# Heuristics for Minimum Brauer Chain Problem

• Fatih Gelgi
• Melih Onus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4263)

## Abstract

The exponentiation problem is computing x n for positive integer exponents n where the quality is measured by number of multiplications it requires. However, finding minimum number of multiplications is an NP-complete problem. This problem is very important for many applications such as RSA encryption and ElGamal decryption. Solving minimum Brauer chain problem is a way to solve the exponentiation problem. In this paper, five heuristics for approximating minimum length Brauer chain for a given number n is discussed. These heuristics are based on some greedy approaches and dynamic programming. As a result, we empirically get 1.1-approximation for the problem.

## Keywords

Brauer chain addition chain exponentiation greedy algorithms dynamic programming

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© Springer-Verlag Berlin Heidelberg 2006

## Authors and Affiliations

• Fatih Gelgi
• 1
• Melih Onus
• 1
1. 1.Department of Computer Science and EngineeringArizona State University