Abstract:

In this paper we construct and consider a new group-based 2-of-2 multisignature scheme, which is built using a bilinear map. This map is an asymmetric pairing of Type 3, and although, for the reason of this paper, it is treated in a completely abstract fashion it ought to be viewed as being actually defined over E(Fqn)[p] × E(F_qnk)[p] → F_qnk[p]. The idea of the scheme is such that there are two signers with two independent keys (sk₁,pk₁) and (sk₂,pk₂), that sign the same message. Unlike the regular digital signature schemes, the signing algorithm is split into two phases. Within the first ot them, both signers independently make so-called pre-signatures with their secret keys and send them to the second phase, where the final signatures is derived. The security analysis is conducted within the euf-cma model by reducing the security of the scheme to the computational hardness of solving the bilinear DiffieHellman inversion problem. The reduction itself is made in the random oracle model.