The CKKS Fully Homomorphic Encryption (FHE) scheme enables approximate arithmetic on encrypted complex numbers for a desired precision. Most implementations use RNS with carefully chosen parameters to balance precision, efficiency, and security. However, a key limitation in RNS-CKKS is the rigid coupling between the scale factor, which determines numerical precision, and the modulus, which ensures security. Since these parameters serve distinct roles—one governing arithmetic correctness and the other defining cryptographic structure—this dependency imposes design constraints, such as a lack of suitable NTT primes and limited precision flexibility, ultimately leading to inefficiencies.

In today’s interconnected world, data has become a valuable asset, leading to a growing interest in protecting it through techniques such as privacy-preserving computation. Two well-known approaches are multi-party computation and homomorphic encryption with use cases such as privacy-preserving machine learning evaluating or training neural networks. For multi-party computation, one of the fundamental arithmetic operations is the secure multiplication in the malicious security model and by extension the multiplication of matrices which is expensive to compute in the malicious model. Transferring the problem of secure matrix multiplication to the homomorphic domain enables savings in communication complexity, reducing the main bottleneck.

Contemporary digital infrastructures and systems use and trust Public-Key Cryptography to exchange keys over insecure communication channels. With the development and progress in the research field of quantum computers, well established schemes like RSA and ECC are more and more threatened. The urgent demand to find and standardize new schemes – which are secure in a post-quantum world – was also realized by the National Institute of Standards and Technology which announced a Post-Quantum Cryptography Standardization Project in 2017. Recently, the round three candidates were announced and one of the alternate candidates is the Key Encapsulation Mechanism scheme BIKE. In this article, we investigate different strategies to efficiently implement the BIKE algorithm on Field-Programmable Gate Arrays (FPGAs). To this extend, we improve already existing polynomial multipliers, propose efficient strategies to realize polynomial inversions, and implement the Black-Gray-Flip decoder for the first time. Additionally, our implementation is designed to be scalable and generic with the BIKE specific parameters. All together, the fastest designs achieve latencies of 2.69 ms for the key generation, 0.1 ms for the encapsulation, and 1.89 ms for the decapsulation considering the lowest security level.