_rw(SSL_SESSION, SSL_SESSION)
         SSL_ctrl(s,SSL_CTRL_SET_CHAIN_CERT_STORE,0,(char *)st)
 # define SSL_set1_chain_cert_store(s,st) \
         SSL_ctrl(s,SSL_CTRL_SET_CHAIN_CERT_STORE,1,(char *)st)
+# define SSL_get1_groups(ctx, s) \
+        SSL_ctrl(ctx,SSL_CTRL_GET_GROUPS,0,(char *)s)
 # define SSL_get1_curves(ctx, s) \
-        SSL_ctrl(ctx,SSL_CTRL_GET_CURVES,0,(char *)s)
+        SSL_get1_groups((ctx), (s))
+# define SSL_CTX_set1_groups(ctx, glist, glistlen) \
+        SSL_CTX_ctrl(ctx,SSL_CTRL_SET_GROUPS,glistlen,(char *)glist)
+# define SSL_CTX_set1_groups_list(ctx, s) \
+        SSL_CTX_ctrl(ctx,SSL_CTRL_SET_GROUPS_LIST,0,(char *)s)
 # define SSL_CTX_set1_curves(ctx, clist, clistlen) \
-        SSL_CTX_ctrl(ctx,SSL_CTRL_SET_CURVES,clistlen,(char *)clist)
+        SSL_CTX_set1_groups((ctx), (clist), (clistlen))
 # define SSL_CTX_set1_curves_list(ctx, s) \
-        SSL_CTX_ctrl(ctx,SSL_CTRL_SET_CURVES_LIST,0,(char *)s)
+        SSL_CTX_set1_groups_list((ctx), (s))
+# define SSL_set1_groups(ctx, glist, glistlen) \
+        SSL_ctrl(ctx,SSL_CTRL_SET_GROUPS,glistlen,(char *)glist)
+# define SSL_set1_groups_list(ctx, s) \
+        SSL_ctrl(ctx,SSL_CTRL_SET_GROUPS_LIST,0,(char *)s)
 # define SSL_set1_curves(ctx, clist, clistlen) \
-        SSL_ctrl(ctx,SSL_CTRL_SET_CURVES,clistlen,(char *)clist)
+        SSL_set1_groups((ctx), (clist), (clistlen))
 # define SSL_set1_curves_list(ctx, s) \
-        SSL_ctrl(ctx,SSL_CTRL_SET_CURVES_LIST,0,(char *)s)
+        SSL_set1_groups_list((ctx), (s))
+# define SSL_get_shared_group(s, n) \
+        SSL_ctrl(s,SSL_CTRL_GET_SHARED_GROUP,n,NULL)
 # define SSL_get_shared_curve(s, n) \
-        SSL_ctrl(s,SSL_CTRL_GET_SHARED_CURVE,n,NULL)
+        SSL_get_shared_group((s), (n))
 # define SSL_CTX_set1_sigalgs(ctx, slist, slistlen) \
         SSL_CTX_ctrl(ctx,SSL_CTRL_SET_SIGALGS,slistlen,(int *)slist)
 # define SSL_CTX_set1_sigalgs_list(ctx, s) \
diff --git a/include/openssl/tls1.h b/include/openssl/tls1.h
index d0cce09263..1fd5788936 100644
--- a/include/openssl/tls1.h
+++ b/include/openssl/tls1.h
@@ -128,9 +128,15 @@ extern "C" {
 # define TLSEXT_TYPE_cert_type           9
 
 /* ExtensionType values from RFC4492 */
-# define TLSEXT_TYPE_elliptic_curves             10
+/*
+ * Prior to TLSv1.3 the supported_groups extension was known as
+ * elliptic_curves
+ */
+# define TLSEXT_TYPE_supported_groups            10
+# define TLSEXT_TYPE_elliptic_curves             TLSEXT_TYPE_supported_groups
 # define TLSEXT_TYPE_ec_point_formats            11
 
