Calculating average joint hamming weight for minimal weight conversion of d integers

Vorapong Suppakitpaisarn*, Masato Edahiro, Hiroshi Imai

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we propose an algorithm to calculate the efficiency of number representations in elliptic curve cryptography, average joint Hamming weight. The method uses Markov chains generated from a minimal weight conversion algorithm of d integers using the minimal weight conversion. With redundant representations using digit sets like {0, ±1}, it is possible to reduce computation time of the cryptosystem. Although larger digit sets make the computation time shorter, it requires longer preprocessing time. Therefore, the average joint Hamming weight is useful to evaluate digit sets. The Markov chains to find the average joint Hamming weight are derived automatically from the conversions. However, the number of states in these Markov chains is generally infinite. In [8], we propose an algorithm to reduce the number of states, but it is still unclear which representations the method can be applied for. In this paper, the finiteness of Markov chain with the existence of a stationary distribution is proven in a class of representation whose digit set D S be a finite set such that there exists a natural number Λ where D S ⊆ {0, ±1, ..., ±Λ} and {0,±1, ±Λ} ⊆ D S. The class covers most of the representation practically used in elliptic curve cryptography such as the representation which digit set are {0, ±1} and {0, ±1, ±3}.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 6th International Workshop, WALCOM 2012, Proceedings
Number of pages12
Publication statusPublished - 2012
Event6th International Workshop on Algorithms and Computation, WALCOM 2012 - Dhaka, Bangladesh
Duration: 2012 Feb 152012 Feb 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7157 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference6th International Workshop on Algorithms and Computation, WALCOM 2012


  • Elliptic Curve Cryptography
  • Finiteness
  • Markov Chain
  • Minimal Weight Conversion
  • Stationary Distribution

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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