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Australasian Conference on Information Security and Privacy

ACISP 1999: Information Security and Privacy pp 314–325Cite as

A Functional Cryptosystem Using a Group Action

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1587))

Abstract

The main purpose of this paper is to examine applications of group theoretical concepts to cryptography. We construct a backward deterministic system employing the action of the modular group on the upper half plane and the amalgamated free product structure of the group. We invent a geometrical algorithm that finds the normal form of an element of the modular group effectively. This algorithm makes our backward deterministic system tractable. Using the backward deterministic system, we invent a public-key cryptosystem in terms of a functional cryptosystem.

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Author information

Authors and Affiliations

  1. Telecommunications Advancement Organization of Japan, 1-1-32 Shin’urashima, Kanagawa-ku, Yokohama, 221-0031, Japan

    Akihiro Yamamura

Authors
  1. Akihiro Yamamura
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Editor information

Editors and Affiliations

  1. School of Information Technology and Computer Science, University of Wollongong, Wollongong, NSW, 2522, Australia

    Josef Pieprzyk , Rei Safavi-Naini  & Jennifer Seberry ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Yamamura, A. (1999). A Functional Cryptosystem Using a Group Action. In: Pieprzyk, J., Safavi-Naini, R., Seberry, J. (eds) Information Security and Privacy. ACISP 1999. Lecture Notes in Computer Science, vol 1587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48970-3_26

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  • DOI: https://doi.org/10.1007/3-540-48970-3_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65756-9

  • Online ISBN: 978-3-540-48970-2

  • eBook Packages: Springer Book Archive

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