Advanced Cryptography from Lattices

As organizations increasingly rely on cloud services and shared infrastructures to store data and delegate resource-intensive computations, it is essential for maintaining privacy, security, and compliance with regulations to i) protect data while ensuring that only authorized individuals or systems can decrypt and use it, and ii) guarantee the correctness of the computation performed by cloud services. Advanced cryptographic primitives tackle both of these challenges: on the one hand, attribute-based encryption (ABE) effectively addresses the problem of selective data sharing while preserving confidentiality of unauthorized messages, on the other hand, succinct arguments (SNARKs) enable end users to verify efficiently that outsourced computation was performed correctly by cloud providers.In recent years, both ABE and SNARKs have seen tremendous research progress, especially in the context of lattice-based cryptography, where both constructions often rely on shared techniques, underscoring the deep synergy between these two cryptographic primitives.Leveraging lattice-based assumption offers several key advantages in this context, which are essential to the proposed project, in particular, enabling the construction of ABE for general circuits, and providing post-quantum security, meaning these constructions are believed to remain secure even in the presence of quantum computers.By exploring and developing new techniques that leverage these synergies, this project aims to advance theory and practice in both domains and construct robust, quantum-secure cryptographic systems that address the complex security and privacy challenges of the digital age.