International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Balanced Non-Adjacent Forms

Marc Joye , Zama
DOI: 10.1007/978-3-030-92078-4_19
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Presentation: Slides
Conference: ASIACRYPT 2021
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.
Video from ASIACRYPT 2021
  title={Balanced Non-Adjacent Forms},
  author={Marc Joye},