Short Undeniable Signatures Based on Group Homomorphisms

This paper is devoted to the design and analysis of short undeniable signatures based on a random oracle. Exploiting their online property, we can achieve signatures with a fully scalable size depending on the security level. To this end, we develop a general framework based on the interpolation of group homomorphisms, leading to the design of a generic undeniable signature scheme called MOVA with batch verification and featuring non-transferability. By selecting group homomorphisms with a small group range, we obtain very short signatures. We also minimize the number of moves of the verification protocols by proposing some variants with only 2 moves in the random oracle model. We provide a formal security analysis of MOVA and assess the security in terms of the signature length. Under reasonable assumptions and with some carefully selected parameters, the MOVA scheme makes it possible to consider signatures of about 50 bits.