Generating Very Large RNS Bases

Residue Number Systems (RNS) are proven to be effective in speeding up computations involving additions and products. For these representations, there exists efficient modular reduction algorithms that can used the context of arithmetic over finite fields or modulo large numbers, especially when cryptographic engineering. Their independence allows random draws bases, which also makes it possible protect against side-channel attacks, even detect them using redundancy. These systems easily scalable, however existence bases for some specific uses remains a difficult question. In this article, we present four techniques extract RNS from sets integers, giving better performance flexibility previous works litterature. While our do not allow solve efficiently every case, provide provably find largest available several cases, improving state-of-the-art on various recent literature.