Date of Award
2020
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Bai, Shi
Abstract
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.
Extent
79 p.
Recommended Citation
Miller, Shaun, "ALGORITHMS IN LATTICE-BASED CRYPTANALYSIS" (2020). Electronic Theses and Dissertations 2020 - Present. 457.
https://digitalcommons.fau.edu/etd_general/457
Identifier
FA00013543
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2020.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.