diff --git a/ext/openssl/extconf.rb b/ext/openssl/extconf.rb
index 5bb045e89..6eb401cf5 100644
--- a/ext/openssl/extconf.rb
+++ b/ext/openssl/extconf.rb
@@ -135,6 +135,11 @@ def find_openssl_library
 # compile options
 have_func("RAND_egd()", "openssl/rand.h")
 
+# added in OpenSSL 1.0.2, not in LibreSSL yet
+have_func("SSL_CTX_set1_sigalgs_list(NULL, NULL)", ssl_h)
+# added in OpenSSL 1.0.2, not in LibreSSL or AWS-LC yet
+have_func("SSL_CTX_set1_client_sigalgs_list(NULL, NULL)", ssl_h)
+
 # added in 1.1.0, currently not in LibreSSL
 have_func("EVP_PBE_scrypt(\"\", 0, (unsigned char *)\"\", 0, 0, 0, 0, 0, NULL, 0)", evp_h)
 
diff --git a/ext/openssl/ossl_ssl.c b/ext/openssl/ossl_ssl.c
index d18eb39d3..30fbb3bbd 100644
--- a/ext/openssl/ossl_ssl.c
+++ b/ext/openssl/ossl_ssl.c
@@ -999,11 +999,10 @@ static VALUE
 build_cipher_string(VALUE v)
 {
     VALUE str, elem;
-    int i;
 
     if (RB_TYPE_P(v, T_ARRAY)) {
         str = rb_str_new(0, 0);
-        for (i = 0; i < RARRAY_LEN(v); i++) {
+        for (long i = 0; i < RARRAY_LEN(v); i++) {
             elem = rb_ary_entry(v, i);
             if (RB_TYPE_P(elem, T_ARRAY)) elem = rb_ary_entry(elem, 0);
             elem = rb_String(elem);
@@ -1024,9 +1023,14 @@ build_cipher_string(VALUE v)
  *    ctx.ciphers = [name, ...]
  *    ctx.ciphers = [[name, version, bits, alg_bits], ...]
  *
- * Sets the list of available cipher suites for this context.  Note in a server
- * context some ciphers require the appropriate certificates.  For example, an
- * RSA cipher suite can only be chosen when an RSA certificate is available.
+ * Sets the list of available cipher suites for TLS 1.2 and below for this
+ * context.
+ *
+ * Note in a server context some ciphers require the appropriate certificates.
+ * For example, an RSA cipher suite can only be chosen when an RSA certificate
+ * is available.
+ *
+ * This method does not affect TLS 1.3 connections. See also #ciphersuites=.
  */
 static VALUE
 ossl_sslctx_set_ciphers(VALUE self, VALUE v)
@@ -1035,6 +1039,7 @@ ossl_sslctx_set_ciphers(VALUE self, VALUE v)
     VALUE str;
 
     rb_check_frozen(self);
+    // Assigning nil is a no-op for compatibility
     if (NIL_P(v))
         return v;
 
@@ -1051,9 +1056,8 @@ ossl_sslctx_set_ciphers(VALUE self, VALUE v)
  * call-seq:
  *    ctx.ciphersuites = "cipher1:cipher2:..."
  *    ctx.ciphersuites = [name, ...]
- *    ctx.ciphersuites = [[name, version, bits, alg_bits], ...]
  *
- * Sets the list of available TLSv1.3 cipher suites for this context.
+ * Sets the list of available TLS 1.3 cipher suites for this context.
  */
 static VALUE
 ossl_sslctx_set_ciphersuites(VALUE self, VALUE v)
@@ -1062,6 +1066,7 @@ ossl_sslctx_set_ciphersuites(VALUE self, VALUE v)
     VALUE str;
 
     rb_check_frozen(self);
+    // Assigning nil is a no-op for compatibility
     if (NIL_P(v))
         return v;
 
