Analysis and implementation of an efficient ring-LPN based commitment scheme

Abstract

We analyze an efficient parallelizable commitment scheme that is statistically binding and computationally hiding under a variant of the decisional Ring-LPN assumption, conjectured to be secure against quantum computers. It works over medium-size binary finite fields, with both commitment and verification being dominated by 38 finite field multiplications. Such efficiency is achieved due to a precise analysis (that takes into account recent attacks against LPN) of underlying parameters. We report an initial parallel implementation by using the standard OpenCL library on three different platforms. On the AMD Radeon HD 7950 GPU, one can commit to 1024-bit messages in 1 bit per 104.7 cycles. We consider the analysis (which results in concrete parameters that subsequent work can try to falsify) together with the implementation the two most important aspects of the current work.