A NEW REPRESENTATION ALGORITHM IN A FREE GROUP

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

File

Download PDF

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, Representation algorithms in some free groups, J. Korea Soc. Math. Educ. Ser. B : Pure Appl. Math. 15 (2008), no. 3, 229–243
3. 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
4. D. Grigoriev and I. Ponomarenko, Homomorphic public key cryptosystems over groups and rings, Complexity of computations and proofs, Quad. Math. 13 (2004), 305–325
5. R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin, New York, 1977