Fast RNS division algorithms for fixed divisors with application to RSA encryption

Residue number systems (RNS) present the advantage of fast addition and multiplication over other number systems. However, the problem of division by fixed divisors in RNS must be considered. Consequently, 2 division algorithms for fixed divisors that achieve time complexity of O(n) are presented. The first algorithm is based on the well-known division method of multiplying by the divisor reciprocal. The 2nd algorithm is based on the Chinese Remainder Theorem (CRT) decoding and table lookup and requires that the divisor D be relatively prime to all moduli. The latter requires more storage but is faster. Furthermore, the 2nd algorithm leads to an efficient RSA implementation, with 4m/b steps per modular multiplication.