Succinct representation of finite abelian groups

Authors:
Arash Farzan;J. Ian Munro
Affiliations:
University of Waterloo, Waterloo, Ontario, Canada;University of Waterloo, Waterloo, Ontario, Canada
Venue:
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Year:
2006

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Abstract

We consider the problem of representing and performing computations on finite abelian groups. Assuming a lg n-bit1 word model and considering any abelian group of order n, we show how to represent the group in constant number of words and perform three fundamental group operations of equality testing, multiplication, and inversion in constant number of word operations, provided we have the platform instruction to reverse the bits of a word.