On Constrained Implementation of Lattice-Based Cryptographic Primitives and Schemes on Smart Cards

Abstract

Most lattice-based cryptographic schemes with a security proof suffer from large key sizes and heavy computations. This is also true for the simpler case of authentication protocols that are used on smart cards as a very-constrained computing environment. Recent progress on ideal lattices has significantly improved the efficiency and made it possible to implement practical lattice-based cryptography on constrained devices. However, to the best of our knowledge, no previous attempts have been made to implement lattice-based schemes on smart cards. In this article, we provide the results of our implementation of several state-of-the-art lattice-based authentication protocols on smart cards and a microcontroller widely used in smart cards. Our results show that only a few of the proposed lattice-based authentication protocols can be implemented using limited resources of such constrained devices; however, cutting-edge ones are suitably efficient to be used practically on smart cards. Moreover, we have implemented fast Fourier transform (FFT) and discrete Gaussian sampling with different typical parameter sets, as well as versatile lattice-based public-key encryptions. These results have noticeable points that help to design or optimize lattice-based schemes for constrained devices.