Advances in Cryptology — AUSCRYPT '92
Volume 718 of the series Lecture Notes in Computer Science pp 385396
Noninteractive generation of shared pseudorandom sequences
 Manuel CerecedoAffiliated withDivision of Electrical and Computer Engineering, Yokohama National University
 , Tsutomu MatsumotoAffiliated withDivision of Electrical and Computer Engineering, Yokohama National University
 , Hideki ImaiAffiliated withInstitute of Industrial Science, University of Tokyo
Abstract
We address the following problem: given a random seed secretly shared among a group of individuals, noninteractively generate pieces corresponding to a much longer shared pseudorandom sequence. Shared randomness is an essential resource in distributed computing and noninteractive ways of generating it can be useful in applications such as Byzantine Agreement, common coin flipping or secure computation protocols.
Our first result is negative: well known cryptographically strong pseudorandom number generators cannot be evaluated without interaction and, in particular, it is shown that constructions that recursively apply a oneway function to a random seed and output at each iteration the simultaneously hard bits in the input of the oneway function are actually incompatible with a homomorphic evaluation.
On the other hand, we show that pseudorandom generators that can be both proven cryptographically strong and sharedly evaluated without interaction do exist. A concrete implementation, under the RSA assumption, is described.
 Title
 Noninteractive generation of shared pseudorandom sequences
 Book Title
 Advances in Cryptology — AUSCRYPT '92
 Book Subtitle
 Workshop on the Theory and Application of Cryptographic Techniques Gold Coast, Queensland, Australia, December 13–16, 1992 Proceedings
 Pages
 pp 385396
 Copyright
 1993
 DOI
 10.1007/3540572201_77
 Print ISBN
 9783540572206
 Online ISBN
 9783540479765
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 718
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Manuel Cerecedo ^{(1)}
 Tsutomu Matsumoto ^{(1)}
 Hideki Imai ^{(2)}
 Author Affiliations

 1. Division of Electrical and Computer Engineering, Yokohama National University, 156 Tokiwadai, Hodogaya, 240, Yokohama, Japan
 2. Institute of Industrial Science, University of Tokyo, 7221 Roppongi, Minatoku, 106, Tokyo, Japan
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