Over the course of the project, substantial progress has been made across its core research axes, leading to significant breakthroughs in multilinear maps, homomorphic encryption, lattice cryptanalysis, and side-channel–resistant implementations. In the area of multilinear maps and indistinguishability obfuscation, we developed powerful new attacks that revealed structural weaknesses in CLT13-based schemes, demonstrating that previously proposed countermeasures could be broken using higher-dimensional lattice reductions. This line of work also showed how to greatly improve the efficiency of obfuscation by applying Kilian’s randomization after encoding, thereby increasing the complexity of known attacks and enabling much smaller parameters. Building on this theoretical foundation, we delivered the first secure implementation of multiparty non-interactive Diffie–Hellman based on CLT13, overcoming longstanding barriers posed by earlier attacks. Additionally, we solved the hidden subset sum problem in polynomial time — an important improvement over earlier exponential-time approaches — and introduced a new bootstrapping technique for CKKS based on blind rotations and modular additions, opening a new direction for approximate homomorphic encryption..
The project also made major contributions to the design of side-channel countermeasures and leakage-resilient primitives. We introduced the first improvement to the wire-shuffling countermeasure, reducing its complexity from O(t \log t) to O(t) while preserving strong probing security guarantees. In lattice-based cryptography, we developed state-of-the-art high-order masking techniques for Kyber, NTRU, and Dilithium, including new conversion gadgets, efficient Boolean-to-arithmetic masking conversions, and optimized masked rejection sampling. Our work on Dilithium in particular produced some of the most efficient high-order masking constructions to date. In addition, we designed new symmetric primitives tailored to homomorphic and leakage-resilient settings, including the Elisabeth stream cipher for hybrid HE, the LWPR model capturing realistic leakage in re-keying mechanisms, the FPM family of prime-field–masked tweakable block ciphers, and the highly efficient small-pSquare instance. Further contributions include new approaches to FHE-based transciphering and novel prime-field masking techniques with strong side-channel security. Collectively, these developments provide a comprehensive set of theoretical and practical advances that significantly raise the bar for secure and efficient cryptographic systems.
