Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON A SECURE BINARY SEQUENCE GENERATED BY A QUADRATIC POLYNOMIAL ON $\mathbb{Z}_{2^n}$

  • Rhee, Min-Surp (Department of Applied Mathematics, Dankook University)
  • Received : 2010.07.22
  • Accepted : 2010.10.28
  • Published : 2011.01.30
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Abstract

Invertible functions with a single cycle property have many cryptographic applications. The main context in which we study them in this paper is pseudo random generation and stream ciphers. In some cryptographic applications we need a generator which generates binary sequences of period long enough. A common way to increase the size of the state and extend the period of a generator is to run in parallel and combine the outputs of several generators with different period. In this paper we will characterize a secure quadratic polynomial on $\mathbb{Z}_{2^n}$, which generates a binary sequence of period long enough and without consecutive elements.

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