diff --git a/ext/openssl/extconf.rb b/ext/openssl/extconf.rb
index 5cb28f309..8812b7de8 100644
--- a/ext/openssl/extconf.rb
+++ b/ext/openssl/extconf.rb
@@ -165,6 +165,9 @@ def find_openssl_library
 have_func("EVP_PBE_scrypt")
 have_func("SSL_CTX_set_post_handshake_auth")
 
+# added in 1.1.1
+have_func("EVP_PKEY_check")
+
 Logging::message "=== Checking done. ===\n"
 
 create_header
diff --git a/ext/openssl/ossl_pkey.c b/ext/openssl/ossl_pkey.c
index 593788e1e..b92c8a663 100644
--- a/ext/openssl/ossl_pkey.c
+++ b/ext/openssl/ossl_pkey.c
@@ -539,6 +539,43 @@ ossl_pkey_inspect(VALUE self)
                       OBJ_nid2sn(nid));
 }
 
+/*
+ * call-seq:
+ *    pkey.to_text -> string
+ *
+ * Dumps key parameters, public key, and private key components contained in
+ * the key into a human-readable text.
+ *
+ * This is intended for debugging purpose.
+ *
+ * See also the man page EVP_PKEY_print_private(3).
+ */
+static VALUE
+ossl_pkey_to_text(VALUE self)
+{
+    EVP_PKEY *pkey;
+    BIO *bio;
+
+    GetPKey(self, pkey);
+    if (!(bio = BIO_new(BIO_s_mem())))
+        ossl_raise(ePKeyError, "BIO_new");
+
+    if (EVP_PKEY_print_private(bio, pkey, 0, NULL) == 1)
+        goto out;
+    OSSL_BIO_reset(bio);
+    if (EVP_PKEY_print_public(bio, pkey, 0, NULL) == 1)
+        goto out;
+    OSSL_BIO_reset(bio);
+    if (EVP_PKEY_print_params(bio, pkey, 0, NULL) == 1)
+        goto out;
+
+    BIO_free(bio);
+    ossl_raise(ePKeyError, "EVP_PKEY_print_params");
+
+  out:
+    return ossl_membio2str(bio);
+}
+
 VALUE
 ossl_pkey_export_traditional(int argc, VALUE *argv, VALUE self, int to_der)
 {
@@ -1077,6 +1114,7 @@ Init_ossl_pkey(void)
     rb_define_method(cPKey, "initialize", ossl_pkey_initialize, 0);
     rb_define_method(cPKey, "oid", ossl_pkey_oid, 0);
     rb_define_method(cPKey, "inspect", ossl_pkey_inspect, 0);
+    rb_define_method(cPKey, "to_text", ossl_pkey_to_text, 0);
     rb_define_method(cPKey, "private_to_der", ossl_pkey_private_to_der, -1);
     rb_define_method(cPKey, "private_to_pem", ossl_pkey_private_to_pem, -1);
     rb_define_method(cPKey, "public_to_der", ossl_pkey_public_to_der, 0);
diff --git a/ext/openssl/ossl_pkey_dh.c b/ext/openssl/ossl_pkey_dh.c
index 6b477b077..ca782bbe5 100644
--- a/ext/openssl/ossl_pkey_dh.c
+++ b/ext/openssl/ossl_pkey_dh.c
@@ -266,76 +266,6 @@ ossl_dh_get_params(VALUE self)
     return hash;
 }
 