+
 /* ExtensionType value from RFC5054 */
 # define TLSEXT_TYPE_srp                         12
 
diff --git a/ssl/s3_lib.c b/ssl/s3_lib.c
index 90c1c66744..dad43753dd 100644
--- a/ssl/s3_lib.c
+++ b/ssl/s3_lib.c
@@ -2969,8 +2969,8 @@ long ssl3_ctrl(SSL *s, int cmd, long larg, void *parg)
             nid = EC_GROUP_get_curve_name(group);
             if (nid == NID_undef)
                 return 0;
-            return tls1_set_curves(&s->tlsext_ellipticcurvelist,
-                                   &s->tlsext_ellipticcurvelist_length,
+            return tls1_set_groups(&s->tlsext_supportedgroupslist,
+                                   &s->tlsext_supportedgroupslist_length,
                                    &nid, 1);
         }
         break;
@@ -3112,20 +3112,21 @@ long ssl3_ctrl(SSL *s, int cmd, long larg, void *parg)
         return ssl_cert_set_current(s->cert, larg);
 
 #ifndef OPENSSL_NO_EC
-    case SSL_CTRL_GET_CURVES:
+    case SSL_CTRL_GET_GROUPS:
         {
             unsigned char *clist;
             size_t clistlen;
             if (!s->session)
                 return 0;
-            clist = s->session->tlsext_ellipticcurvelist;
-            clistlen = s->session->tlsext_ellipticcurvelist_length / 2;
+            clist = s->session->tlsext_supportedgroupslist;
+            clistlen = s->session->tlsext_supportedgroupslist_length / 2;
             if (parg) {
                 size_t i;
                 int *cptr = parg;
                 unsigned int cid, nid;
                 for (i = 0; i < clistlen; i++) {
                     n2s(clist, cid);
+                    /* TODO(TLS1.3): Handle DH groups here */
                     nid = tls1_ec_curve_id2nid(cid, NULL);
                     if (nid != 0)
                         cptr[i] = nid;
@@ -3136,16 +3137,16 @@ long ssl3_ctrl(SSL *s, int cmd, long larg, void *parg)
             return (int)clistlen;
         }
 
-    case SSL_CTRL_SET_CURVES:
-        return tls1_set_curves(&s->tlsext_ellipticcurvelist,
-                               &s->tlsext_ellipticcurvelist_length, parg, larg);
+    case SSL_CTRL_SET_GROUPS:
+        return tls1_set_groups(&s->tlsext_supportedgroupslist,
+                               &s->tlsext_supportedgroupslist_length, parg, larg);
 
-    case SSL_CTRL_SET_CURVES_LIST:
-        return tls1_set_curves_list(&s->tlsext_ellipticcurvelist,
-                                    &s->tlsext_ellipticcurvelist_length, parg);
+    case SSL_CTRL_SET_GROUPS_LIST:
+        return tls1_set_groups_list(&s->tlsext_supportedgroupslist,
+                                    &s->tlsext_supportedgroupslist_length, parg);
 
-    case SSL_CTRL_GET_SHARED_CURVE:
-        return tls1_shared_curve(s, larg);
+    case SSL_CTRL_GET_SHARED_GROUP:
+        return tls1_shared_group(s, larg);
 
 #endif
     case SSL_CTRL_SET_SIGALGS:
@@ -3320,8 +3321,8 @@ long ssl3_ctx_ctrl(SSL_CTX *ctx, int cmd, long larg, void *parg)
             nid = EC_GROUP_get_curve_name(group);
             if (nid == NID_undef)
                 return 0;
-            return tls1_set_curves(&ctx->tlsext_ellipticcurvelist,
-                                   &ctx->tlsext_ellipticcurvelist_length,
+            return tls1_set_groups(&ctx->tlsext_supportedgroupslist,
+                                   &ctx->tlsext_supportedgroupslist_length,
                                    &nid, 1);
         }
         /* break; */
@@ -3417,14 +3418,14 @@ long ssl3_ctx_ctrl(SSL_CTX *ctx, int cmd, long larg, void *parg)
 #endif
 
