Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON SECURE BINARY SEQUENCES GENERATED BY A FUNCTION f(x) = x + (g(x)2 ∨ C) mod 2n

  • Received : 2009.10.05
  • Accepted : 2009.11.11
  • Published : 2009.12.30
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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 will study T-functions which are probably invertible transformation and are very useful in stream ciphers. In this paper we will show that $f(x)=x+(g(x)^2{\vee}C)$ mod $2^n$ is a permutation with a single cycle of length $2^n$ if both the least significant bit and the third significant bit in the constant C are 1, where g(x) is a T-function.

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References

  1. Jin Hong, Dong Hoon Lee, Yongjin Yeom and Daewan Han, A New Class of Single Cycle T-functions, FSE 2005, LNCS 3557, 68-82, 2005.
  2. A Kilmov and A. Shamir, A New Class of Invertible Mappings, CHES 2002, LNCS 2523, 470-483, 2003.
  3. A Kilmov and A. Shamir, Cryptographic Applications of T-Functions, SAC 2003, LNCS 3006, 248-261, 2004.
  4. A Kilmov and A. Shamir, New Cryptographic Primitives Based on Multiword T-Functions, FSE 2004, LNCS 3017, 1-15, 2004.
  5. M.S Rhee, On a characterization of T-functions with one cycle property, J. of the Chungcheong Math. Soc. 21 (2008), no. 2, 259-268.
  6. R. Rivert, M. Robshaw, R. Sidney and Y. L. Yin, The RC6 block cipher, Available from http://www.rsa.com/rsalabs/rc6/.