-/*
- *  call-seq:
- *     dh.to_text -> aString
- *
- * Prints all parameters of key to buffer
- * INSECURE: PRIVATE INFORMATIONS CAN LEAK OUT!!!
- * Don't use :-)) (I's up to you)
- */
-static VALUE
-ossl_dh_to_text(VALUE self)
-{
-    DH *dh;
-    BIO *out;
-    VALUE str;
-
-    GetDH(self, dh);
-    if (!(out = BIO_new(BIO_s_mem()))) {
-	ossl_raise(eDHError, NULL);
-    }
-    if (!DHparams_print(out, dh)) {
-	BIO_free(out);
-	ossl_raise(eDHError, NULL);
-    }
-    str = ossl_membio2str(out);
-
-    return str;
-}
-
-/*
- *  call-seq:
- *     dh.public_key -> aDH
- *
- * Returns a new DH instance that carries just the public information, i.e.
- * the prime _p_ and the generator _g_, but no public/private key yet. Such
- * a pair may be generated using DH#generate_key!. The "public key" needed
- * for a key exchange with DH#compute_key is considered as per-session
- * information and may be retrieved with DH#pub_key once a key pair has
- * been generated.
- * If the current instance already contains private information (and thus a
- * valid public/private key pair), this information will no longer be present
- * in the new instance generated by DH#public_key. This feature is helpful for
- * publishing the Diffie-Hellman parameters without leaking any of the private
- * per-session information.
- *
- * === Example
- *  dh = OpenSSL::PKey::DH.new(2048) # has public and private key set
- *  public_key = dh.public_key # contains only prime and generator
- *  parameters = public_key.to_der # it's safe to publish this
- */
-static VALUE
-ossl_dh_to_public_key(VALUE self)
-{
-    EVP_PKEY *pkey;
-    DH *orig_dh, *dh;
-    VALUE obj;
-
-    obj = rb_obj_alloc(rb_obj_class(self));
-    GetPKey(obj, pkey);
-
-    GetDH(self, orig_dh);
-    dh = DHparams_dup(orig_dh);
-    if (!dh)
-        ossl_raise(eDHError, "DHparams_dup");
-    if (!EVP_PKEY_assign_DH(pkey, dh)) {
-        DH_free(dh);
-        ossl_raise(eDHError, "EVP_PKEY_assign_DH");
-    }
-    return obj;
-}
-
 /*
  *  call-seq:
  *     dh.params_ok? -> true | false
@@ -343,19 +273,38 @@ ossl_dh_to_public_key(VALUE self)
  * Validates the Diffie-Hellman parameters associated with this instance.
  * It checks whether a safe prime and a suitable generator are used. If this
  * is not the case, +false+ is returned.
+ *
+ * See also the man page EVP_PKEY_param_check(3).
  */
 static VALUE
 ossl_dh_check_params(VALUE self)
 {
+    int ret;
+#ifdef HAVE_EVP_PKEY_CHECK
+    EVP_PKEY *pkey;
+    EVP_PKEY_CTX *pctx;
+
+    GetPKey(self, pkey);
+    pctx = EVP_PKEY_CTX_new(pkey, /* engine */NULL);
+    if (!pctx)
+        ossl_raise(eDHError, "EVP_PKEY_CTX_new");
+    ret = EVP_PKEY_param_check(pctx);
+    EVP_PKEY_CTX_free(pctx);
+#else
     DH *dh;
     int codes;
 
     GetDH(self, dh);
-    if (!DH_check(dh, &codes)) {
-	return Qfalse;
-    }
+    ret = DH_check(dh, &codes) == 1 && codes == 0;
+#endif
 
-    return codes == 0 ? Qtrue : Qfalse;
+    if (ret == 1)
+        return Qtrue;
+    else {
+        /* DH_check_ex() will put error entry on failure */
+        ossl_clear_error();
+        return Qfalse;
+    }
 }
 
