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ALGORITHMS IN LATTICE-BASED CRYPTANALYSIS

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Date Issued:
2020
Abstract/Description:
An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision.
Title: ALGORITHMS IN LATTICE-BASED CRYPTANALYSIS.
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Name(s): Miller, Shaun , author
Bai, Shi , Thesis advisor
Florida Atlantic University, Degree grantor
Department of Mathematical Sciences
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2020
Date Issued: 2020
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: online resource
Extent: 79 p.
Language(s): English
Abstract/Description: An adversary armed with a quantum computer has algorithms[66, 33, 34] at their disposal, which are capable of breaking our current methods of encryption. Even with the birth of post-quantum cryptography[52, 62, 61], some of best cryptanalytic algorithms are still quantum [45, 8]. This thesis contains several experiments on the efficacy of lattice reduction algorithms, BKZ and LLL. In particular, the difficulty of solving Learning With Errors is assessed by reducing the problem to an instance of the Unique Shortest Vector Problem. The results are used to predict the behavior these algorithms may have on actual cryptographic schemes with security based on hard lattice problems. Lattice reduction algorithms require several floating-point operations including multiplication. In this thesis, I consider the resource requirements of a quantum circuit designed to simulate floating-point multiplication with high precision.
Identifier: FA00013543 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2020.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Cryptanalysis
Cryptography
Algorithms
Lattices
Quantum computing
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013543
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.