[Resource Topic] 2023/882: Expand-Convolute Codes for Pseudorandom Correlation Generators from LPN

Welcome to the resource topic for 2023/882

Title:
Expand-Convolute Codes for Pseudorandom Correlation Generators from LPN

Authors: Srinivasan Raghuraman, Peter Rindal, Titouan Tanguy

Abstract:

The recent development of pseudorandom correlation generators (PCG) holds tremendous promise for highly efficient MPC protocols. Among other correlations, PCGs allow for the efficient generation of oblivious transfer (OT) and vector oblivious linear evaluations (VOLE) with sublinear communication and concretely good computational overhead. This type of PCG makes use of a so-called LPN-friendly error-correcting code. That is, for large dimensions the code should have very efficient encoding and have high minimum distance.

We investigate existing LPN-friendly codes and find that several candidates are less secure than was believed. Beginning with the recent expand-accumulate codes, we find that for their aggressive parameters, aimed at good concrete efficiency, they achieve a smaller [pseudo] minimum distance than conjectured. This decreases the resulting security parameter of the PCG but it remains unclear by how much. We additionally show that the recently proposed and extremely efficient silver codes achieve only very small minimum distance and result in concretely efficient attacks on the resulting
PCG protocol. As such, silver codes should not be used.

We introduce a new LPN-friendly code which we call \emph{expand-convolute}. These codes have provably high minimum distance and faster encoding time than suitable alternatives, e.g. expand-accumulate. The main contribution of these codes is the introduction of a convolution step that dramatically increases the minimum distance. This in turn allows for a more efficient parameter selection which results in improved concrete performance. In particular, we observe a 3 times improvement in running time for a comparable security level.

ePrint: https://eprint.iacr.org/2023/882

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .