Foundations of Post-Quantum Functional Encryption

Nowadays increasing number of users and organizations store data in third party locations, such as cloud-based service providers. While cloud computing offers convenience, efficiency, and scalability, it also introduces significant security risks. One primary concern is that sensitive data stored in the cloud often remains accessible to potentially untrusted providers. This reliance means users must implicitly trust third-party services to handle their data securely, creating critical challenges in security, privacy, and trust. Nonetheless, these emerging challenges can be effectively addressed through cryptography. Specifically, advanced encryption primitives enable users to encrypt their data in a way that allows fine-grained access to the data (e.g., using attribute-based encryption), and permits cloud providers to perform selective computation on this encrypted data (e.g., using functional encryption). However, the aforementioned cryptographic primitives, that are capable of securing our data within todays and tomorrows highly accessible and ubiquitous cloud-based services, need to account for powerful adversaries. In particular in order to be future-proof they need to provide resistance against attacks based on quantum computers, i.e., post-quantum security. Moreover, due to the highly accessible nature of cloud-based services, we need to provide protection against adversaries that can arbitrarily interact with the deployed systems at any given moment throughout its lifetime, i.e., adaptive security. Furthermore, in order for the advanced encryption schemes to be useful in the cloud computing setting, they not only need to provide these strong security guarantees, but also need to be expressive enough to allow performing arbitrarily complicated computations over the encrypted data, while at the same time maintaining the privacy of that data. Nevertheless, the existing advanced encryption schemes either lack strong security (i.e., adaptive security and post-quantum security) guarantees, or they can only handle very restricted classes of functions over the encrypted data (e.g., inner-product computations). This project targets at designing expressive and future-proof advanced encryption primitives using lattice-based cryptographic assumptions, which are (plausibly) post-quantum secure. On the one hand, we will work on designing new lattice-based schemes. On the other hand, we will study the limits of the existing lattice-based assumptions and techniques in constructing such schemes, and propose new assumptions and security models that can overcome these limitations. Theoretically, techniques developed throughout this project are expected to extend beyond advanced encryption primitives and contribute broadly to the post-quantum cryptographic landscape. Practically, this project will significantly strengthen the foundations of secure data outsourcing, enhancing trust, privacy, and security in the future of cloud computing.