A ROM-less reverse RNS converter for moduli set {2q ?? 1, 2q ?? 3}

Numerous contributions on reverse conversion methods based on the Chinese Remainder Theorem (CRT), for residue number systems (RNS), have been regularly appearing in relevant literature. Reverse conversion is known as a slow RNS operation that becomes more complicated and slower for larger moduli sets. In this study, the authors examine four previous reverse converters for moduli set F = {2^q - 1, 2^q + 3, 2^q + 1, 2^q - 3}. Three of these converters heavily utilise Read Only Memories (ROM), and the other one uses a Montgomery multiplier. In order to cut the costs and improve performance, the authors propose an adder-only two-stage New CRT conversion scheme that uses conjugate grouping of the moduli as {{2^q± 1, 2^q± 3}}. Also, manipulation of multiplicative inverse coefficients that are expressed as a series of power-of-two terms takes place via multi-operand addition instead of using ROMs and/or multipliers. This leads to roughly 22, 19 and 8% improvement in delay, area consumption and power dissipation, respectively, in comparison to the only previous ROM-less design for F. Moreover, use of no ROMs allows for pipelining, if desired. They also address four state-of-the-art converters and compare their performance with the authors (i.e. that of F), where none is faster than the proposed converter. They support their claims with analytical gate-level comparisons and via synthesis results.