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Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons

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Topics in Cryptology – CT-RSA 2018 (CT-RSA 2018)

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Abstract

We present a semantically secure somewhat homomorphic public-key cryptosystem working in sub-groups of \(\mathbb {Z}_{n}^{*}\) of prime power order. Our scheme introduces a novel threshold homomorphic property, which we use to build a two-party protocol for secure integer comparison. In contrast to related work which encrypts and acts on each bit of the input separately, our protocol compares multiple input bits simultaneously within a single ciphertext. Compared to the related protocol of Damgård et al. [9, 10] we present results showing this approach to be both several times faster in computation and lower in communication complexity.

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Notes

  1. 1.

    https://www.keylength.com/en/4/.

  2. 2.

    http://www.secg.org/SEC2-Ver-1.0.pdf.

  3. 3.

    https://ed25519.cr.yp.to/.

  4. 4.

    https://github.com/jedisct1/libsodium.

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Authors and Affiliations

  1. Western University, London, Canada

    Rhys Carlton, Aleksander Essex & Krzysztof Kapulkin

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  1. Rhys Carlton
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  2. Aleksander Essex
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  3. Krzysztof Kapulkin
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Correspondence to Aleksander Essex .

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  1. KU Leuven , Leuven, Belgium

    Nigel P. Smart

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Carlton, R., Essex, A., Kapulkin, K. (2018). Threshold Properties of Prime Power Subgroups with Application to Secure Integer Comparisons. In: Smart, N. (eds) Topics in Cryptology – CT-RSA 2018. CT-RSA 2018. Lecture Notes in Computer Science(), vol 10808. Springer, Cham. https://doi.org/10.1007/978-3-319-76953-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-76953-0_8

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