Revisiting Turning Online Cipher Off.

In [1], a class of constructions was defined based on layers of secure online ciphers interleaved with simple mixing layers (like reversing and block-shifting). Here we show that an SPRP construction proposed in the work cited is insecure. Howevewr, the same construction is secure under the assumption that the underlying construction is online-but-last ciphers. We include a simpler proof for beyond-birthday security of other constructions proposed in the same work. 1