Author Type

Graduate Student

Date of Award

2024

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Bai, Shi

Thesis/Dissertation Co-Chair

Karabina, Koray

Abstract

Euclidean lattices have attracted considerable research interest as they can be used to construct efficient cryptographic schemes that are believed to be quantum-resistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important average-case computational problem in lattice-based cryptography. Following their pioneer work, the NTRU assumption and its variants have been used widely in modern cryptographic constructions such as encryption, signature, etc. Let Rq = Zq[x]/ (xn + 1) be a quotient polynomial ring. The standard NTRU problem asks to recover short polynomials f, g E Rq such that h - g/ f (mod q), given a public key h and the promise that such elements exist. In practice, the degree n is often a power of two. As a generalization of NTRU, the Module-NTRU problems were introduced by Cheon, Kim, Kim, and Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehle, Wallet, and Xagawa (ASIACCS '20). In this thesis, we presented two post-quantum Digital Signature Schemes based on the Module-NTRU problem and its variants.

Extent

87 P.

Comments

Includes bibliography.|Dissertation (PhD)--Florida Atlantic University, 2024.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00014407

Format

pdf

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