 #ifndef OPENSSL_NO_EC
-    case SSL_CTRL_SET_CURVES:
-        return tls1_set_curves(&ctx->tlsext_ellipticcurvelist,
-                               &ctx->tlsext_ellipticcurvelist_length,
+    case SSL_CTRL_SET_GROUPS:
+        return tls1_set_groups(&ctx->tlsext_supportedgroupslist,
+                               &ctx->tlsext_supportedgroupslist_length,
                                parg, larg);
 
-    case SSL_CTRL_SET_CURVES_LIST:
-        return tls1_set_curves_list(&ctx->tlsext_ellipticcurvelist,
-                                    &ctx->tlsext_ellipticcurvelist_length,
+    case SSL_CTRL_SET_GROUPS_LIST:
+        return tls1_set_groups_list(&ctx->tlsext_supportedgroupslist,
+                                    &ctx->tlsext_supportedgroupslist_length,
                                     parg);
 #endif
     case SSL_CTRL_SET_SIGALGS:
diff --git a/ssl/ssl_conf.c b/ssl/ssl_conf.c
index 63687b5ba1..2382030f34 100644
--- a/ssl/ssl_conf.c
+++ b/ssl/ssl_conf.c
@@ -202,17 +202,23 @@ static int cmd_ClientSignatureAlgorithms(SSL_CONF_CTX *cctx, const char *value)
     return rv > 0;
 }
 
-static int cmd_Curves(SSL_CONF_CTX *cctx, const char *value)
+static int cmd_Groups(SSL_CONF_CTX *cctx, const char *value)
 {
     int rv;
     if (cctx->ssl)
-        rv = SSL_set1_curves_list(cctx->ssl, value);
+        rv = SSL_set1_groups_list(cctx->ssl, value);
     /* NB: ctx == NULL performs syntax checking only */
     else
-        rv = SSL_CTX_set1_curves_list(cctx->ctx, value);
+        rv = SSL_CTX_set1_groups_list(cctx->ctx, value);
     return rv > 0;
 }
 
+/* This is the old name for cmd_Groups - retained for backwards compatibility */
+static int cmd_Curves(SSL_CONF_CTX *cctx, const char *value)
+{
+    return cmd_Groups(cctx, value);
+}
+
 #ifndef OPENSSL_NO_EC
 /* ECDH temporary parameters */
 static int cmd_ECDHParameters(SSL_CONF_CTX *cctx, const char *value)
@@ -543,6 +549,7 @@ static const ssl_conf_cmd_tbl ssl_conf_cmds[] = {
     SSL_CONF_CMD_STRING(SignatureAlgorithms, "sigalgs", 0),
     SSL_CONF_CMD_STRING(ClientSignatureAlgorithms, "client_sigalgs", 0),
     SSL_CONF_CMD_STRING(Curves, "curves", 0),
+    SSL_CONF_CMD_STRING(Groups, "groups", 0),
 #ifndef OPENSSL_NO_EC
     SSL_CONF_CMD_STRING(ECDHParameters, "named_curve", SSL_CONF_FLAG_SERVER),
 #endif
diff --git a/ssl/ssl_lib.c b/ssl/ssl_lib.c
index 363b4f4ab8..a6360accea 100644
--- a/ssl/ssl_lib.c
+++ b/ssl/ssl_lib.c
@@ -610,14 +610,14 @@ SSL *SSL_new(SSL_CTX *ctx)
         s->tlsext_ecpointformatlist_length =
             ctx->tlsext_ecpointformatlist_length;
     }
-    if (ctx->tlsext_ellipticcurvelist) {
-        s->tlsext_ellipticcurvelist =
-            OPENSSL_memdup(ctx->tlsext_ellipticcurvelist,
-                           ctx->tlsext_ellipticcurvelist_length);
-        if (!s->tlsext_ellipticcurvelist)
+    if (ctx->tlsext_supportedgroupslist) {
+        s->tlsext_supportedgroupslist =
+            OPENSSL_memdup(ctx->tlsext_supportedgroupslist,
+                           ctx->tlsext_supportedgroupslist_length);
+        if (!s->tlsext_supportedgroupslist)
             goto err;
-        s->tlsext_ellipticcurvelist_length =
-            ctx->tlsext_ellipticcurvelist_length;
+        s->tlsext_supportedgroupslist_length =
+            ctx->tlsext_supportedgroupslist_length;
     }
 #endif
 #ifndef OPENSSL_NO_NEXTPROTONEG
@@ -1001,7 +1001,7 @@ void SSL_free(SSL *s)
     SSL_CTX_free(s->initial_ctx);
 #ifndef OPENSSL_NO_EC
     OPENSSL_free(s->tlsext_ecpointformatlist);
-    OPENSSL_free(s->tlsext_ellipticcurvelist);
+    OPENSSL_free(s->tlsext_supportedgroupslist);
 #endif                          /* OPENSSL_NO_EC */
     sk_X509_EXTENSION_pop_free(s->tlsext_ocsp_exts, X509_EXTENSION_free);
 #ifndef OPENSSL_NO_OCSP
@@ -1857,8 +1857,8 @@ long SSL_CTX_ctrl(SSL_CTX *ctx, int cmd, long larg, void *parg)
     if (ctx == NULL) {
         switch (cmd) {
 #ifndef OPENSSL_NO_EC
-        case SSL_CTRL_SET_CURVES_LIST:
-            return tls1_set_curves_list(NULL, NULL, parg);
+        case SSL_CTRL_SET_GROUPS_LIST:
+            return tls1_set_groups_list(NULL, NULL, parg);
 #endif
         case SSL_CTRL_SET_SIGALGS_LIST:
         case SSL_CTRL_SET_CLIENT_SIGALGS_LIST:
@@ -2630,7 +2630,7 @@ void SSL_CTX_free(SSL_CTX *a)
 
