Fast sign‐detection algorithm for residue number system moduli set {2 ⁿ − 1, 2 ⁿ , 2 ^{n +1} − 1}

Abstract

Sign detection is an essential part of many computer hardware designs, and is not a trivial task in residue number systems because it is a function of all the residues. This study proposes an algorithm for the residue number system with a three-moduli set {2 n − 1, 2 n , 2 n+1 − 1} using New Chinese Remainder Theorem II. The unit is built with one n-bit carry-save adder and a 2n-bit parallel prefix carry-generation unit. In the best case the Synoposys 90 nm synthesis result shows a 24% reduction in the area-delay product than existing algorithms for the same moduli set.

High‐throughput multi‐key elliptic curve cryptosystem based on residue number system

“…Thus addition, subtraction, and multiplication can be concurrently performed on the N residues within N parallel channels, and it is this high‐speed parallel operation that makes the RNS attractive. The drawback of the RNS is its low performance for some arithmetic operations such as magnitude comparison and modular reduction [23].…”

Efficient programmable power‐of‐two scaler for the three‐moduli set {2 n + p , 2 n − 1, 2 n +1 − 1}

“…The latter presented 2 n and 2 n+p scalers for the augmented moduli set {2 n − 1, 2 n+p , 2 n + 1} with efficient hardware structures. Another class of moduli sets in the form of {2 a , 2 b − 1, 2 c − 1} with c = b − 1 or c = b + 1 has also attracted the attention of researchers due to its efficient and modulo-(2 n + 1)-free internal arithmetic operations [21][22][23][24][25][26][27][28]. Based on the impressive theoretical properties of this type of moduli set, different algorithms and hardware implementations for a variety of RNS operations have been proposed in the literature.…”

“…In the search for an efficient hardware implementation of the reverse converter, several contributions have been proposed for the moduli sets [24], and {2 2n , 2 n − 1, 2 n±1 − 1} [25]. For {2 n , 2 n − 1, 2 n+1 − 1}, efficient sign detectors have also been proposed in [26] and [27]. Recently, a remarkable effort resulted in the efficient hardware implementation of a sign-magnitude comparator for the moduli set {2 n , 2 n − 1, 2 n+1 − 1} [28].…”

New algorithms for hardware-efficient implementation of sign detection and magnitude comparison in residue number systems

“…In [Xu15] and [Nir15], two recent sign detection techniques based on different approaches were proposed for the three moduli set {2 n+1 −1, 2 n , 2 n −1}. In [Xu15], the algorithm was developed with the help of new formulation of CRT (modified CRT).…”

“…Its sign detection circuit consists of a carry save adder (CSA), a comparator and a carry propagation unit. However, this method can only be applied to moduli sets that include 2 n as a modulus as it involves floor function unit in the algorithm while the sign detection algorithm [Nir15] was formulated by employing the New CRT-II. Its architecture can be implemented with the help of one n-bit carry save adder (CSA) and one 2n-bit parallel prefix carry generation unit.…”