diff --git a/crypto/newhope/newhope.c b/crypto/newhope/newhope.c
index 29e189f..9f0bb6f 100644
--- a/crypto/newhope/newhope.c
+++ b/crypto/newhope/newhope.c
@@ -46,14 +46,14 @@
   }
 }
 
-void NEWHOPE_keygen(uint8_t *servermsg, NEWHOPE_POLY *sk) {
+void NEWHOPE_offer(uint8_t *offermsg, NEWHOPE_POLY *sk) {
   newhope_poly_getnoise(sk);
   newhope_poly_ntt(sk);
 
-  /* The first part of the server's message is the seed, which compactly encodes
+  /* The first part of the offer message is the seed, which compactly encodes
    * a. */
   NEWHOPE_POLY a;
-  uint8_t *seed = &servermsg[POLY_BYTES];
+  uint8_t *seed = &offermsg[POLY_BYTES];
   RAND_bytes(seed, SEED_LENGTH);
   newhope_poly_uniform(&a, seed);
 
@@ -61,18 +61,18 @@
   newhope_poly_getnoise(&e);
   newhope_poly_ntt(&e);
 
-  /* The second part of the server's message is the polynomial pk = a*sk+e */
+  /* The second part of the offer message is the polynomial pk = a*sk+e */
   NEWHOPE_POLY r, pk;
   newhope_poly_pointwise(&r, sk, &a);
   newhope_poly_add(&pk, &e, &r);
-  newhope_poly_tobytes(servermsg, &pk);
+  newhope_poly_tobytes(offermsg, &pk);
 }
 
-int NEWHOPE_client_compute_key(
-    uint8_t key[SHA256_DIGEST_LENGTH],
-    uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH],
-    const uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH], size_t msg_len) {
-  if (msg_len != NEWHOPE_SERVERMSG_LENGTH) {
+int NEWHOPE_accept(uint8_t key[SHA256_DIGEST_LENGTH],
+                   uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH],
+                   const uint8_t offermsg[NEWHOPE_OFFERMSG_LENGTH],
+                   size_t msg_len) {
+  if (msg_len != NEWHOPE_OFFERMSG_LENGTH) {
     return 0;
   }
 
@@ -80,28 +80,28 @@
   newhope_poly_getnoise(&sp);
   newhope_poly_ntt(&sp);
 
-  /* The first part of the client's message is the polynomial bp=e'+a*s' */
+  /* The first part of the accept message is the polynomial bp=e'+a*s' */
   {
     NEWHOPE_POLY ep;
     newhope_poly_getnoise(&ep);
     newhope_poly_ntt(&ep);
 
-    /* Generate the same |a| as the server, from the server's seed. */
+    /* Generate the same |a| as the peer, from the peer's seed. */
     NEWHOPE_POLY a;
-    const uint8_t *seed = &servermsg[POLY_BYTES];
+    const uint8_t *seed = &offermsg[POLY_BYTES];
     newhope_poly_uniform(&a, seed);
 
     NEWHOPE_POLY bp;
     newhope_poly_pointwise(&bp, &a, &sp);
     newhope_poly_add(&bp, &bp, &ep);
-    newhope_poly_tobytes(clientmsg, &bp);
+    newhope_poly_tobytes(acceptmsg, &bp);
   }
 
   /* v = pk * s' + e'' */
   NEWHOPE_POLY v;
   {
     NEWHOPE_POLY pk;
-    newhope_poly_frombytes(&pk, servermsg);
+    newhope_poly_frombytes(&pk, offermsg);
 
     NEWHOPE_POLY epp;
     newhope_poly_getnoise(&epp);
@@ -111,10 +111,10 @@
     newhope_poly_add(&v, &v, &epp);
   }
 
-  /* The second part of the client's message is the reconciliation data derived
+  /* The second part of the accept message is the reconciliation data derived
    * from v. */
   NEWHOPE_POLY c;
-  uint8_t *reconciliation = &clientmsg[POLY_BYTES];
+  uint8_t *reconciliation = &acceptmsg[POLY_BYTES];
   newhope_helprec(&c, &v);
   encode_rec(&c, reconciliation);
 
@@ -130,21 +130,21 @@
   return 1;
 }
 
-int NEWHOPE_server_compute_key(
-    uint8_t key[SHA256_DIGEST_LENGTH], const NEWHOPE_POLY *sk,
-    const uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH], size_t msg_len) {
-  if (msg_len != NEWHOPE_CLIENTMSG_LENGTH) {
+int NEWHOPE_finish(uint8_t key[SHA256_DIGEST_LENGTH], const NEWHOPE_POLY *sk,
+                   const uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH],
+                   size_t msg_len) {
+  if (msg_len != NEWHOPE_ACCEPTMSG_LENGTH) {
     return 0;
   }
   NEWHOPE_POLY bp;
-  newhope_poly_frombytes(&bp, clientmsg);
+  newhope_poly_frombytes(&bp, acceptmsg);
 