 /*
@@ -412,26 +361,30 @@ Init_ossl_dh(void)
      *   The per-session private key, an OpenSSL::BN.
      *
      * === Example of a key exchange
-     *  dh1 = OpenSSL::PKey::DH.new(2048)
-     *  der = dh1.public_key.to_der #you may send this publicly to the participating party
-     *  dh2 = OpenSSL::PKey::DH.new(der)
-     *  dh2.generate_key! #generate the per-session key pair
-     *  symm_key1 = dh1.compute_key(dh2.pub_key)
-     *  symm_key2 = dh2.compute_key(dh1.pub_key)
+     *   # you may send the parameters (der) and own public key (pub1) publicly
+     *   # to the participating party
+     *   dh1 = OpenSSL::PKey::DH.new(2048)
+     *   der = dh1.to_der
+     *   pub1 = dh1.pub_key
+     *
+     *   # the other party generates its per-session key pair
+     *   dhparams = OpenSSL::PKey::DH.new(der)
+     *   dh2 = OpenSSL::PKey.generate_key(dhparams)
+     *   pub2 = dh2.pub_key
      *
-     *  puts symm_key1 == symm_key2 # => true
+     *   symm_key1 = dh1.compute_key(pub2)
+     *   symm_key2 = dh2.compute_key(pub1)
+     *   puts symm_key1 == symm_key2 # => true
      */
     cDH = rb_define_class_under(mPKey, "DH", cPKey);
     rb_define_method(cDH, "initialize", ossl_dh_initialize, -1);
     rb_define_method(cDH, "initialize_copy", ossl_dh_initialize_copy, 1);
     rb_define_method(cDH, "public?", ossl_dh_is_public, 0);
     rb_define_method(cDH, "private?", ossl_dh_is_private, 0);
-    rb_define_method(cDH, "to_text", ossl_dh_to_text, 0);
     rb_define_method(cDH, "export", ossl_dh_export, 0);
     rb_define_alias(cDH, "to_pem", "export");
     rb_define_alias(cDH, "to_s", "export");
     rb_define_method(cDH, "to_der", ossl_dh_to_der, 0);
-    rb_define_method(cDH, "public_key", ossl_dh_to_public_key, 0);
     rb_define_method(cDH, "params_ok?", ossl_dh_check_params, 0);
 
     DEF_OSSL_PKEY_BN(cDH, dh, p);
diff --git a/ext/openssl/ossl_pkey_dsa.c b/ext/openssl/ossl_pkey_dsa.c
index 1c5a8a737..ab9ac781e 100644
--- a/ext/openssl/ossl_pkey_dsa.c
+++ b/ext/openssl/ossl_pkey_dsa.c
@@ -264,75 +264,6 @@ ossl_dsa_get_params(VALUE self)
     return hash;
 }
 
-/*
- *  call-seq:
- *    dsa.to_text -> aString
- *
- * Prints all parameters of key to buffer
- * INSECURE: PRIVATE INFORMATIONS CAN LEAK OUT!!!
- * Don't use :-)) (I's up to you)
- */
-static VALUE
-ossl_dsa_to_text(VALUE self)
-{
-    DSA *dsa;
-    BIO *out;
-    VALUE str;
-
-    GetDSA(self, dsa);
-    if (!(out = BIO_new(BIO_s_mem()))) {
-	ossl_raise(eDSAError, NULL);
-    }
-    if (!DSA_print(out, dsa, 0)) { /* offset = 0 */
-	BIO_free(out);
-	ossl_raise(eDSAError, NULL);
-    }
-    str = ossl_membio2str(out);
-
-    return str;
-}
-
-/*
- *  call-seq:
- *    dsa.public_key -> aDSA
- *
- * Returns a new DSA instance that carries just the public key information.
- * If the current instance has also private key information, this will no
- * longer be present in the new instance. This feature is helpful for
- * publishing the public key information without leaking any of the private
- * information.
- *
- * === Example
- *  dsa = OpenSSL::PKey::DSA.new(2048) # has public and private information
- *  pub_key = dsa.public_key # has only the public part available
- *  pub_key_der = pub_key.to_der # it's safe to publish this
- *
- *
- */
-static VALUE
-ossl_dsa_to_public_key(VALUE self)
-{
-    EVP_PKEY *pkey, *pkey_new;
-    DSA *dsa;
-    VALUE obj;
-
-    GetPKeyDSA(self, pkey);
-    obj = rb_obj_alloc(rb_obj_class(self));
-    GetPKey(obj, pkey_new);
-
-#define DSAPublicKey_dup(dsa) (DSA *)ASN1_dup( \
-	(i2d_of_void *)i2d_DSAPublicKey, (d2i_of_void *)d2i_DSAPublicKey, (char *)(dsa))
-    dsa = DSAPublicKey_dup(EVP_PKEY_get0_DSA(pkey));
-#undef DSAPublicKey_dup
-    if (!dsa)
-        ossl_raise(eDSAError, "DSAPublicKey_dup");
-    if (!EVP_PKEY_assign_DSA(pkey_new, dsa)) {
-        DSA_free(dsa);
-        ossl_raise(eDSAError, "EVP_PKEY_assign_DSA");
-    }
-    return obj;
-}
-
 /*
  *  call-seq:
  *    dsa.syssign(string) -> aString
@@ -469,12 +400,10 @@ Init_ossl_dsa(void)
 
