Paper 2017/1206

Asymptotically faster quantum algorithms to solve multivariate quadratic equations

Daniel J. Bernstein and Bo-Yin Yang

Abstract

This paper designs and analyzes a quantum algorithm to solve a system of m quadratic equations in n variables over a finite field Fq. In the case m=n and q=2, under standard assumptions, the algorithm takes time 2(t+o(1))n on a mesh-connected computer of area 2(a+o(1))n, where t0.45743 and a0.01467. The area-time product has asymptotic exponent t+a0.47210. For comparison, the area-time product of Grover's algorithm has asymptotic exponent 0.50000. Parallelizing Grover's algorithm to reach asymptotic time exponent 0.45743 requires asymptotic area exponent 0.08514, much larger than 0.01467.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
FXLGroverreversibilityBennett--Tompaparallelizationasymptotics
Contact author(s)
authorcontact-groverxl @ box cr yp to
History
2017-12-18: received
Short URL
https://ia.cr/2017/1206
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/1206,
      author = {Daniel J.  Bernstein and Bo-Yin Yang},
      title = {Asymptotically faster quantum algorithms to solve multivariate quadratic equations},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/1206},
      year = {2017},
      url = {https://eprint.iacr.org/2017/1206}
}
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