Post-Quantum Secure Inner Product Functional Encryption Using Multivariate Public Key Cryptography

Abstract

Functional encryption (FE) is an exciting new public key paradigm that provides solutions to most of the security challenges of cloud computing in a non-interactive manner. In the context of FE, inner product functional encryption (IPFE) is a widely useful cryptographic primitive. It enables a user with secret key $$usk_\\mathbf {y}$$\n associated to a vector $$\\mathbf {y}$$\n to retrieve only $$\\langle \\mathbf {x},\\mathbf {y}\\rangle $$\n from a ciphertext encrypting a vector $$\\mathbf {x}$$\n , not beyond that. In the last few decades, several constructions of IPFE have been designed based on traditional classical cryptosystems, which are vulnerable to large enough quantum computers. However, there are few quantum computer resistants i.e., post-quantum IPFE. Multivariate cryptography is one of the promising candidates of post-quantum cryptography. In this paper, we propose for the first-time multivariate cryptography-based IPFE. Our work achieves non-adaptive simulation-based security under the hardness of the MQ problem.