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A Graph Theoretic Analysis of Double Base Number Systems

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Progress in Cryptology – INDOCRYPT 2007 (INDOCRYPT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4859))

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Abstract

Double base number systems (DBNS) provide an elegant way to represent numbers. These representations also have many interesting and useful properties, which have been exploited to find many applications in Cryptography and Signal Processing. In the current article we present a scheme to represent numbers in double (and multi-) base format by combinatorial objects like graphs and diagraphs. The combinatorial representation leads to proof of some interesting results about the double and multibase representation of integers. These proofs are based on simple combinatorial arguments. In this article we have provided a graph theoretic proof of the recurrence relation satisfied by the number of double base representations of a given integer. The result has been further generalized to more than 2 bases. Also, we have uncovered some interesting properties of the sequence representing the number of double base representation of a positive integer n. It is expected that the combinatorial representation can serve as a tool for a better understanding of the double (and multi-) base number systems.

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Authors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Pradeep Kumar Mishra & Vassil Dimitrov

Authors
  1. Pradeep Kumar Mishra
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  2. Vassil Dimitrov
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K. Srinathan C. Pandu Rangan Moti Yung

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Mishra, P.K., Dimitrov, V. (2007). A Graph Theoretic Analysis of Double Base Number Systems. In: Srinathan, K., Rangan, C.P., Yung, M. (eds) Progress in Cryptology – INDOCRYPT 2007. INDOCRYPT 2007. Lecture Notes in Computer Science, vol 4859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77026-8_12

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  • DOI: https://doi.org/10.1007/978-3-540-77026-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77025-1

  • Online ISBN: 978-3-540-77026-8

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