Reversible Logic Synthesis Benchmarks Page

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you are in... Main\gf2^32mult

Function gf2^32mult finds product of two elements, a and b, of a field GF(2³²)=GF(4,294,967,296). The output, c=ab, is written onto the last 32 bits. Inputs a and b must remain unchanged.

Primitive polynomial	Picture	Machine-readable version	Library	Garbage	Gate count	Quantum cost	Author(s)	Date
x^32+x^7+x^5+x^3+x^2+x+1*	N/A (too large)	here	NCT	64	1,179	5,275	D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan	May, 2014
x^32+x^9+x^3+x^2+1*	N/A (too large)	here	NCT	64	1,117	5,213	D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan	May, 2014

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^m - the number is shown to be minimal

* - Shane Kepley and Prof. Rainer Steinwandt of Florida Atlantic University found an error: the irreducible polynomial as posted originally read x³²+x⁷+x⁵+x³+x+1, whereas the correct irreducible polynomial should have read x³²+x⁷+x⁵+x³+x²+x+1. This page was updated on May 12, 2014 to correct the error. The new circuit file was uploaded, the old circuit file is available here. Also, a new primitive polynomial, x³²+x⁹+x³+x²+1, has been suggested, and a circuit implementation corresponding to it has been added.