Meta-elgamal Signature Schemes Using a Composite Module Meta-elgamal Signature Schemes Using a Composite Modul

Limited distribution notes: This report has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher its distribution outside the University of Technology Chemnitz-Zwickau prior to publication should be limited to peer communications and speciic requests. After outside publication, requests should be lled only by reprints or legally obtained copies of the article. Abstract In 1984 ElGamal published the rst signature scheme based on the discrete logarithm problem. Since then a lot of work was done to modify and generalize this signature scheme. Very important steps of recent research were the discovery of eecient signature schemes with appendix , e.g. by Schnorr, Nyberg/Rueppel or Harn. All these variants can be embedded into a Meta-ElGamal signature scheme. Until now all schemes except one have in common that the veriication is done over a nite eld. In this paper we focus on those schemes where a composite modul n = pq instead of a prime-modul p is used in the Meta-ElGamal signature scheme. An unmodiied scheme is cryptoanalysed in this composite mode, further we introduce some new reened modes and give a security and performance analysis of the various schemes. As a result, some schemes can be used in these modes with slight modiications. Although the security of these schemes can't be proven, the advantages are that even existential forging-easy in prime-based modes without hashing or using a redundancy scheme-seems to be hard in the Meta-ElGamal signature schemes the parameters can be chosen such that the security relays on both the discrete logarithm and the factorization problem.