diff --git a/cryptography/hazmat/bindings/openssl/backend.py b/cryptography/hazmat/bindings/openssl/backend.py
index b65583d..71b94ab 100644
--- a/cryptography/hazmat/bindings/openssl/backend.py
+++ b/cryptography/hazmat/bindings/openssl/backend.py
@@ -140,6 +140,7 @@
 
     def __init__(self, backend, cipher, mode, operation):
         self._backend = backend
+        self._cipher = cipher
 
         ctx = self._backend.lib.EVP_CIPHER_CTX_new()
         ctx = self._backend.ffi.gc(ctx, self._backend.lib.EVP_CIPHER_CTX_free)
@@ -185,9 +186,8 @@
         self._ctx = ctx
 
     def update(self, data):
-        block_size = self._backend.lib.EVP_CIPHER_CTX_block_size(self._ctx)
         buf = self._backend.ffi.new("unsigned char[]",
-                                    len(data) + block_size - 1)
+                                    len(data) + self._cipher.block_size - 1)
         outlen = self._backend.ffi.new("int *")
         res = self._backend.lib.EVP_CipherUpdate(self._ctx, buf, outlen, data,
                                                  len(data))
@@ -195,8 +195,7 @@
         return self._backend.ffi.buffer(buf)[:outlen[0]]
 
     def finalize(self):
-        block_size = self._backend.lib.EVP_CIPHER_CTX_block_size(self._ctx)
-        buf = self._backend.ffi.new("unsigned char[]", block_size)
+        buf = self._backend.ffi.new("unsigned char[]", self._cipher.block_size)
         outlen = self._backend.ffi.new("int *")
         res = self._backend.lib.EVP_CipherFinal_ex(self._ctx, buf, outlen)
         assert res != 0
diff --git a/cryptography/hazmat/primitives/ciphers/algorithms.py b/cryptography/hazmat/primitives/ciphers/algorithms.py
index 32acab1..c135f56 100644
--- a/cryptography/hazmat/primitives/ciphers/algorithms.py
+++ b/cryptography/hazmat/primitives/ciphers/algorithms.py
@@ -115,6 +115,7 @@
 
 class ARC4(object):
     name = "RC4"
+    block_size = 1
     key_sizes = frozenset([40, 56, 64, 80, 128, 192, 256])
 
     def __init__(self, key):