International Association for Cryptologic Research

International Association
for Cryptologic Research


Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding

Maxime Bombar , École Polytechnique, Inria
Geoffroy Couteau , CNRS, IRIF, Université Paris-Cité
Alain Couvreur , Inria, École Polytechnique
Clément Ducros , Université Paris-Cité, IRIF, Inria
DOI: 10.1007/978-3-031-38551-3_18 (login may be required)
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Presentation: Slides
Conference: CRYPTO 2023
Abstract: Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle et al. (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computation, yielding silent secure two-party computation protocols (protocols where the preprocessing phase requires almost no communication). Furthermore, programmable PCGs can be used similarly to generate multiparty correlated randomness to be used in silent secure N-party protocols. Previous works constructed very efficient (non-programmable) PCGs for correlations such as random oblivious transfer. However, the situation is less satisfying for the case of random oblivious linear evaluation (OLE), which generalize oblivious transfers over large field, and are a core resource for secure computation of arithmetic circuits. The state-of-the-art work of (Boyle et al., Crypto 2020) constructed programmable PCGs for OLE, but their work suffers from two important downsides: (1) it only generates OLEs over large fields, and (2) it relies on a relatively new ``splittable'' ring-LPN assumption, which lacks strong security foundations. In this work, we construct new programmable PCGs for the OLE correlation, that overcome both limitations. To this end, we introduce the Quasi-Abelian Syndrome Decoding problem (QASD), a family of assumption which generalizes the well-established Quasi-Cyclic Syndrome Decoding assumption. Building upon QASD, we construct new programmable PCGs for OLEs over any field Fq with q > 2. Furthermore, we provide strong security foundations for QASD, showing that it resists all attacks from the linear test framework (Couteau et al., Crypto 2021) and admits a search-to-decision reduction. In particular, our analysis also sheds light on the security of the ring-LPN assumption used in Boyle et al., Crypto 2020). Using our new PCGs, we obtain the first efficient N-party silent secure computation protocols for computing general arithmetic circuit over Fq for any q > 2.
  title={Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding},
  author={Maxime Bombar and Geoffroy Couteau and Alain Couvreur and Clément Ducros},