 #ifndef OPENSSL_NO_EC
     OPENSSL_free(a->tlsext_ecpointformatlist);
-    OPENSSL_free(a->tlsext_ellipticcurvelist);
+    OPENSSL_free(a->tlsext_supportedgroupslist);
 #endif
     OPENSSL_free(a->alpn_client_proto_list);
 
diff --git a/ssl/ssl_locl.h b/ssl/ssl_locl.h
index 63b001ffee..dbe8813acf 100644
--- a/ssl/ssl_locl.h
+++ b/ssl/ssl_locl.h
@@ -554,8 +554,8 @@ struct ssl_session_st {
 # ifndef OPENSSL_NO_EC
     size_t tlsext_ecpointformatlist_length;
     unsigned char *tlsext_ecpointformatlist; /* peer's list */
-    size_t tlsext_ellipticcurvelist_length;
-    unsigned char *tlsext_ellipticcurvelist; /* peer's list */
+    size_t tlsext_supportedgroupslist_length;
+    unsigned char *tlsext_supportedgroupslist; /* peer's list */
 # endif                         /* OPENSSL_NO_EC */
     /* RFC4507 info */
     unsigned char *tlsext_tick; /* Session ticket */
@@ -868,8 +868,8 @@ struct ssl_ctx_st {
     /* EC extension values inherited by SSL structure */
     size_t tlsext_ecpointformatlist_length;
     unsigned char *tlsext_ecpointformatlist;
-    size_t tlsext_ellipticcurvelist_length;
-    unsigned char *tlsext_ellipticcurvelist;
+    size_t tlsext_supportedgroupslist_length;
+    unsigned char *tlsext_supportedgroupslist;
 # endif                         /* OPENSSL_NO_EC */
 
