diff --git a/tests/data_files/Makefile b/tests/data_files/Makefile
index fa30cf57b0..bbbfa9cd9c 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -709,6 +709,8 @@ keys_rsa_pkcs8_pwd = PolarSSLTest
 ### Basic unencrypted RSA keys from which
 ### all other encrypted RSA keys are derived.
 keys_rsa_base =
+### TODO: the commands require OpenSSL 1.x to work as desired. With
+### OpenSSL 3.x, they produce pkcs8 files.
 rsa_pkcs1_768_clear.pem:
 	$(OPENSSL) genrsa -out $@ 768
 keys_rsa_base += rsa_pkcs1_768_clear.pem
diff --git a/tests/data_files/rsa_pkcs1_768_clear.pem b/tests/data_files/rsa_pkcs1_768_clear.pem
index 0e2d52e05d..33140c3c71 100644
--- a/tests/data_files/rsa_pkcs1_768_clear.pem
+++ b/tests/data_files/rsa_pkcs1_768_clear.pem
@@ -1,13 +1,12 @@
------BEGIN PRIVATE KEY-----
-MIIB5QIBADANBgkqhkiG9w0BAQEFAASCAc8wggHLAgEAAmEA2YljoU8MXSipAQkJ
-KtPH57N8JTyoHo3AXZKqumGGFEUJhoyIp6BtFUHikLGMasMzaK7CUzLZComjhNJP
-gyAxsrjh8bt8eKn4iEP+UkB9KwvnpkrPdP22WiDhUUbKckvXAgMBAAECYQCMHTYS
-3Dt2dY4FoLBK6YXE85Ju2ZbftyXEH4ff7JjTzXPJOhN7BJW+L2WjFPkAeyEdi3Y/
-5zrKVtRQRXpmELeYOpgxy5CZfmknYyForhNwKKGL14GFE4/O50nbsnHzjAECMQD0
-IqQbfR334+BtSn4qczFm5q8QbhTjkQMRQ4bn4xGBKdGU/PwmyJj5DpF54FoRmIEC
-MQDkG9OgZo8VKRsVPUeJXjMQQNChes1Q7+W8A/qnt8IuHaedohEjC4fDFNSEbyl7
-eFcCMQDMokC2PeChySNz2G36fQXav9/bwLnHqeRNUzHAKwegIYJoBMoCZEA8+uYb
-p183woECMBzA2TM92klbjhtmRw8svZkN4n6IYTsTkkzZ342mnyZ6/HblR+239VwE
-0ykCbiMvLwIwcJxV2F1UXJ2wvwNJhGdYPzHW2fWelsB7KIwcHHKEMX0Q/WZ7usQe
-8nhaXrUdJdA0
------END PRIVATE KEY-----
+-----BEGIN RSA PRIVATE KEY-----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+-----END RSA PRIVATE KEY-----
diff --git a/tests/data_files/rsa_pkcs1_769_clear.pem b/tests/data_files/rsa_pkcs1_769_clear.pem
index a04b2c1b2e..25e12bde55 100644
--- a/tests/data_files/rsa_pkcs1_769_clear.pem
+++ b/tests/data_files/rsa_pkcs1_769_clear.pem
@@ -1,13 +1,12 @@
------BEGIN PRIVATE KEY-----
-MIIB5gIBADANBgkqhkiG9w0BAQEFAASCAdAwggHMAgEAAmEBtTOp1rud7hQbMLrQ
-2Q0BfF7CX+XtflbWxy9ZBUpuyGxJCgdw4+PXZGa64DaxHozNM3EHGxvnYc1uuWpl
