Optimal modulus sets for efficient residue-to-binary conversion using the New Chinese Remainder Theorems

In this paper, specific modulus sets that offer efficient implementations of the New Chinese Remainder Theorems (CRT) are presented. Further, the resulting hardware is optimized for specific implementations. For n = 1,2,3,..., the utilized modulus sets are either the co-prime 4-modulus ones {2ⁿ⁺²+3, 2ⁿ⁺¹+1, 2ⁿ+1, 2} and {2, 2ⁿ+1, 2ⁿ⁺¹+1, 2ⁿ⁺²+3}, which can be used for the New CRT I and CRT II, or the non co-prime modulus set {2ⁿ⁺²+1, 2ⁿ⁺², 2ⁿ⁺¹+1, 2}, which can be used for the New CRT III. RNS implementations that use the special modulus sets eliminate the huge summations, inverse modulo operators, and dividers, while their further hardware optimization reduces the multiplication terms.