     /* ext status type used for CSR extension (OCSP Stapling) */
@@ -1078,9 +1078,9 @@ struct ssl_st {
     size_t tlsext_ecpointformatlist_length;
     /* our list */
     unsigned char *tlsext_ecpointformatlist;
-    size_t tlsext_ellipticcurvelist_length;
+    size_t tlsext_supportedgroupslist_length;
     /* our list */
-    unsigned char *tlsext_ellipticcurvelist;
+    unsigned char *tlsext_supportedgroupslist;
 # endif                         /* OPENSSL_NO_EC */
     /* TLS Session Ticket extension override */
     TLS_SESSION_TICKET_EXT *tlsext_session_ticket;
@@ -2053,10 +2053,10 @@ SSL_COMP *ssl3_comp_find(STACK_OF(SSL_COMP) *sk, int n);
 __owur int tls1_ec_curve_id2nid(int curve_id, unsigned int *pflags);
 __owur int tls1_ec_nid2curve_id(int nid);
 __owur int tls1_check_curve(SSL *s, const unsigned char *p, size_t len);
-__owur int tls1_shared_curve(SSL *s, int nmatch);
-__owur int tls1_set_curves(unsigned char **pext, size_t *pextlen,
+__owur int tls1_shared_group(SSL *s, int nmatch);
+__owur int tls1_set_groups(unsigned char **pext, size_t *pextlen,
                            int *curves, size_t ncurves);
-__owur int tls1_set_curves_list(unsigned char **pext, size_t *pextlen,
+__owur int tls1_set_groups_list(unsigned char **pext, size_t *pextlen,
                                 const char *str);
 __owur int tls1_check_ec_tmp_key(SSL *s, unsigned long id);
 __owur EVP_PKEY *ssl_generate_pkey_curve(int id);
diff --git a/ssl/ssl_sess.c b/ssl/ssl_sess.c
index 291796e8ad..825e706561 100644
--- a/ssl/ssl_sess.c
+++ b/ssl/ssl_sess.c
@@ -132,7 +132,7 @@ SSL_SESSION *ssl_session_dup(SSL_SESSION *src, int ticket)
     dest->tlsext_hostname = NULL;
 #ifndef OPENSSL_NO_EC
     dest->tlsext_ecpointformatlist = NULL;
-    dest->tlsext_ellipticcurvelist = NULL;
+    dest->tlsext_supportedgroupslist = NULL;
 #endif
     dest->tlsext_tick = NULL;
 #ifndef OPENSSL_NO_SRP
@@ -198,11 +198,11 @@ SSL_SESSION *ssl_session_dup(SSL_SESSION *src, int ticket)
         if (dest->tlsext_ecpointformatlist == NULL)
             goto err;
     }
-    if (src->tlsext_ellipticcurvelist) {
-        dest->tlsext_ellipticcurvelist =
-            OPENSSL_memdup(src->tlsext_ellipticcurvelist,
-                           src->tlsext_ellipticcurvelist_length);
-        if (dest->tlsext_ellipticcurvelist == NULL)
+    if (src->tlsext_supportedgroupslist) {
+        dest->tlsext_supportedgroupslist =
+            OPENSSL_memdup(src->tlsext_supportedgroupslist,
+                           src->tlsext_supportedgroupslist_length);
+        if (dest->tlsext_supportedgroupslist == NULL)
             goto err;
     }
 #endif
@@ -753,8 +753,8 @@ void SSL_SESSION_free(SSL_SESSION *ss)
 #ifndef OPENSSL_NO_EC
     ss->tlsext_ecpointformatlist_length = 0;
     OPENSSL_free(ss->tlsext_ecpointformatlist);
-    ss->tlsext_ellipticcurvelist_length = 0;
-    OPENSSL_free(ss->tlsext_ellipticcurvelist);
+    ss->tlsext_supportedgroupslist_length = 0;
+    OPENSSL_free(ss->tlsext_supportedgroupslist);
 #endif                          /* OPENSSL_NO_EC */
 #ifndef OPENSSL_NO_PSK
     OPENSSL_free(ss->psk_identity_hint);
diff --git a/ssl/statem/statem_srvr.c b/ssl/statem/statem_srvr.c
index ba3457d2e0..142c637dc9 100644
--- a/ssl/statem/statem_srvr.c
+++ b/ssl/statem/statem_srvr.c
@@ -1736,7 +1736,7 @@ int tls_construct_server_key_exchange(SSL *s, WPACKET *pkt)
         }
 
