Supersingular Isogenies in cryptography
Event details
| Date | 03.09.2019 |
| Hour | 13:00 › 15:00 |
| Speaker | Khashayar Barooti |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam
Exam president: Prof. Arjen Lenstra
Thesis advisor: Prof. Serge Vaudenay
Co-examiner: Prof. Michael Kapralov
Abstract
As classical problems such as factorization, and discrete logarithm are falling short with the threat of quantum computers, some new hard problems are attracting more interest in the cryptographic community. One of these problems is computing isogenies between two supersingular elliptic curves. Supersingular curves have some interesting properties which make them useful for various cryptographic constructions, such as hash functions, signature schemes and key exchange protocols. In this report, we provide some theoretical background on this subject, introduce some schemes based on the hardness of isogeny computation, and finally discuss the difference in the supersingular case and the ordinary curve case.
Background papers
Constructing elliptic curve isogenies in quantum subexponential time, by Andrew M. Childs, David Jao, Vladimir Soukharev.
Cryptographic Hash Functions from Expander Graphs, by Denis X. CharlesKristin E. Lauter, Eyal Z. Goren.
Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies, by David JaoLuca De Feo.
Exam president: Prof. Arjen Lenstra
Thesis advisor: Prof. Serge Vaudenay
Co-examiner: Prof. Michael Kapralov
Abstract
As classical problems such as factorization, and discrete logarithm are falling short with the threat of quantum computers, some new hard problems are attracting more interest in the cryptographic community. One of these problems is computing isogenies between two supersingular elliptic curves. Supersingular curves have some interesting properties which make them useful for various cryptographic constructions, such as hash functions, signature schemes and key exchange protocols. In this report, we provide some theoretical background on this subject, introduce some schemes based on the hardness of isogeny computation, and finally discuss the difference in the supersingular case and the ordinary curve case.
Background papers
Constructing elliptic curve isogenies in quantum subexponential time, by Andrew M. Childs, David Jao, Vladimir Soukharev.
Cryptographic Hash Functions from Expander Graphs, by Denis X. CharlesKristin E. Lauter, Eyal Z. Goren.
Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies, by David JaoLuca De Feo.
Practical information
- General public
- Free