diff --git a/cryptography/primitives/block/base.py b/cryptography/primitives/block/base.py
index 2a6a5c3..207c83d 100644
--- a/cryptography/primitives/block/base.py
+++ b/cryptography/primitives/block/base.py
@@ -23,6 +23,12 @@
         self._ctx = api.create_block_cipher_context(cipher, mode)
         self._operation = None
 
+    @property
+    def name(self):
+        return "{0}-{1}-{2}".format(
+            self.cipher.name, self.cipher.key_size, self.mode.name,
+        )
+
     def encrypt(self, plaintext):
         if self._ctx is None:
             raise ValueError("BlockCipher was already finalized")
diff --git a/tests/primitives/test_block.py b/tests/primitives/test_block.py
index 7dccda4..aa670be 100644
--- a/tests/primitives/test_block.py
+++ b/tests/primitives/test_block.py
@@ -19,6 +19,13 @@
 
 
 class TestBlockCipher(object):
+    def test_cipher_name(self):
+        cipher = BlockCipher(
+            ciphers.AES(binascii.unhexlify(b"0" * 32)),
+            modes.CBC(binascii.unhexlify(b"0" * 32), padding.NoPadding())
+        )
+        assert cipher.name == "AES-128-CBC"
+
     def test_use_after_finalize(self):
         cipher = BlockCipher(
             ciphers.AES(binascii.unhexlify(b"0" * 32)),