Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
We present new candidates for quantum-resistant public-key cryptosystems based on the
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
We present new candidates for quantum-resistant public-key cryptosystems based on the
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …
Mathematics of isogeny based cryptography
L De Feo - arXiv preprint arXiv:1711.04062, 2017 - arxiv.org
These lectures notes were written for a summer school on Mathematics for post-quantum
cryptography in Thi\es, Senegal. They try to provide a guide for Masters' students to get …
cryptography in Thi\es, Senegal. They try to provide a guide for Masters' students to get …
On the quaternion-isogeny path problem
Let-power norm. In practice the algorithm is efficient and, subject to heuristics on expected
distributions of primes, runs in expected polynomial time. This solves the underlying problem …
distributions of primes, runs in expected polynomial time. This solves the underlying problem …
Hidden stabilizers, the isogeny to endomorphism ring problem and the cryptanalysis of pSIDH
Abstract The Isogeny to Endomorphism Ring Problem (IsERP) asks to compute the
endomorphism ring of the codomain of an isogeny between supersingular curves in …
endomorphism ring of the codomain of an isogeny between supersingular curves in …
Ramanujan graphs in cryptography
A Costache, B Feigon, K Lauter, M Massierer… - Research Directions in …, 2019 - Springer
In this paper we study the security of a proposal for Post-Quantum Cryptography from both a
number theoretic and cryptographic perspective. Charles–Goren–Lauter in 2006 proposed …
number theoretic and cryptographic perspective. Charles–Goren–Lauter in 2006 proposed …
Super-golden-gates for PU (2)
O Parzanchevski, P Sarnak - Advances in Mathematics, 2018 - Elsevier
To each of the symmetry groups of the Platonic solids we adjoin a carefully designed
involution yielding topological generators of PU (2) which have optimal covering properties …
involution yielding topological generators of PU (2) which have optimal covering properties …
Applications of Finite non-Abelian Simple Groups to Cryptography in the Quantum Era
MIG Vasco, D Kahrobaei, E McKemmie - La Matematica, 2024 - Springer
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting
computational problems and modeling tools useful in a cryptographic context. In this note …
computational problems and modeling tools useful in a cryptographic context. In this note …
Shorter quantum circuits via single-qubit gate approximation
We give a novel procedure for approximating general single-qubit unitaries from a finite
universal gate set by reducing the problem to a novel magnitude approximation problem …
universal gate set by reducing the problem to a novel magnitude approximation problem …
New constructions of collapsing hashes
M Zhandry - Annual International Cryptology Conference, 2022 - Springer
Collapsing is a post-quantum strengthening of collision resistance, needed to lift many
classical results to the quantum setting. Unfortunately, the only existing standard-model …
classical results to the quantum setting. Unfortunately, the only existing standard-model …