Reversible Logic Synthesis Benchmarks Page


you are in... Main\gf2^131mult

Function gf2^131mult finds product of two elements, a and b, of a field GF(2131). The output, c=ab, is written onto the last 131 bits. Inputs a and b must remain unchanged.  Solving Discrete Logarithm over Elliptic Curve Group over GF(2131) by a quantum computer with a Shor-like attack requires implementing gf2^131mult.  A successful attack unlocks Level-I unsolved Certicom challenge.  
 

Primitive polynomial

Picture

Machine-readable version

Model

Garbage

Gate count

Quantum cost

Author(s)

Date

x131+x7+x6+ x5+ x4+x+1

N/A (too large)

here

CNT

262

17,811

86,455

D. Cheung, D. Maslov, J. Mathew, and D. K. Pradhan

January, 2018

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m - the number is shown to be minimal