Reversible Logic Synthesis Benchmarks Page

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you are in... Main\gf2^163mult

Function gf2^163mult finds product of two elements, a and b, of a field GF(2¹⁶³). The output, c=ab, is written onto the last 163 bits. Inputs a and b must remain unchanged. Solving Discrete Logarithm over Elliptic Curve Group over GF(2¹⁶³) by a quantum computer with a Shor-like attack requires implementing gf2^163mult. A successful attack unlocks a Level-II unsolved Certicom challenge.

Primitive polynomial	Picture	Machine-readable version	Model	Garbage	Gate count	Quantum cost	Author(s)	Date
x^163+x^7+x^6+ x^3+1	N/A (too large)	here	CNT	326	27,055	133,331	D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan	January, 2018

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^m - the number is shown to be minimal