Lattice-based unidirectional infinite-use proxy re-signatures with private re-signature key

Abstract In a proxy re-signature scheme, a semi-trusted proxy can convert Alice's (also called as delegatee's) signature into Bob's (also called as delegator's) signature on the same message. However, the proxy itself cannot produce any signatures on behalf of either Alice or Bob. There exists some unidirectional one-use and multi-use (a message can be re-signed a polynomial number of times) proxy re-signature schemes. In some scenarios of big data, it is required to design unidirectional infinite-use (a message can be re-signed infinite number of times) proxy re-signature schemes. In this paper, we propose the first unidirectional infinite-use proxy re-signature scheme and identity-based unidirectional infinite-use proxy re-signature scheme with private re-signature keys based on lattice and prove that they are secure in the random oracle model.