     rb_define_method(cDSA, "public?", ossl_dsa_is_public, 0);
     rb_define_method(cDSA, "private?", ossl_dsa_is_private, 0);
-    rb_define_method(cDSA, "to_text", ossl_dsa_to_text, 0);
     rb_define_method(cDSA, "export", ossl_dsa_export, -1);
     rb_define_alias(cDSA, "to_pem", "export");
     rb_define_alias(cDSA, "to_s", "export");
     rb_define_method(cDSA, "to_der", ossl_dsa_to_der, 0);
-    rb_define_method(cDSA, "public_key", ossl_dsa_to_public_key, 0);
     rb_define_method(cDSA, "syssign", ossl_dsa_sign, 1);
     rb_define_method(cDSA, "sysverify", ossl_dsa_verify, 2);
 
diff --git a/ext/openssl/ossl_pkey_ec.c b/ext/openssl/ossl_pkey_ec.c
index deca4f43b..af59cfabd 100644
--- a/ext/openssl/ossl_pkey_ec.c
+++ b/ext/openssl/ossl_pkey_ec.c
@@ -412,32 +412,6 @@ ossl_ec_key_to_der(VALUE self)
     else
         return ossl_pkey_export_spki(self, 1);
 }
-
-/*
- *  call-seq:
- *     key.to_text   => String
- *
- *  See the OpenSSL documentation for EC_KEY_print()
- */
-static VALUE ossl_ec_key_to_text(VALUE self)
-{
-    EC_KEY *ec;
-    BIO *out;
-    VALUE str;
-
-    GetEC(self, ec);
-    if (!(out = BIO_new(BIO_s_mem()))) {
-	ossl_raise(eECError, "BIO_new(BIO_s_mem())");
-    }
-    if (!EC_KEY_print(out, ec, 0)) {
-	BIO_free(out);
-	ossl_raise(eECError, "EC_KEY_print");
-    }
-    str = ossl_membio2str(out);
-
-    return str;
-}
-
 /*
  *  call-seq:
  *     key.generate_key!   => self
@@ -464,20 +438,35 @@ static VALUE ossl_ec_key_generate_key(VALUE self)
 }
 
 /*
- *  call-seq:
- *     key.check_key   => true
+ * call-seq:
+ *    key.check_key   => true
  *
- *  Raises an exception if the key is invalid.
+ * Raises an exception if the key is invalid.
  *
- *  See the OpenSSL documentation for EC_KEY_check_key()
+ * See also the man page EVP_PKEY_public_check(3).
  */
 static VALUE ossl_ec_key_check_key(VALUE self)
 {
+#ifdef HAVE_EVP_PKEY_CHECK
+    EVP_PKEY *pkey;
+    EVP_PKEY_CTX *pctx;
+    int ret;
+
+    GetPKey(self, pkey);
+    pctx = EVP_PKEY_CTX_new(pkey, /* engine */NULL);
+    if (!pctx)
+        ossl_raise(eDHError, "EVP_PKEY_CTX_new");
+    ret = EVP_PKEY_public_check(pctx);
+    EVP_PKEY_CTX_free(pctx);
+    if (ret != 1)
+        ossl_raise(eECError, "EVP_PKEY_public_check");
+#else
     EC_KEY *ec;
 
