No abstract

A major drawback of nearly all currently existing digital signature schemes is their computational requirements. Fast algorithms exist for PCs or hardware accelerated smart cards, but not for low-end embedded devices which are found in e.g. sensor networks. Such algorithms are also necessary for introduction of inexpensive signature creation devices to the civil sphere. Our purpose is to analyze a class of problems that are based on graph theoretic problems instead of modular arithmetics, and to provide very fast signature creation for embedded systems at the cost of somewhat longer signatures.

In the last decade using digital signatures in authentication and authorization protocols just as in e-business scenarios became more and more important and indispensable. New algorithms with different features for various applications are presented continuously. The IzoSign digital signature creation algorithm was introduced by the authors of this paper at CANS 2007. At that time, random key generation was proposed, which was later found vulnerable with high probability to a vertex matching attack (Kutylowski, 2007). We hereby analyze and generalize this kind of attacks, build a key generation algorithm that withstands such attacks, and then give a (theoretic) construction for key generation which (under the P = NP or NP = EXP assumptions) is hard to break.