         /* Get NID of appropriate shared curve */
-        nid = tls1_shared_curve(s, -2);
+        nid = tls1_shared_group(s, -2);
         curve_id = tls1_ec_nid2curve_id(nid);
         if (curve_id == 0) {
             SSLerr(SSL_F_TLS_CONSTRUCT_SERVER_KEY_EXCHANGE,
diff --git a/ssl/t1_ext.c b/ssl/t1_ext.c
index 30b304669f..bbec1359ca 100644
--- a/ssl/t1_ext.c
+++ b/ssl/t1_ext.c
@@ -242,7 +242,7 @@ int SSL_extension_supported(unsigned int ext_type)
         /* Internally supported extensions. */
     case TLSEXT_TYPE_application_layer_protocol_negotiation:
     case TLSEXT_TYPE_ec_point_formats:
-    case TLSEXT_TYPE_elliptic_curves:
+    case TLSEXT_TYPE_supported_groups:
     case TLSEXT_TYPE_heartbeat:
 #ifndef OPENSSL_NO_NEXTPROTONEG
     case TLSEXT_TYPE_next_proto_neg:
diff --git a/ssl/t1_lib.c b/ssl/t1_lib.c
index e79c37eee0..a7aa955223 100644
--- a/ssl/t1_lib.c
+++ b/ssl/t1_lib.c
@@ -268,8 +268,8 @@ static int tls1_get_curvelist(SSL *s, int sess,
 {
     size_t pcurveslen = 0;
     if (sess) {
-        *pcurves = s->session->tlsext_ellipticcurvelist;
-        pcurveslen = s->session->tlsext_ellipticcurvelist_length;
+        *pcurves = s->session->tlsext_supportedgroupslist;
+        pcurveslen = s->session->tlsext_supportedgroupslist_length;
     } else {
         /* For Suite B mode only include P-256, P-384 */
         switch (tls1_suiteb(s)) {
@@ -288,8 +288,8 @@ static int tls1_get_curvelist(SSL *s, int sess,
             pcurveslen = 2;
             break;
         default:
-            *pcurves = s->tlsext_ellipticcurvelist;
-            pcurveslen = s->tlsext_ellipticcurvelist_length;
+            *pcurves = s->tlsext_supportedgroupslist;
+            pcurveslen = s->tlsext_supportedgroupslist_length;
         }
         if (!*pcurves) {
             *pcurves = eccurves_default;
@@ -356,13 +356,13 @@ int tls1_check_curve(SSL *s, const unsigned char *p, size_t len)
 }
 
 /*-
- * For nmatch >= 0, return the NID of the |nmatch|th shared curve or NID_undef
+ * For nmatch >= 0, return the NID of the |nmatch|th shared group or NID_undef
  * if there is no match.
  * For nmatch == -1, return number of matches
- * For nmatch == -2, return the NID of the curve to use for
+ * For nmatch == -2, return the NID of the group to use for
  * an EC tmp key, or NID_undef if there is no match.
  */
-int tls1_shared_curve(SSL *s, int nmatch)
+int tls1_shared_group(SSL *s, int nmatch)
 {
     const unsigned char *pref, *supp;
     size_t num_pref, num_supp, i, j;
@@ -434,34 +434,35 @@ int tls1_shared_curve(SSL *s, int nmatch)
     return NID_undef;
 }
 
