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International Conference on Security and Cryptography for Networks

SCN 2012: Security and Cryptography for Networks pp 426–444Cite as

Probabilistically Correct Secure Arithmetic Computation for Modular Conversion, Zero Test, Comparison, MOD and Exponentiation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7485))

Abstract

When secure arithmetic is required, computation based on secure multiplication (MULT) is much more efficient than computation based on secure Boolean circuits. However, a typical application may also require other building blocks, such as comparison, exponentiation and the modulo (MOD) operation. Secure solutions for these functions proposed in the literature rely on bit-decomposition or other bit-oriented methods, which require O(ℓ) MULTs for ℓ-bit inputs. In the absence of a known bit-length independent solution, the complexity of the whole computation is often dominated by these non-arithmetic functions.

In this paper, we resolve the above problem for the case of two-party protocols against a malicious adversary. We start with a general modular conversion, which converts secret shares over distinct moduli. For this, we propose a probabilistically correct protocol with a complexity that is independent of ℓ. Then, we show that when these non-arithmetic functions are based on secure modular conversions, they can be computed in constant rounds and O(k) MULTs, where k is a parameter with an error rate of 2− Ω(k).

An extended version of this paper, which is [37], is at IACR e-Print Archive 2011/560.

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Authors and Affiliations

  1. National Taiwan University, Taipei, Taiwan

    Ching-Hua Yu

  2. Center for Information Tech. and Innovation, Academia Sinica, Taipei, Taiwan

    Ching-Hua Yu & Bo-Yin Yang

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  1. Ching-Hua Yu
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  1. Dipartimento di Informatica, Università di Salerno, via Ponte don Melillo, 84084, Fisciano, SA, Italy

    Ivan Visconti  & Roberto De Prisco  & 

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Yu, CH., Yang, BY. (2012). Probabilistically Correct Secure Arithmetic Computation for Modular Conversion, Zero Test, Comparison, MOD and Exponentiation. In: Visconti, I., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2012. Lecture Notes in Computer Science, vol 7485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32928-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-32928-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32927-2

  • Online ISBN: 978-3-642-32928-9

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