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Balanced Non-adjacent Forms

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Advances in Cryptology – ASIACRYPT 2021 (ASIACRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13092))

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Abstract

Integers can be decomposed in multiple ways. The choice of a recoding technique is generally dictated by performance considerations. The usual metric for optimizing the decomposition is the Hamming weight. In this work, we consider a different metric and propose new modified forms (i.e., integer representations using signed digits) that satisfy minimality requirements under the new metric. Specifically, we introduce what we call balanced non-adjacent forms and prove that they feature a minimal Euclidean weight. We also present efficient algorithms to produce these new minimal forms. We analyze their asymptotic and exact distributions. We extend the definition to modular integers and show similar optimality results. The balanced non-adjacent forms find natural applications in fully homomorphic encryption as they optimally reduce the noise variance in LWE-type ciphertexts.

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Authors and Affiliations

  1. Zama, Paris, France

    Marc Joye

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  1. Marc Joye
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Correspondence to Marc Joye .

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  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Joye, M. (2021). Balanced Non-adjacent Forms. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13092. Springer, Cham. https://doi.org/10.1007/978-3-030-92078-4_19

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