On Kabatianskii-Krouk-Smeets signatures

Abstract

Kabastianskii, Krouk and Smeets proposed in 1997 a digital signature scheme based on random error-correcting codes. In this paper we investigate the security and the efficiency of their proposal. We show that a passive attacker who may intercept just a few signatures can recover the private key. We give precisely the number of signatures required to achieve this goal. This enables us to prove that all the schemes given in the original paper can be broken with at most 20 signatures. We improve the efficiency of these schemes by firstly providing parameters that enable to sign about 40 messages, and secondly, by describing a way to extend these few-times signatures into classical multi-time signatures. We finally study their key sizes and a mean to reduce them by means of more compact matrices. © Springer-Verlag Berlin Heidelberg 2007.