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Proving a Shuffle Using Representations of the Symmetric Group

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Book cover Information Security and Cryptology – ICISC 2008 (ICISC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5461))

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Abstract

Shuffling protocol proposed in Crypto 2005 by Peng et al. is improved so that the number of communication rounds for the verification is reduced. We use an idea of linear representations of the symmetric group and a property of the incidence matrices of 1-subsets and 2-subsets of a finite set. The proposed protocol is valid for mix networks implemented with Paillier encryption schemes with which we can apply some known zero-knowledge proofs following the same line of approaches of Peng et al. [24]. The overall cost for the verification, if we fully implement our idea, is more expensive than that of the original protocol by Peng et al. We, however, can control the level of computation cost for the verification by using the idea of λ-designs properly.

This research is supported by Foundation of ubiquitous computing and networking project(UCN) Project, the Ministry of Knowledge Economy(MKE) 21st Century Frontier R&D Program in Korea and a result of subproject UCN 08B3-B-30S.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, San5 Woncheon-Dong, Youngtong-Gu, Suwon, 443-749, Korea

    Soojin Cho

  2. Department of Information and Computer Engineering, Ajou University, San5 Woncheon-Dong, Youngtong-Gu, Suwon, 443-749, Korea

    Manpyo Hong

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  1. Soojin Cho
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Editors and Affiliations

  1. Department of Electronic and Electrical Engineering, Pohang University of Science and Technology (POSTECH), San 31 Hyoja-dong, Nam-gu,, 790-784, Pohang, Kyungbuk, Korea

    Pil Joong Lee

  2. Department of Mathematical Sciences, Seoul National University, 599 Gwanakno, Gwanak-gu, 151-742, Seoul, Korea

    Jung Hee Cheon

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Cho, S., Hong, M. (2009). Proving a Shuffle Using Representations of the Symmetric Group. In: Lee, P.J., Cheon, J.H. (eds) Information Security and Cryptology – ICISC 2008. ICISC 2008. Lecture Notes in Computer Science, vol 5461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00730-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-00730-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00729-3

  • Online ISBN: 978-3-642-00730-9

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