1Lattice-Based Signatures: Optimization and Implementation on Reconfigurable Hardware

Abstract—Nearly all of the currently used signature schemes, such as RSA or DSA, are based either on the factoring assumption or the presumed intractability of the discrete logarithm problem. As a consequence, the appearance of quantum computers or algorithmic advances on these problems may lead to the unpleasant situation that a large number of today’s schemes will most likely need to be replaced with more secure alternatives. In this work we present such an alternative – an efficient signature scheme whose security is derived from the hardness of lattice problems. It is based on recent theoretical advances in lattice-based cryptography and is highly optimized for practicability and use in embedded systems. The public and secret keys are roughly 1.5 kB and 0.3 kB long, while the signature size is approximately 1.1 kB for a security level of around 80 bits. We provide implementation results on reconfigurable hardware (Spartan/Virtex-6) and demonstrate that the scheme is scalable, has low area consumption, and even outperforms classical schemes. Index Terms—Public key cryptosystems, reconfigurable hardware, signature scheme, ideal lattices, FPGA. F