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 ≥ 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 countermeasure against slide attacks. We show an indifferentiability attack for the case d = 2 and 3 rounds.

This letter examines outline measures of strength against the differential and linear cryptanalysis. These measures are useful to estimate the number of rounds giving an immune iterated cipher. This letter reports that the outline measures of strength are useful to relatively estimate the strength of generalized feistel ciphers.

Nyberg and Knudsen proved that the maximum average of differential probability (ADPmax) and the maximum average of linear probability (ALPmax) of Feistel cipher with over 4 rounds can be evaluated as ADPmax 2DCP2max and ALPmax 2LCP2max using the maximum of defferential characteristic probability (DCPmax) and the maximum of linear characteristic probability (LCPmax) per round. This paper shows ADPmax DCP2max and ALPmax LCP2max if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.