diff --git a/lib/protocol/kex.js b/lib/protocol/kex.js
index 811e631b..0c2a1184 100644
--- a/lib/protocol/kex.js
+++ b/lib/protocol/kex.js
@@ -1539,6 +1539,17 @@ const createKeyExchange = (() => {
     }
   }
 
+  // Oakley Group 2 (RFC 2409 section 6.2), used by diffie-hellman-group1-sha1.
+  // BoringSSL (e.g. Electron) does not provide it as a named group, so it is
+  // always built from its prime and generator instead.
+  const MODP2_PRIME = Buffer.from(
+    'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74'
+    + '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437'
+    + '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED'
+    + 'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF',
+    'hex'
+  );
+
   class DHExchange extends KeyExchange {
     constructor(groupName, hashName, ...args) {
       super(...args);
@@ -1566,7 +1577,9 @@ const createKeyExchange = (() => {
     }
     generateKeys() {
       if (!this._dh) {
-        this._dh = createDiffieHellmanGroup(this.groupName);
+        this._dh = (this.groupName === 'modp2'
+                    ? createDiffieHellman(MODP2_PRIME, 2)
+                    : createDiffieHellmanGroup(this.groupName));
         this._public = this._dh.generateKeys();
       }
     }
diff --git a/test/test-kex-group1.js b/test/test-kex-group1.js
new file mode 100644
index 00000000..25f240fd
--- /dev/null
+++ b/test/test-kex-group1.js
@@ -0,0 +1,36 @@
+'use strict';
+
+// Some crypto backends (e.g. BoringSSL, as used by Electron) do not provide the
+// legacy 'modp1' and 'modp2' named groups. Remove them before loading the
+// library to make sure diffie-hellman-group1-sha1 does not need them.
+const crypto = require('crypto');
+const createDiffieHellmanGroup = crypto.createDiffieHellmanGroup;
+crypto.createDiffieHellmanGroup = (name) => {
+  if (name === 'modp1' || name === 'modp2')
+    throw new Error('Unknown DH group');
+  return createDiffieHellmanGroup(name);
+};
+
+const { fixtureKey, mustCall, setup } = require('./common.js');
+
+const debug = false;
+
+const algorithms = { kex: [ 'diffie-hellman-group1-sha1' ] };
+const { client, server } = setup(
+  'diffie-hellman-group1-sha1 without named group support',
+  {
+    client: { username: 'Password User', password: '12345', algorithms },
+    server: { hostKeys: [ fixtureKey('ssh_host_rsa_key').raw ], algorithms },
+    debug,
+  }
+);
+
+server.on('connection', mustCall((conn) => {
+  conn.on('authentication', mustCall((ctx) => {
+    ctx.accept();
+  }));
+}));
+
+client.on('ready', mustCall(() => {
+  client.end();
+}));