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Public-Key Cryptosystems with Primitive Power Roots of Unity

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Part of the book series:Lecture Notes in Computer Science ((LNSC,volume 5107))

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Abstract

We first consider a variant of the Schmidt-Samoa–Takagi encryption scheme without losing additively homomorphic properties. We show that this variant is secure in the sense of IND-CPA under the decisional composite residuosity assumption, and of OW-CPA under the assumption on the hardness of factoringn = p2q. Second, we introduce new cryptographic properties “affine” and “pre-image restriction”, which are closely related to homomorphism. Intuitively, “affine” is a tuple of functions which have a special homomorphic property, and “pre-image restriction” is a function which can restrict the receiver to having information on the encrypted message. Then, we propose an encryption scheme with primitive power roots of unity in\(({\mathbb Z}/n^{s+1})^{\times}\). We show that our scheme has the above cryptographic properties.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, W8-55, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8552, Japan

    Takato Hirano, Koichiro Wada & Keisuke Tanaka

Authors
  1. Takato Hirano

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  2. Koichiro Wada

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  3. Keisuke Tanaka

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Yi Mu Willy Susilo Jennifer Seberry

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© 2008 Springer-Verlag Berlin Heidelberg

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Hirano, T., Wada, K., Tanaka, K. (2008). Public-Key Cryptosystems with Primitive Power Roots of Unity. In: Mu, Y., Susilo, W., Seberry, J. (eds) Information Security and Privacy. ACISP 2008. Lecture Notes in Computer Science, vol 5107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70500-0_8

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