@@ -1074,6 +1079,63 @@ ossl_sslctx_set_ciphersuites(VALUE self, VALUE v)
     return v;
 }
 
+#ifdef HAVE_SSL_CTX_SET1_SIGALGS_LIST
+/*
+ * call-seq:
+ *    ctx.sigalgs = "sigalg1:sigalg2:..."
+ *
+ * Sets the list of "supported signature algorithms" for this context.
+ *
+ * For a TLS client, the list is used in the "signature_algorithms" extension
+ * in the ClientHello message. For a server, the list is used by OpenSSL to
+ * determine the set of shared signature algorithms. OpenSSL will pick the most
+ * appropriate one from it.
+ *
+ * See also #client_sigalgs= for the client authentication equivalent.
+ */
+static VALUE
+ossl_sslctx_set_sigalgs(VALUE self, VALUE v)
+{
+    SSL_CTX *ctx;
+
+    rb_check_frozen(self);
+    GetSSLCTX(self, ctx);
+
+    if (!SSL_CTX_set1_sigalgs_list(ctx, StringValueCStr(v)))
+        ossl_raise(eSSLError, "SSL_CTX_set1_sigalgs_list");
+
+    return v;
+}
+#endif
+
+#ifdef HAVE_SSL_CTX_SET1_CLIENT_SIGALGS_LIST
+/*
+ * call-seq:
+ *    ctx.client_sigalgs = "sigalg1:sigalg2:..."
+ *
+ * Sets the list of "supported signature algorithms" for client authentication
+ * for this context.
+ *
+ * For a TLS server, the list is sent to the client as part of the
+ * CertificateRequest message.
+ *
+ * See also #sigalgs= for the server authentication equivalent.
+ */
+static VALUE
+ossl_sslctx_set_client_sigalgs(VALUE self, VALUE v)
+{
+    SSL_CTX *ctx;
+
+    rb_check_frozen(self);
+    GetSSLCTX(self, ctx);
+
+    if (!SSL_CTX_set1_client_sigalgs_list(ctx, StringValueCStr(v)))
+        ossl_raise(eSSLError, "SSL_CTX_set1_client_sigalgs_list");
+
+    return v;
+}
+#endif
+
 #ifndef OPENSSL_NO_DH
 /*
  * call-seq:
@@ -2887,6 +2949,12 @@ Init_ossl_ssl(void)
     rb_define_method(cSSLContext, "ciphers",     ossl_sslctx_get_ciphers, 0);
     rb_define_method(cSSLContext, "ciphers=",    ossl_sslctx_set_ciphers, 1);
     rb_define_method(cSSLContext, "ciphersuites=", ossl_sslctx_set_ciphersuites, 1);
+#ifdef HAVE_SSL_CTX_SET1_SIGALGS_LIST // Not in LibreSSL yet
+    rb_define_method(cSSLContext, "sigalgs=", ossl_sslctx_set_sigalgs, 1);
+#endif
+#ifdef HAVE_SSL_CTX_SET1_CLIENT_SIGALGS_LIST // Not in LibreSSL or AWS-LC yet
+    rb_define_method(cSSLContext, "client_sigalgs=", ossl_sslctx_set_client_sigalgs, 1);
+#endif
 #ifndef OPENSSL_NO_DH
     rb_define_method(cSSLContext, "tmp_dh=", ossl_sslctx_set_tmp_dh, 1);
 #endif
diff --git a/test/openssl/test_ssl.rb b/test/openssl/test_ssl.rb
index 4642063f4..61c26b5dd 100644
--- a/test/openssl/test_ssl.rb
+++ b/test/openssl/test_ssl.rb
@@ -1968,6 +1968,84 @@ def test_ciphers_method_bogus_csuite
     ) { ssl_ctx.ciphers = 'BOGUS' }
   end
 
