<abstract xmlns="http://www.w3.org/1999/xhtml"> Factorizable logarithmic signatures for finite groups are the essential component of the cryptosystems MST1 and MST3. The problem of finding efficient algorithms for factoring group elements with respect to a given class of logarithmic signatures is therefore of vital importance in the investigation of these cryptosystems. In this paper we are concerned about the factorization algorithms with respect to transversal and fused transversal logarithmic signatures for finite abelian groups. More precisely we present algorithms and their complexity for factoring group elements with respect to these classes of logarithmic signatures. In particular, we show a factoring algorithm with respect to the class of fused transversal logarithmic signatures and also its complexity based on an idea of Blackburn, Cid and Mullan for finite abelian groups.</abstract>

Factorizable logarithmic signatures for finite groups are the essential component of the cryptosystems MST1 and MST3. The problem of finding efficient algorithms for factoring group elements with respect to a given class of logarithmic signatures is therefore of vital importance in the investigation of these cryptosystems. In this paper we are concerned about the factorization algorithms with respect to transversal and fused transversal logarithmic signatures for finite abelian groups. More precisely we present algorithms and their complexity for factoring group elements with respect to these classes of logarithmic signatures. In particular, we show a factoring algorithm with respect to the class of fused transversal logarithmic signatures and also its complexity based on an idea of Blackburn, Cid and Mullan for finite abelian groups.

LOGARITHMIC SIGNATURES FOR ABELIAN GROUPS AND THEIR FACTORIZATION

Institute of Business Inform. Technology Lucerne University of Appl. Sci. and Arts Zentralstrasse 9 CH-6002 Lucerne SWITZERLAND

Institute for Experimental Math. University of Duisburg-Essen Ellernstrasse 29 D–45326 Essen GERMANY

University of Paderborn Warburger Strasse 100 D–33098 Paderborn GERMANY

Tatra Mountains Mathematical Publications

{"article-title":"LOGARITHMIC SIGNATURES FOR ABELIAN GROUPS AND THEIR FACTORIZATION"}

Factorizable logarithmic signatures for finite groups are the essential component of the cryptosystems MST1 and MST3. The problem of finding efficient...

LOGARITHMIC SIGNATURES FOR ABELIAN GROUPS AND THEIR FACTORIZATION

Published Online: Feb 18, 2014

Page range: 21 - 33

DOI: https://doi.org/10.2478/tmmp-2013-0033

This content is open access.