Real-Valued Somewhat-Pseudorandom Unitaries

Zvika Brakerski, Nir Magrafta

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

Abstract

We explore a very simple distribution of unitaries: random (binary) phase—Hadamard—random (binary) phase—random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar unitaries for any polynomial set of orthogonal input states (in any basis) with polynomial multiplicity. This shows that even though real-valued unitaries cannot be completely pseudorandom (Haug, Bharti, Koh, arXiv:2306.11677), we can still obtain some pseudorandom properties without giving up on the simplicity of a real-valued unitary. Our analysis shows that an even simpler construction: applying a random (binary) phase followed by a random computational-basis permutation, would suffice, assuming that the input is orthogonal and flat (that is, has high min-entropy when measured in the computational basis). Using quantum-secure one-way functions (which imply quantum-secure pseudorandom functions and permutations), we obtain an efficient cryptographic instantiation of the above.

Original languageEnglish
Title of host publicationTheory of Cryptography - 22nd International Conference, TCC 2024, Proceedings
EditorsElette Boyle, Mohammad Mahmoody
PublisherSpringer Science and Business Media B.V.
Pages36-59
Number of pages24
ISBN (Print)9783031780165
DOIs
StatePublished - 2025
Event22nd Theory of Cryptography Conference, TCC 2024 - Milan, Italy
Duration: 2 Dec 20246 Dec 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume15365 LNCS
ISSN (Print)0302-9743

Conference

Conference22nd Theory of Cryptography Conference, TCC 2024
Country/TerritoryItaly
CityMilan
Period2/12/246/12/24

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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