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Eurocode ’92 pp 185-200 | Cite as

Rational Interval Maps and Cryptography

  • S. Harari
  • P. Liardet
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)

Abstract

In Eurocrypt 1991 Habutsu, Nishio, Sasase, Mori [4] introduced a cryptosystem using tent maps (denoted HNSM in the sequel). Though the functions that are used have good chaotic properties this system seems to has many weaknesses [7]. A general framework for such cryptosystems can be described as follow. Let ε = {E i ; i = 0,..., M} be a family of so-called plaintext-spaces and for each i = 1,..., M, let L i be an integer ≥ 2 and let T i = {T i,ℓ ; = 1,...,L i } be a family of cipher-maps T i,ℓ : E iℒ1E i . We assume that there exist maps S i : E i E i−1 such that for all ∈ {1,..., L i } one has S i o T i,ℓ = Id Ei−1. The key is given by {S 1,..., S M ) and the cryptogram of a given paintext yE 0 is any element in
where the union is taken over all finite sequences ( 1,..., M ) in . Usually all the plaintext-spaces are identical to a same space E and we choose the same family of enciphering maps. Therefore, the system is given by a deciphering map Σ: E → E and a family of right inverse maps of Σ: T 1,..., T L , L ≥ 2. The integer M corresponds to the number of iterations and the key is (Σ, M). To avoid attacks on the enciphering algorithm, the choice of the cryptogram depends on a random process which produces a uniform-like distribution of the ciphertext in E M . It seem that the firt use of such a scheme was considered in terms of cellular automata by S. Wolfram in Crypto’85 [8] and recently H. Gutowitz in [3] proposed a scheme, according to this model, of an enciphering/deciphering system at high rate. The HNSM system uses tent maps Φ t for keys, namely t is a parameter in]0,1[ and Φ t is the piecewise linear map defined by Φ t (x) = x/t for 0 ≤ xt and for t < x ≤ 1.

Keywords

Cellular Automaton Rational Number Unit Interval Ergodic Measure Ergodic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • S. Harari
    • 1
  • P. Liardet
    • 2
  1. 1.Groupe d’Étude du Codage de ToulonUniversité de Toulon et du VarLa GardeFrance
  2. 2.URA CNRS No225 Equipe DSA, case 96Université de ProvenceMarseille cedex 3France

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