Constructing Variable-Length PRPs and SPRPs from Fixed-Length PRPs

Authors:
Debra L. Cook;Moti Yung;Angelos Keromytis
Affiliations:
Columbia University, New York, USA;Google, Inc. and Columbia University, New York, USA;Department of Computer Science, Columbia University, New York, USA
Venue:
Information Security and Cryptology
Year:
2009

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Abstract

We create variable-length pseudorandom permutations (PRPs) and strong PRPs (SPRPs) accepting any input length chosen from the range of b to 2b bits from fixed-length, b -bit PRPs. We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length that is fixed in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits. We also prove that these are the minimum number of rounds required.