diff --git a/ext/openssl/ossl_x509crl.c b/ext/openssl/ossl_x509crl.c
index 368270ce1..4f3177bfb 100644
--- a/ext/openssl/ossl_x509crl.c
+++ b/ext/openssl/ossl_x509crl.c
@@ -350,7 +350,11 @@ ossl_x509crl_sign(VALUE self, VALUE key, VALUE digest)
 
     GetX509CRL(self, crl);
     pkey = GetPrivPKeyPtr(key); /* NO NEED TO DUP */
-    md = ossl_evp_get_digestbyname(digest);
+    if (NIL_P(digest)) {
+	md = NULL; /* needed for some key types, e.g. Ed25519 */
+    } else {
+	md = ossl_evp_get_digestbyname(digest);
+    }
     if (!X509_CRL_sign(crl, pkey, md)) {
 	ossl_raise(eX509CRLError, NULL);
     }
diff --git a/ext/openssl/ossl_x509req.c b/ext/openssl/ossl_x509req.c
index 37ba03728..4a4d3f286 100644
--- a/ext/openssl/ossl_x509req.c
+++ b/ext/openssl/ossl_x509req.c
@@ -312,7 +312,11 @@ ossl_x509req_sign(VALUE self, VALUE key, VALUE digest)
 
     GetX509Req(self, req);
     pkey = GetPrivPKeyPtr(key); /* NO NEED TO DUP */
-    md = ossl_evp_get_digestbyname(digest);
+    if (NIL_P(digest)) {
+        md = NULL; /* needed for some key types, e.g. Ed25519 */
+    } else {
+        md = ossl_evp_get_digestbyname(digest);
+    }
     if (!X509_REQ_sign(req, pkey, md)) {
 	ossl_raise(eX509ReqError, NULL);
     }
diff --git a/test/openssl/test_pkey.rb b/test/openssl/test_pkey.rb
index 811d5103d..aae6b7e07 100644
--- a/test/openssl/test_pkey.rb
+++ b/test/openssl/test_pkey.rb
@@ -90,6 +90,8 @@ def test_hmac_sign_verify
   def test_ed25519
     # Ed25519 is not FIPS-approved.
     omit_on_fips
+    # See EVP_PKEY_sign in Changelog for 3.7.0: https://github.com/libressl/portable/blob/master/ChangeLog
+    omit "Ed25519 not supported" unless openssl?(1, 1, 1) || libressl?(3, 7, 0)
 
     # Test vector from RFC 8032 Section 7.1 TEST 2
     priv_pem = <<~EOF
@@ -102,15 +104,8 @@ def test_ed25519
     MCowBQYDK2VwAyEAPUAXw+hDiVqStwqnTRt+vJyYLM8uxJaMwM1V8Sr0Zgw=
     -----END PUBLIC KEY-----
     EOF
-    begin
-      priv = OpenSSL::PKey.read(priv_pem)
-      pub = OpenSSL::PKey.read(pub_pem)
-    rescue OpenSSL::PKey::PKeyError => e
-      # OpenSSL < 1.1.1
-      pend "Ed25519 is not implemented" unless openssl?(1, 1, 1)
-
-      raise e
-    end
+    priv = OpenSSL::PKey.read(priv_pem)
+    pub = OpenSSL::PKey.read(pub_pem)
     assert_instance_of OpenSSL::PKey::PKey, priv
     assert_instance_of OpenSSL::PKey::PKey, pub
     assert_equal priv_pem, priv.private_to_pem
diff --git a/test/openssl/test_x509cert.rb b/test/openssl/test_x509cert.rb
index 76359552e..6c16218f3 100644
--- a/test/openssl/test_x509cert.rb
+++ b/test/openssl/test_x509cert.rb
@@ -292,24 +292,11 @@ def test_sign_and_verify_dsa_md5
   end
 
   def test_sign_and_verify_ed25519
-    # See test_ed25519 in test_pkey.rb
-
     # Ed25519 is not FIPS-approved.
     omit_on_fips
-
-    begin
-      ed25519  = OpenSSL::PKey::generate_key("ED25519")
-    rescue OpenSSL::PKey::PKeyError => e
-      # OpenSSL < 1.1.1
-      #
-      pend "Ed25519 is not implemented" unless openssl?(1, 1, 1)
-
-      raise e
-    end
-
     # See ASN1_item_sign_ctx in ChangeLog for 3.8.1: https://github.com/libressl/portable/blob/master/ChangeLog
-    pend 'ASN1 signing with Ed25519 not yet working' unless openssl? or libressl?(3, 8, 1)
-
+    omit "Ed25519 not supported" unless openssl?(1, 1, 1) || libressl?(3, 8, 1)
+    ed25519 = OpenSSL::PKey::generate_key("ED25519")
     cert = issue_cert(@ca, ed25519, 1, [], nil, nil, digest: nil)
     assert_equal(true, cert.verify(ed25519))
   end
diff --git a/test/openssl/test_x509crl.rb b/test/openssl/test_x509crl.rb
index 146ee0730..e5fa6f998 100644
--- a/test/openssl/test_x509crl.rb
+++ b/test/openssl/test_x509crl.rb
@@ -204,6 +204,23 @@ def test_sign_and_verify
     assert_equal(false, crl.verify(@dsa512))
   end
 