-int tls1_set_curves(unsigned char **pext, size_t *pextlen,
-                    int *curves, size_t ncurves)
+int tls1_set_groups(unsigned char **pext, size_t *pextlen,
+                    int *groups, size_t ngroups)
 {
-    unsigned char *clist, *p;
+    unsigned char *glist, *p;
     size_t i;
     /*
-     * Bitmap of curves included to detect duplicates: only works while curve
+     * Bitmap of groups included to detect duplicates: only works while group
      * ids < 32
      */
     unsigned long dup_list = 0;
-    clist = OPENSSL_malloc(ncurves * 2);
-    if (clist == NULL)
+    glist = OPENSSL_malloc(ngroups * 2);
+    if (glist == NULL)
         return 0;
-    for (i = 0, p = clist; i < ncurves; i++) {
+    for (i = 0, p = glist; i < ngroups; i++) {
         unsigned long idmask;
         int id;
-        id = tls1_ec_nid2curve_id(curves[i]);
+        /* TODO(TLS1.3): Convert for DH groups */
+        id = tls1_ec_nid2curve_id(groups[i]);
         idmask = 1L << id;
         if (!id || (dup_list & idmask)) {
-            OPENSSL_free(clist);
+            OPENSSL_free(glist);
             return 0;
         }
         dup_list |= idmask;
         s2n(id, p);
     }
     OPENSSL_free(*pext);
-    *pext = clist;
-    *pextlen = ncurves * 2;
+    *pext = glist;
+    *pextlen = ngroups * 2;
     return 1;
 }
 
@@ -500,8 +501,8 @@ static int nid_cb(const char *elem, int len, void *arg)
     return 1;
 }
 
-/* Set curves based on a colon separate list */
-int tls1_set_curves_list(unsigned char **pext, size_t *pextlen, const char *str)
+/* Set groups based on a colon separate list */
+int tls1_set_groups_list(unsigned char **pext, size_t *pextlen, const char *str)
 {
     nid_cb_st ncb;
     ncb.nidcnt = 0;
@@ -509,7 +510,7 @@ int tls1_set_curves_list(unsigned char **pext, size_t *pextlen, const char *str)
         return 0;
     if (pext == NULL)
         return 1;
-    return tls1_set_curves(pext, pextlen, ncb.nid_arr, ncb.nidcnt);
+    return tls1_set_groups(pext, pextlen, ncb.nid_arr, ncb.nidcnt);
 }
 
 /* For an EC key set TLS id and required compression based on parameters */
@@ -706,7 +707,7 @@ int tls1_check_ec_tmp_key(SSL *s, unsigned long cid)
         return 1;
     }
     /* Need a shared curve */
-    if (tls1_shared_curve(s, 0))
+    if (tls1_shared_group(s, 0))
         return 1;
     return 0;
 }
@@ -1117,16 +1118,17 @@ int ssl_add_clienthello_tlsext(SSL *s, WPACKET *pkt, int *al)
         }
 
         /*
-         * Add TLS extension EllipticCurves to the ClientHello message
+         * Add TLS extension supported_groups to the ClientHello message
          */
-        pcurves = s->tlsext_ellipticcurvelist;
+        /* TODO(TLS1.3): Add support for DHE groups */
+        pcurves = s->tlsext_supportedgroupslist;
         if (!tls1_get_curvelist(s, 0, &pcurves, &num_curves)) {
             SSLerr(SSL_F_SSL_ADD_CLIENTHELLO_TLSEXT, ERR_R_INTERNAL_ERROR);
             return 0;
         }
 
-        if (!WPACKET_put_bytes_u16(pkt, TLSEXT_TYPE_elliptic_curves)
-                   /* Sub-packet for curves extension */
+        if (!WPACKET_put_bytes_u16(pkt, TLSEXT_TYPE_supported_groups)
+                   /* Sub-packet for supported_groups extension */
                 || !WPACKET_start_sub_packet_u16(pkt)
                 || !WPACKET_start_sub_packet_u16(pkt)) {
             SSLerr(SSL_F_SSL_ADD_CLIENTHELLO_TLSEXT, ERR_R_INTERNAL_ERROR);
@@ -1982,22 +1984,22 @@ static int ssl_scan_clienthello_tlsext(SSL *s, CLIENTHELLO_MSG *hello, int *al)
                     return 0;
                 }
             }
-        } else if (currext->type == TLSEXT_TYPE_elliptic_curves) {
-            PACKET elliptic_curve_list;
+        } else if (currext->type == TLSEXT_TYPE_supported_groups) {
+            PACKET supported_groups_list;
 
