Fast base extension and precise scaling in RNS for look-up table implementations

Both base extension and scaling are fundamental operations in residue computing and several techniques have been proposed previously for their efficient implementation. Using look-up tables, the best result (log₂ n table took-up cycles, where n is the number of residue moduli in the system) has been obtained by using the Chinese remainder theorem (CRT) at the expenses of a redundant representation of the numbers and of an approximated scaling. The CRT approach is reconsidered and it is shown that the same average time performances (log₂ n lookup cycles) can be achieved without any redundancy and with a precise result for scaling