The ISC International Journal of Information Security

Abstract The security of public key cryptography relies on the complexity of certain mathematical hard problems. It is vital to comprehend the intricacy of these problems to develop secure cryptographic schemes and security protocols. This paper provides an overview of some widely recognized hard problems associated with the discrete logarithm problem, including the reductions among them. Furthermore, we introduce a novel hard problem that is equivalent to the discrete logarithm problem, which also has a decisional version. Additionally, a set of new problems is presented, which can be instrumental in the design of secure encryption schemes. This paper is intended to provide crucial insights into the realm of hard problems in cryptography, facilitating a better understanding of security measures.

Abstract A convertible limited (multi-) verifier signature (CL(M)VS) provides controlled verifiability and preserves the privacy of the signer. Furthermore, limited verifier(s) can designate the signature to a third party or convert it into a publicly verifiable signature upon necessity. In this proposal, we first present a generic construction of convertible limited verifier signature (CLVS) into which the existing secure CLVS schemes fit. Afterwards, we extend this generic construction to address the unsolved question of designing an efficient construction with more than two limited verifiers. To this effect, two generic CLMVS constructions are presented, which are proven to be efficient in that they generate a unique signature for more than two limited verifiers. Given the first generic construction, each limited verifier checks the validity of the signature solely, while in the second, cooperation of all limited verifiers is imperative. Thereupon, on the ground of our second generic construction, we present the first pairing-based CLMVS scheme secure in the standard model, which is of a strong confirmation property as well. Finally, we employ the proposed CLMVS scheme for one limited verifier (CLVS) so as to design a new electronic voting protocol.