Encrypted Matrix Inversion with Concrete

During the third season of the Zama Bounty Program, an encrypted matrix inversion algorithm was successfully developed by Github user LCressot, focusing on the mathematical operation crucial for tasks such as numerical optimization, solving systems of equations, learning regression models, and principal-component analysis. This implementation introduced a fixed-point class, QFloat, to replace floating-point computations and optimized algorithms for both 2x2 matrices and larger matrices using LU decomposition. The QFloat class allows for precise operations by representing numbers as arrays of integers, facilitating various arithmetic operations and comparisons. For larger matrices, LU decomposition was utilized to break down matrices into lower and upper triangular matrices, enhancing computational efficiency and accuracy. Additionally, Full Homomorphic Encryption (FHE) optimizations were applied to improve performance, allowing parallel computations and precomputed inverse values for division, albeit at the cost of some precision. The development showcases a compilation-heavy use case, highlighting the potential for further enhancements in the compilation process and fixed-point number handling in future bounty programs.