diff --git a/src/cryptography/x509/base.py b/src/cryptography/x509/base.py
index a3b334a..63c2e3c 100644
--- a/src/cryptography/x509/base.py
+++ b/src/cryptography/x509/base.py
@@ -17,7 +17,7 @@
 from cryptography.x509.name import Name
 
 
-_UNIX_EPOCH = datetime.datetime(1970, 1, 1)
+_EARLIEST_UTC_TIME = datetime.datetime(1950, 1, 1)
 
 
 def _reject_duplicate_extension(extension, extensions):
@@ -516,9 +516,9 @@
         if self._not_valid_before is not None:
             raise ValueError('The not valid before may only be set once.')
         time = _convert_to_naive_utc_time(time)
-        if time <= _UNIX_EPOCH:
-            raise ValueError('The not valid before date must be after the unix'
-                             ' epoch (1970 January 1).')
+        if time < _EARLIEST_UTC_TIME:
+            raise ValueError('The not valid before date must be on or after'
+                             ' 1950 January 1).')
         if self._not_valid_after is not None and time > self._not_valid_after:
             raise ValueError(
                 'The not valid before date must be before the not valid after '
@@ -539,9 +539,9 @@
         if self._not_valid_after is not None:
             raise ValueError('The not valid after may only be set once.')
         time = _convert_to_naive_utc_time(time)
-        if time <= _UNIX_EPOCH:
-            raise ValueError('The not valid after date must be after the unix'
-                             ' epoch (1970 January 1).')
+        if time < _EARLIEST_UTC_TIME:
+            raise ValueError('The not valid after date must be on or after'
+                             ' 1950 January 1.')
         if (self._not_valid_before is not None and
                 time < self._not_valid_before):
             raise ValueError(
@@ -620,9 +620,9 @@
         if self._last_update is not None:
             raise ValueError('Last update may only be set once.')
         last_update = _convert_to_naive_utc_time(last_update)
-        if last_update <= _UNIX_EPOCH:
-            raise ValueError('The last update date must be after the unix'
-                             ' epoch (1970 January 1).')
+        if last_update < _EARLIEST_UTC_TIME:
+            raise ValueError('The last update date must be on or after'
+                             ' 1950 January 1.')
         if self._next_update is not None and last_update > self._next_update:
             raise ValueError(
                 'The last update date must be before the next update date.'
@@ -638,9 +638,9 @@
         if self._next_update is not None:
             raise ValueError('Last update may only be set once.')
         next_update = _convert_to_naive_utc_time(next_update)
-        if next_update <= _UNIX_EPOCH:
-            raise ValueError('The last update date must be after the unix'
-                             ' epoch (1970 January 1).')
+        if next_update < _EARLIEST_UTC_TIME:
+            raise ValueError('The last update date must be on or after'
+                             ' 1950 January 1.')
         if self._last_update is not None and next_update < self._last_update:
             raise ValueError(
                 'The next update date must be after the last update date.'
@@ -720,9 +720,9 @@
         if self._revocation_date is not None:
             raise ValueError('The revocation date may only be set once.')
         time = _convert_to_naive_utc_time(time)
-        if time <= _UNIX_EPOCH:
-            raise ValueError('The revocation date must be after the unix'
-                             ' epoch (1970 January 1).')
+        if time < _EARLIEST_UTC_TIME:
+            raise ValueError('The revocation date must be on or after'
+                             ' 1950 January 1.')
         return RevokedCertificateBuilder(
             self._serial_number, time, self._extensions
         )
diff --git a/src/cryptography/x509/ocsp.py b/src/cryptography/x509/ocsp.py
index 97933b1..aae9b62 100644
--- a/src/cryptography/x509/ocsp.py
+++ b/src/cryptography/x509/ocsp.py
@@ -13,7 +13,7 @@
 from cryptography import x509
 from cryptography.hazmat.primitives import hashes
 from cryptography.x509.base import (
-    _UNIX_EPOCH, _convert_to_naive_utc_time, _reject_duplicate_extension
+    _EARLIEST_UTC_TIME, _convert_to_naive_utc_time, _reject_duplicate_extension
 )
 
 
@@ -154,9 +154,9 @@
                 raise TypeError("revocation_time must be a datetime object")
 
             revocation_time = _convert_to_naive_utc_time(revocation_time)
-            if revocation_time <= _UNIX_EPOCH:
-                raise ValueError('The revocation_time must be after the unix'
-                                 ' epoch (1970 January 1).')
+            if revocation_time < _EARLIEST_UTC_TIME:
+                raise ValueError('The revocation_time must be on or after'
+                                 ' 1950 January 1.')
 