     GetEC(self, ec);
     if (EC_KEY_check_key(ec) != 1)
 	ossl_raise(eECError, "EC_KEY_check_key");
+#endif
 
     return Qtrue;
 }
@@ -1601,7 +1590,6 @@ void Init_ossl_ec(void)
     rb_define_method(cEC, "export", ossl_ec_key_export, -1);
     rb_define_alias(cEC, "to_pem", "export");
     rb_define_method(cEC, "to_der", ossl_ec_key_to_der, 0);
-    rb_define_method(cEC, "to_text", ossl_ec_key_to_text, 0);
 
 
     rb_define_alloc_func(cEC_GROUP, ossl_ec_group_alloc);
diff --git a/ext/openssl/ossl_pkey_rsa.c b/ext/openssl/ossl_pkey_rsa.c
index 43f82cb29..1c5476cdc 100644
--- a/ext/openssl/ossl_pkey_rsa.c
+++ b/ext/openssl/ossl_pkey_rsa.c
@@ -390,7 +390,7 @@ ossl_rsa_private_decrypt(int argc, VALUE *argv, VALUE self)
  *   data = "Sign me!"
  *   pkey = OpenSSL::PKey::RSA.new(2048)
  *   signature = pkey.sign_pss("SHA256", data, salt_length: :max, mgf1_hash: "SHA256")
- *   pub_key = pkey.public_key
+ *   pub_key = OpenSSL::PKey.read(pkey.public_to_der)
  *   puts pub_key.verify_pss("SHA256", signature, data,
  *                           salt_length: :auto, mgf1_hash: "SHA256") # => true
  */
@@ -587,91 +587,6 @@ ossl_rsa_get_params(VALUE self)
     return hash;
 }
 
-/*
- * call-seq:
- *   rsa.to_text => String
- *
- * THIS METHOD IS INSECURE, PRIVATE INFORMATION CAN LEAK OUT!!!
- *
- * Dumps all parameters of a keypair to a String
- *
- * Don't use :-)) (It's up to you)
- */
-static VALUE
-ossl_rsa_to_text(VALUE self)
-{
-    RSA *rsa;
-    BIO *out;
-    VALUE str;
-
-    GetRSA(self, rsa);
-    if (!(out = BIO_new(BIO_s_mem()))) {
-	ossl_raise(eRSAError, NULL);
-    }
-    if (!RSA_print(out, rsa, 0)) { /* offset = 0 */
-	BIO_free(out);
-	ossl_raise(eRSAError, NULL);
-    }
-    str = ossl_membio2str(out);
-
-    return str;
-}
-
-/*
- * call-seq:
- *    rsa.public_key -> RSA
- *
- * Makes new RSA instance containing the public key from the private key.
- */
-static VALUE
-ossl_rsa_to_public_key(VALUE self)
-{
-    EVP_PKEY *pkey, *pkey_new;
-    RSA *rsa;
-    VALUE obj;
-
-    GetPKeyRSA(self, pkey);
-    obj = rb_obj_alloc(rb_obj_class(self));
-    GetPKey(obj, pkey_new);
-
-    rsa = RSAPublicKey_dup(EVP_PKEY_get0_RSA(pkey));
-    if (!rsa)
-        ossl_raise(eRSAError, "RSAPublicKey_dup");
-    if (!EVP_PKEY_assign_RSA(pkey_new, rsa)) {
-        RSA_free(rsa);
-        ossl_raise(eRSAError, "EVP_PKEY_assign_RSA");
-    }
-    return obj;
-}
-
-/*
- * TODO: Test me
-
-static VALUE
-ossl_rsa_blinding_on(VALUE self)
-{
-    RSA *rsa;
-
-    GetRSA(self, rsa);
-
-    if (RSA_blinding_on(rsa, ossl_bn_ctx) != 1) {
-	ossl_raise(eRSAError, NULL);
-    }
-    return self;
-}
-
-static VALUE
-ossl_rsa_blinding_off(VALUE self)
-{
-    RSA *rsa;
-
-    GetRSA(self, rsa);
-    RSA_blinding_off(rsa);
-
-    return self;
-}
- */
-
 /*
  * Document-method: OpenSSL::PKey::RSA#set_key
  * call-seq:
@@ -738,12 +653,10 @@ Init_ossl_rsa(void)
 
