How to Construct Super-Pseudorandom Permutations with Short Keys

Tetsu IWATA
Kaoru KUROSAWA

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.1    pp.2-13
Publication Date: 2007/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.1.2
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Cryptography
Keyword: 
Luby-Rackoff theory,  super-pseudorandomness,  Feistel permutation,  MISTY-type permutation,  

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Summary: 
It is known that a super-pseudorandom permutation can be constructed from a pseudorandom function f and two universal hash functions, h and h′. It is a four round Feistel permutation denoted by φ(hk,f,f,h′k′). In this paper, we show how to re-use the secret key for f in this construction. Specifically, we show that (1) the same key can be used for both h and h′, and (2) the key for h and h′can be derived from f. As a result, our construction requires only the key for f as a secret key, and it preserves computational efficiency and security. We show the full security proof of our construction. Also, we derive a similar result for a five round MISTY-type permutation.

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