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A NEW REPRESENTATION ALGORITHM IN A FREE GROUP

Choi, Su-Jeong

  • Published : 2009.10.31

Abstract

This paper presents a new representation algorithm which computes the representation for elements of a free group generated by two linear fractional transformations and also the justification of the algorithm in order to show how it operates correctly and efficiently according to inputs.

Keywords

linear fractional transformation;free group;representation;algorithm

References

  1. S. J. Choi, Cryptanalysis of a homomorphic public-key cryptosystem over a finite group, Ph.D. thesis, University of London, 2006
  2. S. J. Choi, S. R. Blackburn, and P. R. Wild, Cryptanalysis of a homomorphic public-key cryptosystem over a finite group, J. Math. Crypt. 1 (2007), no. 4, 351–358 https://doi.org/10.1515/jmc.2007.017
  3. D. Grigoriev and I. Ponomarenko, Homomorphic public key cryptosystems over groups and rings, Complexity of computations and proofs, Quad. Math. 13 (2004), 305–325
  4. R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin, New York, 1977
  5. S. J. Choi, Representation algorithms in some free groups, J. Korea Soc. Math. Educ. Ser. B : Pure Appl. Math. 15 (2008), no. 3, 229–243