Jules Dumezy

While FHE enables computation on encrypted data, protecting the program itself remains a theoretical and practical challenge, often forcing practitioners to choose between exposing proprietary logic or suffering impractical performance penalties. This paper introduces HEGIDE, an oblivious processor based on the (discrete) Cheon-Kim-Kim-Song (CKKS) scheme that bridges the gap between theoretical Private Function Evaluation (PFE) and its practical realization. Central to our contribution is OSReM (Oblivious Shift Register Memory), a novel memory architecture that circumvents the linear complexity of standard FHE-RAM writes. By treating memory as a shift register, OSReM enables low-latency, constant-time writes without the need for expensive full-memory bootstrapping. HEGIDE leverages a MIMD (Multiple Instruction, Multiple Data) design, utilizing CKKS packing to evaluate distinct program threads in parallel, thus maximizing throughput. While the processor architecture natively supports arbitrary word sizes and instructions, we provide a compiler that manages memory scheduling to abstract the complexity of the shift-register design. We provide a proof-of-concept full implementation of HEGIDE using the OpenFHE library. Experimental results demonstrate the efficiency of our approach, achieving an amortized cycle time of just 7 ms for a 16-bit processor - two orders of magnitude faster in throughput than comparable approaches - offering a viable path for the secure execution of proprietary algorithms on encrypted data.

Fully Homomorphic Encryption (FHE) enables computation over encrypted data and is considered a fundamental tool for privacy-preserving systems. Despite significant theoretical progress, its practical adoption remains limited. One contributing factor is the absence of reusable, application-level components suitable for integration into real-world systems. This work introduces a library of FHE components developed through a competition-based framework. The components are outcomes of a series of formalized challenges published on the FHERMA platform, each targeting a specific challenge—such as comparison, sorting, or matrix operations—under concrete cryptographic and performance constraints. This initial release includes contributions from independent researchers and reflects a variety of approaches across different FHE schemes. The library is intended to expand over time as new challenges are introduced and solved, forming a foundation for building and evaluating privacy-preserving applications.

The Cheon-Kim-Kim-Song (CKKS) scheme is a fully homomorphic encryption scheme that traditionally supports only the evaluation of smooth functions. Recent works have enabled the evaluation of arbitrary (discontinuous) integer functions represented as lookup tables (LUT) on small inputs using the method of functional bootstrapping (FBT). Although well-suited for small integers (up to around 10 bits), the efficiency of FBT quickly declines for large LUTs, and a considerable increase in both runtime and memory requirements is observed. Building on CKKS functional bootstrapping, we propose in this paper two functional bootstrapping algorithms, specifically designed to target larger LUTs (up to 20 bits). For a 16-bit LUT, our implementation in OpenFHE achieves a speed-up of 47.5 in amortized time and 95.1 in latency for single-threaded execution, compared to the state-of-the-art CKKS-based functional bootstrapping method of Alexandru et al. (CRYPTO'25).