New Lattice Two-Stage Sampling Technique and Its Applications to Functional Encryption – Stronger Security and Smaller Ciphertexts

Abstract

This work proposes a new lattice two-stage sampling technique, generalizing the prior two-stage sampling method of Gentry, Peikert, and Vaikuntanathan (STOC ’08). By using our new technique as a key building block, we can significantly improve security and efficiency of the current state of the arts of simulation-based functional encryption. Particularly, our functional encryption achieves (Q, poly) simulation-based semi-adaptive security that allows arbitrary pre- and post-challenge key queries, and has succinct ciphertexts with only an additive O(Q) overhead. Additionally, our two-stage sampling technique can derive new feasibilities of indistinguishability-based adaptively-secure IB - FE for inner products and semi-adaptively-secure AB - FE for inner products, breaking several technical limitations of the recent work by Abdalla, Catalano, Gay, and Ursu (Asiacrypt ’20).