Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON A T-FUNCTION f(x)=x+h(x) WITH A SINGLE CYCLE ON ℤ2n

  • Received : 2011.10.25
  • Accepted : 2011.11.18
  • Published : 2011.12.30
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Abstract

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. When n is large (e.g., n = 64) such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them we study T-functions which are probably invertible and are very useful in stream ciphers. In this paper we study some conditions on a T-function h(x) such that f(x) = x + h(x) has a single cycle on ${\mathbb{Z}}_{2^n}$.

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References

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