-g3kvTu5qfAzZuKjnGXVIVc3aneHMTYQeUzWcGrSxJdtfhRr5AgMBAAECYQDVGAxU
-/HdannQuSTAYSu2JeApXgZNDPAJNbXd/S6s5hwYGnF/aw6etaSD2vdGQqWDblwjk
-hUxvweEe2bCobFuYXTzO7l7glvfNpHn2VOy44SFW51YG1JGyJ3qpm6DQ+30CMQG8
-3YQ7tWfTExA+mE7AxHuG1XPHGwANEEeZL7WmmkIUs6nCpUM5tyeXelXDbAZ3c9MC
-MQD7lwqpfq18pTA1Hzz+6sAaD5Pdiyo2zi3m3ke4azsCxiPTENNO8cSwjBqi8ITA
-EoMCMFJMOJZDLP3jXPH3gzouHxwGiPCgkhXYmSZBqT009FyYECOuJw2aUHy5aPxK
-E7gteQIxAOPRzRzYkh6JstKXu/MV/ehbbMkzqIFCSHyDkaxkpWYIqA4LcV1OPo6j
-/8bGR19qIwIxAaxBZhV5njcSqf5lhJ5ftLMWiXQEzKO8pdOkLOeqT35zVPzpz0LD
-ZF3/s0smY+YZHg==
------END PRIVATE KEY-----
+-----BEGIN RSA PRIVATE KEY-----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+-----END RSA PRIVATE KEY-----
diff --git a/tests/data_files/rsa_pkcs1_770_clear.pem b/tests/data_files/rsa_pkcs1_770_clear.pem
index 6e90126f86..0a707a8b7e 100644
--- a/tests/data_files/rsa_pkcs1_770_clear.pem
+++ b/tests/data_files/rsa_pkcs1_770_clear.pem
@@ -1,13 +1,12 @@
------BEGIN PRIVATE KEY-----
-MIIB5wIBADANBgkqhkiG9w0BAQEFAASCAdEwggHNAgEAAmEDS2vbf8jg+A02Gcl2
-91UaWDaGIAopYPuRhxcYRmA+pPJjWtU0Pyqiojuf0gmILgDSX43uVlx4ZWi0yP90
-9jUNMxZPTU2wQleHjuVAk10eGknKxnKh2YX43vWyy1zaLKcxAgMBAAECYQEY6b+d
-/AYSGDRgul1JW6r+nopluXy2tJNv7x1Cs2OqBKFa65APSeAJMNq2Vj5pNBOnzaHK
-NPv4S0Z/HOh8DylYdJXW6+4lVZqYrLwC1XVhejmVERnKNOB0nO4qPAjHTQECMQHh
-c8/cL9618nOYJwJigr5NiNIJ1h0htUhllNHzGBqtQG7YrN50p9x1HQfzKSVGnGkC
-MQHAd7y2zJenNtfwTR976ooaun+FZ6ixOF3ctuFg37o1WzthSS2EgIlrhNl8LmrI
-+4kCMQHE62NO+8WjGwv9xizrKZ4HaMBXOpM7Q8Rws5jy/OkTtXrR4YaA7e1qSz5Q
-VZPYookCMQCEIYMjZKIl7R2wOjjVfKPV/i7GMmVcWZwmBGfg7+ngAJI9Np9Hk8tp
-N0oQsWha8OkCMQF4Y76OsODPpqgnt6RrwkzEBYe5ubRQ+yvskgthKzFWIkVYhUbA
-iCclTg3LxTkuF9I=
------END PRIVATE KEY-----
+-----BEGIN RSA PRIVATE KEY-----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+-----END RSA PRIVATE KEY-----
diff --git a/tests/data_files/rsa_pkcs1_776_clear.pem b/tests/data_files/rsa_pkcs1_776_clear.pem
index cbf421f2ef..e62f7b195b 100644
--- a/tests/data_files/rsa_pkcs1_776_clear.pem