     rb_define_method(cRSA, "public?", ossl_rsa_is_public, 0);
     rb_define_method(cRSA, "private?", ossl_rsa_is_private, 0);
-    rb_define_method(cRSA, "to_text", ossl_rsa_to_text, 0);
     rb_define_method(cRSA, "export", ossl_rsa_export, -1);
     rb_define_alias(cRSA, "to_pem", "export");
     rb_define_alias(cRSA, "to_s", "export");
     rb_define_method(cRSA, "to_der", ossl_rsa_to_der, 0);
-    rb_define_method(cRSA, "public_key", ossl_rsa_to_public_key, 0);
     rb_define_method(cRSA, "public_encrypt", ossl_rsa_public_encrypt, -1);
     rb_define_method(cRSA, "public_decrypt", ossl_rsa_public_decrypt, -1);
     rb_define_method(cRSA, "private_encrypt", ossl_rsa_private_encrypt, -1);
diff --git a/lib/openssl/pkey.rb b/lib/openssl/pkey.rb
index 53ee52f98..569559e1c 100644
--- a/lib/openssl/pkey.rb
+++ b/lib/openssl/pkey.rb
@@ -10,6 +10,30 @@ module OpenSSL::PKey
   class DH
     include OpenSSL::Marshal
 
+    # :call-seq:
+    #    dh.public_key -> dhnew
+    #
+    # Returns a new DH instance that carries just the \DH parameters.
+    #
+    # Contrary to the method name, the returned DH object contains only
+    # parameters and not the public key.
+    #
+    # This method is provided for backwards compatibility. In most cases, there
+    # is no need to call this method.
+    #
+    # For the purpose of re-generating the key pair while keeping the
+    # parameters, check OpenSSL::PKey.generate_key.
+    #
+    # Example:
+    #   # OpenSSL::PKey::DH.generate by default generates a random key pair
+    #   dh1 = OpenSSL::PKey::DH.generate(2048)
+    #   p dh1.priv_key #=> #<OpenSSL::BN 1288347...>
+    #   dhcopy = dh1.public_key
+    #   p dhcopy.priv_key #=> nil
+    def public_key
+      DH.new(to_der)
+    end
+
     # :call-seq:
     #    dh.compute_key(pub_bn) -> string
     #
@@ -89,6 +113,22 @@ def new(*args, &blk) # :nodoc:
   class DSA
     include OpenSSL::Marshal
 
+    # :call-seq:
+    #    dsa.public_key -> dsanew
+    #
+    # Returns a new DSA instance that carries just the \DSA parameters and the
+    # public key.
+    #
+    # This method is provided for backwards compatibility. In most cases, there
+    # is no need to call this method.
+    #
+    # For the purpose of serializing the public key, to PEM or DER encoding of
+    # X.509 SubjectPublicKeyInfo format, check PKey#public_to_pem and
+    # PKey#public_to_der.
+    def public_key
+      OpenSSL::PKey.read(public_to_der)
+    end
+
     class << self
       # :call-seq:
       #    DSA.generate(size) -> dsa
@@ -159,6 +199,21 @@ def to_bn(conversion_form = group.point_conversion_form)
   class RSA
     include OpenSSL::Marshal
 
