Reversible Logic Synthesis Benchmarks Page

Function gf2^7mult finds product of two elements of a field GF(2⁷), a=a₀+a₁x+a₂x²+a₃x³+a₄x⁴+a₅x⁵+a₆x⁶ and b=b₀+b₁x+b₂x²+b₃x³+b₄x⁴+b₅x⁵+b₆x⁶ with the output, ab=c=c₀+c₁x+c₂x²+c₃x³+c₄x⁴+c₅x⁵+c₆x⁶ written on the last 7 bits. Inputs a and b must remain unchanged.
 

Primitive polynomial	Picture	Machine-readable version	Model	Garbage	Gate count	Quantum cost	Author(s)	Date
x7+x+1	here	here	CNT	14	55	251	D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan	July, 2010

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^m - the number is shown to be minimal