-            /* Each NamedCurve is 2 bytes and we must have at least 1. */
+            /* Each group is 2 bytes and we must have at least 1. */
             if (!PACKET_as_length_prefixed_2(&currext->data,
-                                             &elliptic_curve_list)
-                || PACKET_remaining(&elliptic_curve_list) == 0
-                || (PACKET_remaining(&elliptic_curve_list) % 2) != 0) {
+                                             &supported_groups_list)
+                || PACKET_remaining(&supported_groups_list) == 0
+                || (PACKET_remaining(&supported_groups_list) % 2) != 0) {
                 return 0;
             }
 
             if (!s->hit) {
-                if (!PACKET_memdup(&elliptic_curve_list,
-                                   &s->session->tlsext_ellipticcurvelist,
+                if (!PACKET_memdup(&supported_groups_list,
+                                   &s->session->tlsext_supportedgroupslist,
                                    &s->
-                                   session->tlsext_ellipticcurvelist_length)) {
+                                   session->tlsext_supportedgroupslist_length)) {
                     *al = TLS1_AD_INTERNAL_ERROR;
                     return 0;
                 }
diff --git a/ssl/t1_trce.c b/ssl/t1_trce.c
index c8d00532d8..52c72b2450 100644
--- a/ssl/t1_trce.c
+++ b/ssl/t1_trce.c
@@ -448,7 +448,7 @@ static ssl_trace_tbl ssl_exts_tbl[] = {
     {TLSEXT_TYPE_client_authz, "client_authz"},
     {TLSEXT_TYPE_server_authz, "server_authz"},
     {TLSEXT_TYPE_cert_type, "cert_type"},
-    {TLSEXT_TYPE_elliptic_curves, "elliptic_curves"},
+    {TLSEXT_TYPE_supported_groups, "supported_groups"},
     {TLSEXT_TYPE_ec_point_formats, "ec_point_formats"},
     {TLSEXT_TYPE_srp, "srp"},
     {TLSEXT_TYPE_signature_algorithms, "signature_algorithms"},
@@ -466,7 +466,7 @@ static ssl_trace_tbl ssl_exts_tbl[] = {
     {TLSEXT_TYPE_extended_master_secret, "extended_master_secret"}
 };
 
-static ssl_trace_tbl ssl_curve_tbl[] = {
+static ssl_trace_tbl ssl_groups_tbl[] = {
     {1, "sect163k1 (K-163)"},
     {2, "sect163r1"},
     {3, "sect163r2 (B-163)"},
@@ -665,13 +665,13 @@ static int ssl_print_extension(BIO *bio, int indent, int server, int extype,
             return 0;
         return ssl_trace_list(bio, indent + 2, ext + 1, xlen, 1, ssl_point_tbl);
 
-    case TLSEXT_TYPE_elliptic_curves:
+    case TLSEXT_TYPE_supported_groups:
         if (extlen < 2)
             return 0;
         xlen = (ext[0] << 8) | ext[1];
         if (extlen != xlen + 2)
             return 0;
-        return ssl_trace_list(bio, indent + 2, ext + 2, xlen, 2, ssl_curve_tbl);
+        return ssl_trace_list(bio, indent + 2, ext + 2, xlen, 2, ssl_groups_tbl);
 
     case TLSEXT_TYPE_signature_algorithms:
 
@@ -1009,7 +1009,7 @@ static int ssl_print_server_keyex(BIO *bio, int indent, SSL *ssl,
                 return 0;
             curve = (msg[1] << 8) | msg[2];
             BIO_printf(bio, "named_curve: %s (%d)\n",
-                       ssl_trace_str(curve, ssl_curve_tbl), curve);
+                       ssl_trace_str(curve, ssl_groups_tbl), curve);
             msg += 3;
             msglen -= 3;
             if (!ssl_print_hexbuf(bio, indent + 2, "point", 1, &msg, &msglen))