   NEWHOPE_POLY v;
   newhope_poly_pointwise(&v, sk, &bp);
   newhope_poly_invntt(&v);
 
   NEWHOPE_POLY c;
-  const uint8_t *reconciliation = &clientmsg[POLY_BYTES];
+  const uint8_t *reconciliation = &acceptmsg[POLY_BYTES];
   decode_rec(reconciliation, &c);
 
   uint8_t k[KEY_LENGTH];
diff --git a/crypto/newhope/newhope_test.c b/crypto/newhope/newhope_test.c
index 5d96007..f3e011f 100644
--- a/crypto/newhope/newhope_test.c
+++ b/crypto/newhope/newhope_test.c
@@ -22,34 +22,32 @@
 #include "internal.h"
 
 
-#define NTESTS 1000
+#define NTESTS 1
 
 static int test_keys(void) {
   NEWHOPE_POLY *sk = NEWHOPE_POLY_new();
-  uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH];
-  uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH];
-  uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH];
+  uint8_t offer_key[SHA256_DIGEST_LENGTH], accept_key[SHA256_DIGEST_LENGTH];
+  uint8_t offermsg[NEWHOPE_OFFERMSG_LENGTH];
+  uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH];
   int i;
 
   for (i = 0; i < NTESTS; i++) {
     /* Alice generates a public key */
-    NEWHOPE_keygen(servermsg, sk);
+    NEWHOPE_offer(offermsg, sk);
 
     /* Bob derives a secret key and creates a response */
-    if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg,
-                                    sizeof(servermsg))) {
-      fprintf(stderr, "ERROR client key exchange failed\n");
+    if (!NEWHOPE_accept(accept_key, acceptmsg, offermsg, sizeof(offermsg))) {
+      fprintf(stderr, "ERROR accept key exchange failed\n");
       return 0;
     }
 
     /* Alice uses Bob's response to get her secret key */
-    if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg,
-                                    sizeof(clientmsg))) {
-      fprintf(stderr, "ERROR server key exchange failed\n");
+    if (!NEWHOPE_finish(offer_key, sk, acceptmsg, sizeof(acceptmsg))) {
+      fprintf(stderr, "ERROR finish key exchange failed\n");
       return 0;
     }
 
-    if (memcmp(server_key, client_key, SHA256_DIGEST_LENGTH) != 0) {
+    if (memcmp(offer_key, accept_key, SHA256_DIGEST_LENGTH) != 0) {
       fprintf(stderr, "ERROR keys did not agree\n");
       return 0;
     }
@@ -61,33 +59,31 @@
 
 static int test_invalid_sk_a(void) {
   NEWHOPE_POLY *sk = NEWHOPE_POLY_new();
-  uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH];
-  uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH];
-  uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH];
+  uint8_t offer_key[SHA256_DIGEST_LENGTH], accept_key[SHA256_DIGEST_LENGTH];
+  uint8_t offermsg[NEWHOPE_OFFERMSG_LENGTH];
+  uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH];
   int i;
 
   for (i = 0; i < NTESTS; i++) {
     /* Alice generates a public key */
-    NEWHOPE_keygen(servermsg, sk);
+    NEWHOPE_offer(offermsg, sk);
 
     /* Bob derives a secret key and creates a response */
-    if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg,
-                                    sizeof(servermsg))) {
-      fprintf(stderr, "ERROR client key exchange failed\n");
+    if (!NEWHOPE_accept(accept_key, acceptmsg, offermsg, sizeof(offermsg))) {
+      fprintf(stderr, "ERROR accept key exchange failed\n");
       return 0;
     }
 
     /* Corrupt the secret key */
-    NEWHOPE_keygen(servermsg /* not used below */, sk);
+    NEWHOPE_offer(offermsg /* not used below */, sk);
 
     /* Alice uses Bob's response to get her secret key */
-    if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg,
-                                    sizeof(clientmsg))) {
-      fprintf(stderr, "ERROR server key exchange failed\n");
+    if (!NEWHOPE_finish(offer_key, sk, acceptmsg, sizeof(acceptmsg))) {
+      fprintf(stderr, "ERROR finish key exchange failed\n");
       return 0;
     }
 
