Non-cryptographic primitive for pseudorandom permutation

Authors:
Tetsu Iwata;Tomonobu Yoshino;Kaoru Kurosawa
Affiliations:
Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan;Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan
Venue:
Theoretical Computer Science
Year:
2003

Citing 6
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Abstract

Four round Feistel permutation (like DES) is super-pseudorandom if each round function is random or a secret universal hash function. A similar result is known for five round MISTY type permutation. It seems that each round function must be at least either random or secret in both cases.In this paper, however, we show that the second round permutation g in five round MISTY type permutation need not be cryptographic at all, i.e., no randonmess nor secrecy is required. g has only to satisfy that g(x)⊕x ≠ g(x')⊕x' for any x ≠ x'. This is the first example such that a non-cryptographic primitive is substituted to construct the minimum round super-pseudorandom permutation. Further we show efficient constructions of super-pseudorandom permutations by using above mentioned g.