Reversible Logic Synthesis Benchmarks Page

Function gf2^127mult finds product of two elements, a and b, of a field GF(2¹²⁷). The output, c=ab, is written onto the last 127 bits. Inputs a and b must remain unchanged.
 

Primitive polynomial	Picture	Machine-readable version	Model	Garbage	Gate count	Quantum cost	Author(s)	Date
x127+x+1	N/A (too large)	here	CNT	254	16,255	80,771	D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan	July, 2010

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^m - the number is shown to be minimal