Paper 2026/921 Original: eprint.iacr.org/2026/921 ↗

Adaptively Secure Permissive Unbounded Inner Product Functional Encryption from Lattices

Abstract

Inner product functional encryption (IPFE) in unbounded setting for permissive relation offers a powerful cryptographic approach for enforcing fine-grained access control over sensitive information in untrusted cloud settings and has found growing applicability in areas such as cloud security, controlled access to electronic health records, network privacy, mobile data protection, the Internet of Things and many more. In spite of its importance, the profile of this primitive is not extensive. In this work, we propose the first permissive and unbounded public key IPFE scheme, providing post-quantum security guarantees in privacy-preserving environments. Our construction is lattice-based, achieves adaptive security and builds on modified ALS-IPFE scheme of Abdalla et al. (ASIACRYPT 2020). The unbounded setting and permissive relation between message vector and secret key vector supported by our scheme make it more flexible and practical for adapting to real-world application. We establish the adaptive indistinguishability of our construction within the random oracle model, by providing formal proof assuming the hardness of the learning with errors problem. Our scheme is the first of its kind in the post-quantum setting as existing permissive unbounded IPFE are pairing-based and derive their security from classical number-theoretic assumptions. Furthermore, as exhibited by our experimental results our proposed scheme is computationally lightweight.