Communicated by L. R. Knudsen.
How to build a secure blockcipher is one of the central problems in symmetric cryptography. While the popular approach, initiated by the seminal paper of Luby and Rackoff, is based on a pseudorandom function, Minematsu (in: Dunkelman (ed.) FSE, 2009) and Minematsu and Iwata (in: Chen (ed.) IMA, 2011) proposed different schemes to efficiently achieve a better security. The point of these works is that they use tweakable blockcipher (TBC) as an internal module rather than pseudorandom function. This paper further extends the previous schemes and considers the case that the target blockcipher has much larger block size than that of the TBC we use. Assuming the tweak of TBC is long, we propose a scheme similar to unbalanced Feistel cipher that achieves stronger security than the previous schemes of Minematsu and Minematsu-Iwata. We also present a blockcipher-based instantiation of our scheme for the encryption over some unusual domains, such as decimal space, as a typical problem of format-preserving encryption.