A comprehensive analysis of constant-time polynomial inversion for post-quantum cryptosystems

Post-quantum cryptosystems have currently seen a surge in interest thanks to the current standardization initiative by the U.S.A. National Institute of Standards and Technology (NIST). A common primitive in post-quantum cryptosystems, in particular in code-based ones, is the computation of the inverse of a binary polynomial in a binary polynomial ring. In this work, we analyze, realize in software, and benchmark a broad spectrum of binary polynomial inversion algorithms, targeting operand sizes which are relevant for the current second round candidates in the NIST standardization process. We evaluate advantages and shortcomings of the different inversion algorithms, including their capability to run in constant-time, thus preventing timing side-channel attacks.