-    if (memcmp(server_key, client_key, SHA256_DIGEST_LENGTH) == 0) {
+    if (memcmp(offer_key, accept_key, SHA256_DIGEST_LENGTH) == 0) {
       fprintf(stderr, "ERROR invalid sk_a\n");
       return 0;
     }
@@ -99,34 +95,32 @@
 
 static int test_invalid_ciphertext(void) {
   NEWHOPE_POLY *sk = NEWHOPE_POLY_new();
-  uint8_t server_key[SHA256_DIGEST_LENGTH], client_key[SHA256_DIGEST_LENGTH];
-  uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH];
-  uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH];
+  uint8_t offer_key[SHA256_DIGEST_LENGTH], accept_key[SHA256_DIGEST_LENGTH];
+  uint8_t offermsg[NEWHOPE_OFFERMSG_LENGTH];
+  uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH];
   int i;
 
   for (i = 0; i < 10; i++) {
     /* Alice generates a public key */
-    NEWHOPE_keygen(servermsg, sk);
+    NEWHOPE_offer(offermsg, sk);
 
     /* Bob derives a secret key and creates a response */
-    if (!NEWHOPE_client_compute_key(client_key, clientmsg, servermsg,
-                                    sizeof(servermsg))) {
-      fprintf(stderr, "ERROR client key exchange failed\n");
+    if (!NEWHOPE_accept(accept_key, acceptmsg, offermsg, sizeof(offermsg))) {
+      fprintf(stderr, "ERROR accept key exchange failed\n");
       return 0;
     }
 
     /* Change some byte in the "ciphertext" */
-    clientmsg[42] ^= 1;
+    acceptmsg[42] ^= 1;
 
     /* Alice uses Bob's response to get her secret key */
-    if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg,
-                                    sizeof(clientmsg))) {
-      fprintf(stderr, "ERROR server key exchange failed\n");
+    if (!NEWHOPE_finish(offer_key, sk, acceptmsg, sizeof(acceptmsg))) {
+      fprintf(stderr, "ERROR finish key exchange failed\n");
       return 0;
     }
 
-    if (!memcmp(server_key, client_key, SHA256_DIGEST_LENGTH)) {
-      fprintf(stderr, "ERROR invalid clientmsg\n");
+    if (!memcmp(offer_key, accept_key, SHA256_DIGEST_LENGTH)) {
+      fprintf(stderr, "ERROR invalid acceptmsg\n");
       return 0;
     }
   }
diff --git a/include/openssl/newhope.h b/include/openssl/newhope.h
index af573ba..48c82fe 100644
--- a/include/openssl/newhope.h
+++ b/include/openssl/newhope.h
@@ -38,37 +38,38 @@
 /* NEWHOPE_POLY_free frees |p|. */
 OPENSSL_EXPORT void NEWHOPE_POLY_free(NEWHOPE_POLY *p);
 
-/* NEWHOPE_SERVERMSG_LENGTH is the length of the server's message to the
- * client. */
-#define NEWHOPE_SERVERMSG_LENGTH (((1024 * 14) / 8) + 32)
+/* NEWHOPE_OFFERMSG_LENGTH is the length of the offering party's message to the
+ * accepting party. */
+#define NEWHOPE_OFFERMSG_LENGTH (((1024 * 14) / 8) + 32)
 
-/* NEWHOPE_CLIENTMSG_LENGTH is the length of the client's message to the
- * server. */
-#define NEWHOPE_CLIENTMSG_LENGTH (((1024 * 14) / 8) + 1024 / 4)
+/* NEWHOPE_ACCEPTMSG_LENGTH is the length of the accepting party's message to
+ * the offering party. */
+#define NEWHOPE_ACCEPTMSG_LENGTH (((1024 * 14) / 8) + 1024 / 4)
 
-/* NEWHOPE_keygen initializes |out_msg| and |out_sk| for a new key
- * exchange. |msg| must have room for |NEWHOPE_SERVERMSG_LENGTH| bytes. Neither
+/* NEWHOPE_offer initializes |out_msg| and |out_sk| for a new key
+ * exchange. |msg| must have room for |NEWHOPE_OFFERMSG_LENGTH| bytes. Neither
  * output may be cached. */
-OPENSSL_EXPORT void NEWHOPE_keygen(uint8_t out_msg[NEWHOPE_SERVERMSG_LENGTH],
-                                   NEWHOPE_POLY *out_sk);
+OPENSSL_EXPORT void NEWHOPE_offer(uint8_t out_msg[NEWHOPE_OFFERMSG_LENGTH],
+                                  NEWHOPE_POLY *out_sk);
 
-/* NEWHOPE_server_compute_key completes a key exchange given a client message
- * |msg| and the previously generated server secret |sk|. The result of the
- * key exchange is written to |out_key|, which must have space for
+/* NEWHOPE_accept completes a key exchange given an offer message |msg|. The
+ * result of the key exchange is written to |out_key|, which must have space for
+ * |SHA256_DIGEST_LENGTH| bytes. The message to be send to the offering party is
+ * written to |out_msg|, which must have room for |NEWHOPE_ACCEPTMSG_LENGTH|
+ * bytes. Returns 1 on success and 0 on error. */
+OPENSSL_EXPORT int NEWHOPE_accept(uint8_t out_key[SHA256_DIGEST_LENGTH],
+                                  uint8_t out_msg[NEWHOPE_ACCEPTMSG_LENGTH],
+                                  const uint8_t msg[NEWHOPE_OFFERMSG_LENGTH],
+                                  size_t msg_len);
+
+/* NEWHOPE_finish completes a key exchange for the offering party, given an
+ * accept message |msg| and the previously generated secret |sk|. The result of
+ * the key exchange is written to |out_key|, which must have space for
  * |SHA256_DIGEST_LENGTH| bytes. Returns 1 on success and 0 on error. */
-OPENSSL_EXPORT int NEWHOPE_server_compute_key(
-    uint8_t out_key[SHA256_DIGEST_LENGTH], const NEWHOPE_POLY *sk,
-    const uint8_t msg[NEWHOPE_CLIENTMSG_LENGTH], size_t msg_len);
-
-/* NEWHOPE_client_compute_key completes a key exchange given a server message
- * |msg|. The result of the key exchange is written to |out_key|, which must
- * have space for |SHA256_DIGEST_LENGTH| bytes. The message to be send to the
- * client is written to |out_msg|, which must have room for
- * |NEWHOPE_CLIENTMSG_LENGTH| bytes. Returns 1 on success and 0 on error. */
-OPENSSL_EXPORT int NEWHOPE_client_compute_key(
-    uint8_t out_key[SHA256_DIGEST_LENGTH],
-    uint8_t out_msg[NEWHOPE_CLIENTMSG_LENGTH],
-    const uint8_t msg[NEWHOPE_SERVERMSG_LENGTH], size_t msg_len);
+OPENSSL_EXPORT int NEWHOPE_finish(uint8_t out_key[SHA256_DIGEST_LENGTH],
+                                  const NEWHOPE_POLY *sk,
+                                  const uint8_t msg[NEWHOPE_ACCEPTMSG_LENGTH],
+                                  size_t msg_len);
 
 
 #if defined(__cplusplus)
diff --git a/tool/speed.cc b/tool/speed.cc
index 68d78e2..58c7382 100644
--- a/tool/speed.cc
+++ b/tool/speed.cc
@@ -522,15 +522,14 @@
 
   TimeResults results;
   NEWHOPE_POLY *sk = NEWHOPE_POLY_new();
-  uint8_t clientmsg[NEWHOPE_CLIENTMSG_LENGTH];
-  RAND_bytes(clientmsg, sizeof(clientmsg));
+  uint8_t acceptmsg[NEWHOPE_ACCEPTMSG_LENGTH];
+  RAND_bytes(acceptmsg, sizeof(acceptmsg));
 
-  if (!TimeFunction(&results, [sk, &clientmsg]() -> bool {
-        uint8_t server_key[SHA256_DIGEST_LENGTH];
-        uint8_t servermsg[NEWHOPE_SERVERMSG_LENGTH];
-        NEWHOPE_keygen(servermsg, sk);
-        if (!NEWHOPE_server_compute_key(server_key, sk, clientmsg,
-                                        NEWHOPE_CLIENTMSG_LENGTH)) {
+  if (!TimeFunction(&results, [sk, &acceptmsg]() -> bool {
+        uint8_t key[SHA256_DIGEST_LENGTH];
+        uint8_t offermsg[NEWHOPE_OFFERMSG_LENGTH];
+        NEWHOPE_offer(offermsg, sk);
+        if (!NEWHOPE_finish(key, sk, acceptmsg, NEWHOPE_ACCEPTMSG_LENGTH)) {
           return false;
         }
         return true;
@@ -540,7 +539,7 @@
   }
 
   NEWHOPE_POLY_free(sk);
-  results.Print("newhope server key exchange");
+  results.Print("newhope key exchange");
   return true;
 }