+  def test_sigalgs
+    omit "SSL_CTX_set1_sigalgs_list() not supported" if libressl?
+
+    svr_exts = [
+      ["keyUsage", "keyEncipherment,digitalSignature", true],
+      ["subjectAltName", "DNS:localhost", false],
+    ]
+    ecdsa_key = Fixtures.pkey("p256")
+    ecdsa_cert = issue_cert(@svr, ecdsa_key, 10, svr_exts, @ca_cert, @ca_key)
+
+    ctx_proc = -> ctx {
+      # Unset values set by start_server
+      ctx.cert = ctx.key = ctx.extra_chain_cert = nil
+      ctx.add_certificate(@svr_cert, @svr_key, [@ca_cert]) # RSA
+      ctx.add_certificate(ecdsa_cert, ecdsa_key, [@ca_cert]) # ECDSA
+    }
+    start_server(ctx_proc: ctx_proc) do |port|
+      ctx1 = OpenSSL::SSL::SSLContext.new
+      ctx1.sigalgs = "rsa_pss_rsae_sha256"
+      server_connect(port, ctx1) { |ssl|
+        assert_kind_of(OpenSSL::PKey::RSA, ssl.peer_cert.public_key)
+        ssl.puts("abc"); ssl.gets
+      }
+
+      ctx2 = OpenSSL::SSL::SSLContext.new
+      ctx2.sigalgs = "ed25519:ecdsa_secp256r1_sha256"
+      server_connect(port, ctx2) { |ssl|
+        assert_kind_of(OpenSSL::PKey::EC, ssl.peer_cert.public_key)
+        ssl.puts("abc"); ssl.gets
+      }
+    end
+
+    # Frozen
+    ssl_ctx = OpenSSL::SSL::SSLContext.new
+    ssl_ctx.freeze
+    assert_raise(FrozenError) { ssl_ctx.sigalgs = "ECDSA+SHA256:RSA+SHA256" }
+
+    # Bogus
+    ssl_ctx = OpenSSL::SSL::SSLContext.new
+    assert_raise(TypeError) { ssl_ctx.sigalgs = nil }
+    assert_raise(OpenSSL::SSL::SSLError) { ssl_ctx.sigalgs = "BOGUS" }
+  end
+
+  def test_client_sigalgs
+    omit "SSL_CTX_set1_client_sigalgs_list() not supported" if libressl? || aws_lc?
+
+    cli_exts = [
+      ["keyUsage", "keyEncipherment,digitalSignature", true],
+      ["subjectAltName", "DNS:localhost", false],
+    ]
+    ecdsa_key = Fixtures.pkey("p256")
+    ecdsa_cert = issue_cert(@cli, ecdsa_key, 10, cli_exts, @ca_cert, @ca_key)
+
+    ctx_proc = -> ctx {
+      store = OpenSSL::X509::Store.new
+      store.add_cert(@ca_cert)
+      store.purpose = OpenSSL::X509::PURPOSE_SSL_CLIENT
+      ctx.cert_store = store
+      ctx.verify_mode = OpenSSL::SSL::VERIFY_PEER|OpenSSL::SSL::VERIFY_FAIL_IF_NO_PEER_CERT
+      ctx.client_sigalgs = "ECDSA+SHA256"
+    }
+    start_server(ctx_proc: ctx_proc, ignore_listener_error: true) do |port|
+      ctx1 = OpenSSL::SSL::SSLContext.new
+      ctx1.add_certificate(@cli_cert, @cli_key) # RSA
+      assert_handshake_error {
+        server_connect(port, ctx1) { |ssl|
+          ssl.puts("abc"); ssl.gets
+        }
+      }
+
+      ctx2 = OpenSSL::SSL::SSLContext.new
+      ctx2.add_certificate(ecdsa_cert, ecdsa_key) # ECDSA
+      server_connect(port, ctx2) { |ssl|
+        ssl.puts("abc"); ssl.gets
+      }
+    end
+  end
+
   def test_connect_works_when_setting_dh_callback_to_nil
     omit "AWS-LC does not support DHE ciphersuites" if aws_lc?