Efficient Algorithms for Sign Detection in RNS Using Approximate Reciprocals

The residue number system (RNS) is a method for representing an integer x as n-tuple of its residues with respect to given set moduli. In RNS, addition, subtraction, and multiplication can be carried out by independent operations each modulus. Therefore, n-fold speedup achieved parallel processing. main disadvantage RNS that we cannot efficiently compare the magnitude two integers or determine sign integer. Two general methods comparison are transform in mixed-radix radix representation using Chinese remainder theorem (CRT). We used CRT derive equation approximating value relative M, product Then, propose algorithms evaluate output bit. expected steps these order n. use lookup table (n+3) times large which reasonably small most applications including cryptography.