+    # :call-seq:
+    #    rsa.public_key -> rsanew
+    #
+    # Returns a new RSA instance that carries just the public key components.
+    #
+    # This method is provided for backwards compatibility. In most cases, there
+    # is no need to call this method.
+    #
+    # For the purpose of serializing the public key, to PEM or DER encoding of
+    # X.509 SubjectPublicKeyInfo format, check PKey#public_to_pem and
+    # PKey#public_to_der.
+    def public_key
+      OpenSSL::PKey.read(public_to_der)
+    end
+
     class << self
       # :call-seq:
       #    RSA.generate(size, exponent = 65537) -> RSA
diff --git a/test/openssl/test_pkey.rb b/test/openssl/test_pkey.rb
index 0a516f98e..4a539d8c4 100644
--- a/test/openssl/test_pkey.rb
+++ b/test/openssl/test_pkey.rb
@@ -169,4 +169,9 @@ def test_compare?
       key1.compare?(key4)
     end
   end
+
+  def test_to_text
+    rsa = Fixtures.pkey("rsa1024")
+    assert_include rsa.to_text, "publicExponent"
+  end
 end
diff --git a/test/openssl/test_pkey_dh.rb b/test/openssl/test_pkey_dh.rb
index 279ce1984..f80af8f84 100644
--- a/test/openssl/test_pkey_dh.rb
+++ b/test/openssl/test_pkey_dh.rb
@@ -86,6 +86,22 @@ def test_key_exchange
     assert_equal(dh.compute_key(dh2.pub_key), dh2.compute_key(dh.pub_key))
   end
 
+  def test_params_ok?
+    dh0 = Fixtures.pkey("dh1024")
+
+    dh1 = OpenSSL::PKey::DH.new(OpenSSL::ASN1::Sequence([
+      OpenSSL::ASN1::Integer(dh0.p),
+      OpenSSL::ASN1::Integer(dh0.g)
+    ]))
+    assert_equal(true, dh1.params_ok?)
+
+    dh2 = OpenSSL::PKey::DH.new(OpenSSL::ASN1::Sequence([
+      OpenSSL::ASN1::Integer(dh0.p + 1),
+      OpenSSL::ASN1::Integer(dh0.g)
+    ]))
+    assert_equal(false, dh2.params_ok?)
+  end
+
   def test_dup
     dh = Fixtures.pkey("dh1024")
     dh2 = dh.dup
diff --git a/test/openssl/test_pkey_rsa.rb b/test/openssl/test_pkey_rsa.rb
index d1e68dbc9..5f8d04e75 100644
--- a/test/openssl/test_pkey_rsa.rb
+++ b/test/openssl/test_pkey_rsa.rb
@@ -69,29 +69,28 @@ def test_private
   end
 
   def test_new
-    key = OpenSSL::PKey::RSA.new 512
-    pem  = key.public_key.to_pem
-    OpenSSL::PKey::RSA.new pem
-    assert_equal([], OpenSSL.errors)
-  end
+    key = OpenSSL::PKey::RSA.new(512)
+    assert_equal 512, key.n.num_bits
+    assert_equal 65537, key.e
+    assert_not_nil key.d
 
-  def test_new_exponent_default
-    assert_equal(65537, OpenSSL::PKey::RSA.new(512).e)
+    # Specify public exponent
+    key2 = OpenSSL::PKey::RSA.new(512, 3)
+    assert_equal 512, key2.n.num_bits
+    assert_equal 3, key2.e
+    assert_not_nil key2.d
   end
 
-  def test_new_with_exponent
-    1.upto(30) do |idx|
-      e = (2 ** idx) + 1
-      key = OpenSSL::PKey::RSA.new(512, e)
-      assert_equal(e, key.e)
-    end
-  end
+  def test_s_generate
+    key1 = OpenSSL::PKey::RSA.generate(512)
+    assert_equal 512, key1.n.num_bits
+    assert_equal 65537, key1.e
 
-  def test_generate
-    key = OpenSSL::PKey::RSA.generate(512, 17)
-    assert_equal 512, key.n.num_bits
-    assert_equal 17, key.e
-    assert_not_nil key.d
+    # Specify public exponent
+    key2 = OpenSSL::PKey::RSA.generate(512, 3)
+    assert_equal 512, key2.n.num_bits
+    assert_equal 3, key2.e
+    assert_not_nil key2.d
   end
 
   def test_new_break