Feistel Ciphers Based on a Single Primitive

We consider Feistel ciphers instantiated with tweakable block ciphers (TBCs) and ideal ciphers (ICs). The indistinguishability security of the TBC-based Feistel cipher is known, and the indifferentiability security of the IC-based Feistel cipher is also known, where independently keyed TBCs and independent ICs are assumed. In this paper, we analyze the security of a single-keyed TBC-based Feistel cipher and a single IC-based Feistel cipher. We characterize the security depending on the number of rounds. More precisely, we cover the case of contracting Feistel ciphers that have \(d\ge 2\) lines, and the results on Feistel ciphers are obtained as a special case by setting \(d=2\) . Our indistinguishability security analysis shows that it is provably secure with \(d+1\) rounds. Our indifferentiability result shows that, regardless of the number of rounds, it cannot be secure. Our attacks are a type of a slide attack, and we consider a structure that uses a round constant, which is a well-known counter measure against slide attacks. We show an indifferentiability attack for the case \(d=2\) and 3 rounds.