Design of Quantum Circuits for Galois Field Squaring and Exponentiation

Edgard Muñoz-Coreas, Himanshu Thapliyal

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


This work presents an algorithm to generate depth, quantum gate and qubit optimized circuits for GF(2m) squaring in the polynomial basis. Further, to the best of our knowledge the proposed quantum squaring circuit algorithm is the only work that considers depth as a metric to be optimized. We compared circuits generated by our proposed algorithm against the state of the art and determine that they require 50% fewer qubits and offer gates savings that range from 37% to 68%. Further, existing quantum exponentiation are based on either modular or integer arithmetic. However, Galois arithmetic is a useful tool to design resource efficient quantum exponentiation circuit applicable in quantum cryptanalysis. Therefore, we present the quantum circuit implementation of Galois field exponentiation based on the proposed quantum Galois field squaring circuit. We calculated a qubit savings ranging between 44% to 50% and quantum gate savings ranging between 37% to 68% compared to identical quantum exponentiation circuit based on existing squaring circuits.

Original languageEnglish
Title of host publicationProceedings - 2017 IEEE Computer Society Annual Symposium on VLSI, ISVLSI 2017
EditorsRicardo Reis, Mircea Stan, Michael Huebner, Nikolaos Voros
Number of pages6
ISBN (Electronic)9781509067626
StatePublished - Jul 20 2017
Event2017 IEEE Computer Society Annual Symposium on VLSI, ISVLSI 2017 - Bochum, North Rhine-Westfalia, Germany
Duration: Jul 3 2017Jul 5 2017

Publication series

NameProceedings of IEEE Computer Society Annual Symposium on VLSI, ISVLSI
ISSN (Print)2159-3469
ISSN (Electronic)2159-3477


Conference2017 IEEE Computer Society Annual Symposium on VLSI, ISVLSI 2017
CityBochum, North Rhine-Westfalia

Bibliographical note

Publisher Copyright:
© 2017 IEEE.


  • Galois field arithmetic
  • quantum computing

ASJC Scopus subject areas

  • Hardware and Architecture
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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