Concrete Boolean and Conway’s Game of Life: A Tutorial

Optalysys explores the implementation of Conway's Game of Life using fully homomorphic encryption (FHE) with the Concrete library, developed by Zama, to demonstrate the potential of secure computation on encrypted data. FHE allows computations to be performed on encrypted data without needing decryption, offering significant security advantages, yet it is often complex to implement. Optalysys, although not specialists in cryptography, leveraged Concrete's user-friendly interface to execute complex FHE applications, such as the Game of Life, on their novel optical computing hardware. The Game of Life, a cellular automaton played on a grid with simple rules leading to complex behaviors, was successfully simulated entirely in encrypted space using Boolean operations. The article details the process of constructing Boolean algorithms for the simulation, including the development of an accumulator circuit to calculate cell states and the use of encrypted Boolean operations for updates, showcasing how Concrete-Boolean enables more accessible and efficient FHE applications.