             if (
                 revocation_reason is not None and
diff --git a/tests/x509/test_x509.py b/tests/x509/test_x509.py
index 55f5ddd..c8c863f 100644
--- a/tests/x509/test_x509.py
+++ b/tests/x509/test_x509.py
@@ -2027,6 +2027,35 @@
         cert = cert_builder.sign(private_key, hashes.SHA256(), backend)
         assert cert.not_valid_after == utc_time
 
+    @pytest.mark.requires_backend_interface(interface=RSABackend)
+    @pytest.mark.requires_backend_interface(interface=X509Backend)
+    def test_earliest_time(self, backend):
+        time = datetime.datetime(1950, 1, 1)
+        private_key = RSA_KEY_2048.private_key(backend)
+        cert_builder = x509.CertificateBuilder().subject_name(
+            x509.Name([x509.NameAttribute(NameOID.COUNTRY_NAME, u'US')])
+        ).issuer_name(
+            x509.Name([x509.NameAttribute(NameOID.COUNTRY_NAME, u'US')])
+        ).serial_number(
+            1
+        ).public_key(
+            private_key.public_key()
+        ).not_valid_before(
+            time
+        ).not_valid_after(
+            time
+        )
+        cert = cert_builder.sign(private_key, hashes.SHA256(), backend)
+        assert cert.not_valid_before == time
+        assert cert.not_valid_after == time
+        parsed = Certificate.load(
+            cert.public_bytes(serialization.Encoding.DER)
+        )
+        not_before = parsed['tbs_certificate']['validity']['not_before']
+        not_after = parsed['tbs_certificate']['validity']['not_after']
+        assert not_before.chosen.tag == 23  # UTCTime
+        assert not_after.chosen.tag == 23  # UTCTime
+
     def test_invalid_not_valid_after(self):
         with pytest.raises(TypeError):
             x509.CertificateBuilder().not_valid_after(104204304504)
@@ -2036,7 +2065,7 @@
 
         with pytest.raises(ValueError):
             x509.CertificateBuilder().not_valid_after(
-                datetime.datetime(1960, 8, 10)
+                datetime.datetime(1940, 8, 10)
             )
 
     def test_not_valid_after_may_only_be_set_once(self):
@@ -2082,7 +2111,7 @@
 
         with pytest.raises(ValueError):
             x509.CertificateBuilder().not_valid_before(
-                datetime.datetime(1960, 8, 10)
+                datetime.datetime(1940, 8, 10)
             )
 
     def test_not_valid_before_may_only_be_set_once(self):
diff --git a/tests/x509/test_x509_crlbuilder.py b/tests/x509/test_x509_crlbuilder.py
index e90fd3f..5f220bc 100644
--- a/tests/x509/test_x509_crlbuilder.py
+++ b/tests/x509/test_x509_crlbuilder.py
@@ -62,10 +62,10 @@
         with pytest.raises(TypeError):
             builder.last_update("notadatetime")
 
-    def test_last_update_before_unix_epoch(self):
+    def test_last_update_before_1950(self):
         builder = x509.CertificateRevocationListBuilder()
         with pytest.raises(ValueError):
-            builder.last_update(datetime.datetime(1960, 8, 10))
+            builder.last_update(datetime.datetime(1940, 8, 10))
 
     def test_set_last_update_twice(self):
         builder = x509.CertificateRevocationListBuilder().last_update(
@@ -97,10 +97,10 @@
         with pytest.raises(TypeError):
             builder.next_update("notadatetime")
 
-    def test_next_update_before_unix_epoch(self):
+    def test_next_update_before_1950(self):
         builder = x509.CertificateRevocationListBuilder()
         with pytest.raises(ValueError):
-            builder.next_update(datetime.datetime(1960, 8, 10))
+            builder.next_update(datetime.datetime(1940, 8, 10))
 
     def test_set_next_update_twice(self):
         builder = x509.CertificateRevocationListBuilder().next_update(
diff --git a/tests/x509/test_x509_revokedcertbuilder.py b/tests/x509/test_x509_revokedcertbuilder.py
index e3a0650..75c6b26 100644
--- a/tests/x509/test_x509_revokedcertbuilder.py
+++ b/tests/x509/test_x509_revokedcertbuilder.py
@@ -80,10 +80,10 @@
         with pytest.raises(TypeError):
             x509.RevokedCertificateBuilder().revocation_date("notadatetime")
 
-    def test_revocation_date_before_unix_epoch(self):
+    def test_revocation_date_before_1950(self):
         with pytest.raises(ValueError):
             x509.RevokedCertificateBuilder().revocation_date(
-                datetime.datetime(1960, 8, 10)
+                datetime.datetime(1940, 8, 10)
             )
 
     def test_set_revocation_date_twice(self):