An Ideal Lattice Signcryption Scheme for Data Protection

Abstract

Signcryption simultaneously provides confidentiality and authenticity, rendering it well-suited for secure data transmission. However, most existing signcryption constructions rely on number-theoretic hard problems, which renders them susceptible to quantum attacks. For this reason, this paper designs a trapdoor-free signcryption scheme over ideal lattices. Our scheme employs bimodal Gaussian rejection sampling to reduce the rejection constant from e12α+12α2 to e12α2, and leverages the Number Theoretic Transform for faster polynomial multiplication. Furthermore, we demonstrate that the scheme simultaneously satisfies IND-CPA confidentiality and EUF-CMA unforgeability based on the R-LWE and R-SIS hardness assumptions within the random oracle model. In contrast to present lattice-based signcryption schemes, the proposed construction achieves smaller key sizes and lower computational cost, making it suitable for privacy-preserving applications.