Signcryption schemes with insider security in an ideal permutation model

Signcryption aims to provide both confidentiality and authentication of messages more efficiently than performing encryption and signing independently. The "Commit-then-Sign & Encrypt" (CtS&E) method allows to perform encryption and signing in parallel. Parallel execution of cryptographic algorithms decreases the computation time needed to signcrypt messages. CtS&E uses weaker cryptographic primitives in a generic way to achieve a strong security notion of signcryption. Various message pre-processing schemes, also known as message padding, have been used in signcryption as a commitment scheme in CtS&E. Due to its elegance and versatility, the sponge structure turns out to be a useful tool for designing new padding schemes such as SpAEP [T. K. Bansal, D. Chang and S. K. Sanadhya, Sponge based CCA2 secure asymmetric encryption for arbitrary length message, in: Information Security and Privacy - ACISP 2015, Lecture Notes in Comput. Sci. 9144, Springer, Berlin (2015), 93-106], while offering further avenues for optimization and parallelism in the context of signcryption. In this work, we design a generic and efficient signcryption scheme featuring parallel encryption and signature on top of a sponge-based message-padding underlying structure. Unlike other existing schemes, the proposed scheme also supports arbitrarily long messages. We prove the construction secure when instantiated from weakly secure asymmetric primitives such as a trapdoor one-way encryption and a universal unforgeable signature. With a careful analysis and simple tweaks, we demonstrate how different combinations of weakly secure probabilistic and deterministic encryption and signature schemes can be used to construct a strongly secure signcryption scheme, further broadening the choices of underlying primitives to cover essentially any combination thereof. To the best of our knowledge, this is the first signcryption scheme based on the sponge structure that also offers strong security using weakly secure underlying asymmetric primitives, even deterministic ones, along with the ability to handle long messages, efficiently.