Paper 2025/1761

Automated Proof for Quadratic Functional Encryption: Finding Attacks and New Constructions

Abstract

Quadratic functional encryption (QFE for short) is a cryptographic primitive which can output the value of a quadratic function between two vectors, without leaking other information on the plaintext vectors. Since the first breakthrough of Baltico et al. (Crypto 2017), there are already many constructions for QFE from bilinear groups. However, constructing more efficient QFE schemes and proving their security has always been a challenging task. While generic bilinear group model (GBGM for short) can be used to construct highly efficient QFE schemes and proving their security, obtaining a security proof under GBGM is difficult and may contain undiscovered mistakes. In this paper, we solve this problem by presenting new techniques which finally lead to an automated proof tool for QFE schemes, and can also be used to find potential attacks. Our automated proof tool shows that the RPB+19 scheme (Riffel et al, NIPS'19) which is the most efficient QFE scheme in the literature and already used in several works, is in fact insecure, and also gives an attack for the scheme. Finally, we present two new QFE schemes, each shares same efficiency with the RPB+19 scheme from one aspect, and prove their security using our automated proof tool. Our new schemes are more efficient than all existing QFE schemes other than the RPB+19 scheme, which means that they are most efficient among all existing ``secure'' QFE schemes.