+++ b/tests/data_files/rsa_pkcs1_776_clear.pem
@@ -1,13 +1,12 @@
------BEGIN PRIVATE KEY-----
-MIIB6AIBADANBgkqhkiG9w0BAQEFAASCAdIwggHOAgEAAmIA2ddFQYzrl74kgTjz
-Pwv1/FaIisF994XKewWKHiWEWsiWJN/74nJH3yVHxMYs7THYKix9v689xfv5s12+
-o6fernc1xhgWeKHsa40d4L8ECwjpzkfYdPdHDcsIk8GT/JeEWwIDAQABAmE//F1Z
-Xb0tuyoZ0tKQKEE+t2Qv7ZnEhMXu0Le7FyYDTHvdpPTllM/LmbW09MjpewSM4eVk
-2RhSSp5sJICT4nCiLx4yOqR6OvLtH3ZIETG9HGFLFiQWJjczUDFQ7WSb1BlhAjEP
-PbkpPmmN2deZxeifjCOymWYqVVdGjLXUKO6Qstksgz7AtbSeGKSzQKys1jpVNwvT
-AjEOSwEInewxEpBxRb8wuaitMdO9XmKtoqthLkDR7ftjiL+DdUQmvNZpOvUWkowz
-APhZAjEI73Dco0CS70IdXw/waeKL1K825m2SaPA4//5NSu1T0WY66MyJW31DsgkK
-E1aDmxANAjEEyKfU6X53Qj5kGzMNrOY+6bFz7VZbxVlVEnURjnSYcNmgtywTRxsA
-Z4JGhtAz9fwpAjEBs5I5adCIv7hC5jmtDTlbYEvepIRPu7vlFxPd4+dpmwl/kLB6
-6UO1U5XLxyraxdBb
------END PRIVATE KEY-----
+-----BEGIN RSA PRIVATE KEY-----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+-----END RSA PRIVATE KEY-----
diff --git a/tests/data_files/rsa_pkcs1_784_clear.pem b/tests/data_files/rsa_pkcs1_784_clear.pem
index 03eb10e126..b7b424b02b 100644
--- a/tests/data_files/rsa_pkcs1_784_clear.pem
+++ b/tests/data_files/rsa_pkcs1_784_clear.pem
@@ -1,13 +1,12 @@
------BEGIN PRIVATE KEY-----
-MIIB7QIBADANBgkqhkiG9w0BAQEFAASCAdcwggHTAgEAAmMAvbHZtyhktEvbWBdx
-axUmmPLrlPu3qWyD/uWhht5mggzVgJuA5rCPdzZuSJOhzneTWyJeldIvN0jI8K+z
-tOb2rWY0eLikyaI5T/j3BcpnMSvz6Igwdd8ZXHKxsixyH/Wb/JMCAwEAAQJiGxeb
-kJ0kRNvQp/QxLqoGqTGIk+6ffIMTFwSU3T5GRayvkX6kGk59LvmHJrZvFZ3eXZbI
-QDclNOS96CGaw7LdTM8L8iFAsYVg6xGDqJrJ+VRU5sOut2ZcvTKwjZXhrTvvQwEC
-MgDd9eo/pDyuDlYTZF10V4AZhOZ9oNT1EYfx57jDSQhNNc6vbdYcSAhi6ykowHTW
-C+D5AjIA2skwnxXPAl16rbwpIFMK1BrAsYeZfPOxpKIPXiGMQNCdVOQERYyG1vK5
-2bQ1eO446wIxePaABtb2ytS9TCwyUiktgrrO8kAoTraTI95o7uRqRcnBLhHp0dff
-2ijWcYMRKWWn4QIyAMoS9yCIcRm7I1siJk4fxSmgyAdwufhp0NLBiDYmADfBNv+4
-VqWyJLyVlciZJKZcSR8CMTfLvGlWObOndbb+I1IrAFZM4vK7TopDTeBAS2+5fIST
-o3H7yyLP1EfKMqdEvgfNEz0=
------END PRIVATE KEY-----
+-----BEGIN RSA PRIVATE KEY-----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+-----END RSA PRIVATE KEY-----