+  def test_sign_and_verify_ed25519
+    # Ed25519 is not FIPS-approved.
+    omit_on_fips
+    # See ASN1_item_sign_ctx in ChangeLog for 3.8.1: https://github.com/libressl/portable/blob/master/ChangeLog
+    omit "Ed25519 not supported" unless openssl?(1, 1, 1) || libressl?(3, 8, 1)
+    ed25519 = OpenSSL::PKey::generate_key("ED25519")
+    cert = issue_cert(@ca, ed25519, 1, [], nil, nil, digest: nil)
+    crl = issue_crl([], 1, Time.now, Time.now+1600, [],
+                    cert, ed25519, nil)
+    assert_equal(false, crl_error_returns_false { crl.verify(@rsa1024) })
+    assert_equal(false, crl_error_returns_false { crl.verify(@rsa2048) })
+    assert_equal(false, crl.verify(OpenSSL::PKey::generate_key("ED25519")))
+    assert_equal(true,  crl.verify(ed25519))
+    crl.version = 0
+    assert_equal(false, crl.verify(ed25519))
+  end
+
   def test_revoked_to_der
     # revokedCertificates     SEQUENCE OF SEQUENCE  {
     #      userCertificate         CertificateSerialNumber,
diff --git a/test/openssl/test_x509req.rb b/test/openssl/test_x509req.rb
index b98754b8c..1bf457ecf 100644
--- a/test/openssl/test_x509req.rb
+++ b/test/openssl/test_x509req.rb
@@ -17,21 +17,21 @@ def issue_csr(ver, dn, key, digest)
     req = OpenSSL::X509::Request.new
     req.version = ver
     req.subject = dn
-    req.public_key = key.public_key
+    req.public_key = key
     req.sign(key, digest)
     req
   end
 
   def test_public_key
     req = issue_csr(0, @dn, @rsa1024, OpenSSL::Digest.new('SHA256'))
-    assert_equal(@rsa1024.public_key.to_der, req.public_key.to_der)
+    assert_equal(@rsa1024.public_to_der, req.public_key.public_to_der)
     req = OpenSSL::X509::Request.new(req.to_der)
-    assert_equal(@rsa1024.public_key.to_der, req.public_key.to_der)
+    assert_equal(@rsa1024.public_to_der, req.public_key.public_to_der)
 
     req = issue_csr(0, @dn, @dsa512, OpenSSL::Digest.new('SHA256'))
-    assert_equal(@dsa512.public_key.to_der, req.public_key.to_der)
+    assert_equal(@dsa512.public_to_der, req.public_key.public_to_der)
     req = OpenSSL::X509::Request.new(req.to_der)
-    assert_equal(@dsa512.public_key.to_der, req.public_key.to_der)
+    assert_equal(@dsa512.public_to_der, req.public_key.public_to_der)
   end
 
   def test_version
@@ -132,6 +132,21 @@ def test_sign_and_verify_dsa_md5
       issue_csr(0, @dn, @dsa512, OpenSSL::Digest.new('MD5')) }
   end
 
+  def test_sign_and_verify_ed25519
+    # Ed25519 is not FIPS-approved.
+    omit_on_fips
+    # See ASN1_item_sign_ctx in ChangeLog for 3.8.1: https://github.com/libressl/portable/blob/master/ChangeLog
+    omit "Ed25519 not supported" unless openssl?(1, 1, 1) || libressl?(3, 8, 1)
+    ed25519 = OpenSSL::PKey::generate_key("ED25519")
+    req = issue_csr(0, @dn, ed25519, nil)
+    assert_equal(false, request_error_returns_false { req.verify(@rsa1024) })
+    assert_equal(false, request_error_returns_false { req.verify(@rsa2048) })
+    assert_equal(false, req.verify(OpenSSL::PKey::generate_key("ED25519")))
+    assert_equal(true, req.verify(ed25519))
+    req.public_key = @rsa1024.public_key
+    assert_equal(false, req.verify(ed25519))
+  end
+
   def test_dup
     req = issue_csr(0, @dn, @rsa1024, OpenSSL::Digest.new('SHA256'))
     assert_equal(req.to_der, req.dup.to_der)