Ideal lattices in cryptography

• Thesis title in Czech: Ideálové mříže v kryptografii
• Thesis title in English: Ideal lattices in cryptography
• Key words: ideálová mriežka|cyklická mriežka|NTRU mriežka
• English key words: ideal lattice|cyclic lattice|NTRU lattice
• Academic year of topic announcement: 2020/2021
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Algebra (32-KA)
• Supervisor: doc. Mgr. Vítězslav Kala, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 19.03.2021
• Date of assignment: 19.03.2021
• Confirmed by Study dept. on: 07.04.2021
• Date and time of defence: 14.09.2021 09:00
• Date of electronic submission: 22.07.2021
• Date of submission of printed version: 22.07.2021
• Date of proceeded defence: 14.09.2021
• Opponents: doc. Mgr. Pavel Příhoda, Ph.D.
• Advisors: Pavlo Yatsyna, Ph.D.

Guidelines

One of the possible simplifying approaches to lattice-based cryptography is using ideal lattices. After briefly describing the basic ideas of lattice-based cryptography (e.g., from [MR]), the student will cover the basics of ideal lattices and the algorithm for deciding if a given lattice is ideal [DL]; she will give full details of the proofs and provide more examples. She will then extend these results to NTRU lattices [CS], [DL, Section 2.7]. The student may further potentially consider the application to efficient collision-resistant hash functions [MR, Section 4].

References

[CS] Don Coppersmith and Adi Shamir. Lattice attacks on NTRU. In Advances in cryptology—EUROCRYPT ’97 (Konstanz), volume 1233 of Lecture Notes in Comput. Sci., pages 52–61. Springer, Berlin, 1997.
[DL] Jintai Ding and Richard Lindner. Identifying ideal lattices. IACR Cryptol. ePrint Arch., 2007:322, 2007.
[MR] Daniele Micciancio and Oded Regev. Lattice-based cryptography. In Post- quantum cryptography, pages 147–191. Springer, Berlin, 2009.