Results 51 to 60 of about 3,064 (192)
Efficient Commutative PQC Algorithms on Isogenies of Edwards Curves
CryptographyThe article presents the author’s works in the field of modifications and modeling of the Post-Quantum Cryptography (PQC) Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm on non-cyclic supersingular Edwards curves and its predecessor ...
Anatoly Bessalov +2 more
doaj +1 more source
Constructing elliptic curve isogenies in quantum subexponential time
Journal of Mathematical Cryptology, 2014 Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew +2 more
doaj +1 more source
Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
wiley +1 more source
An atlas of the Richelot isogeny graph
, 2022 International audienceWe describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny graph of principally polarized abelian surfaces, considering the action of automorphisms.
Florit, Enric, Smith, Benjamin
core +4 more sources
Highly Vectorized SIKE for AVX-512
Transactions on Cryptographic Hardware and Embedded Systems, 2022 It is generally accepted that a large-scale quantum computer would be capable to break any public-key cryptosystem used today, thereby posing a serious threat to the security of the Internet’s public-key infrastructure.
Hao Cheng +3 more
doaj +1 more source
Dual Isogenies and Their Application to Public-Key Compression for Isogeny-Based Cryptography
, 2019 The isogeny-based protocols SIDH and SIKE have received much attention for being post-quantum key agreement candidates that retain relatively small keys. A recent line of work has proposed and further improved compression of public keys, leading to the inclusion of public-key compression in the SIKE proposal for Round 2 of the NIST Post-Quantum ...
Naehrig, M., Renes, J.
openaire +3 more sources
Wild conductor exponents of curves
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We give an explicit formula for wild conductor exponents of plane curves over Qp$\mathbb {Q}_p$ in terms of standard invariants of explicit extensions of Qp$\mathbb {Q}_p$, generalising a formula for hyperelliptic curves. To do so, we prove a general result relating the wild conductor exponent of a simply branched cover of the projective line ...
Harry Spencer
wiley +1 more source
Pairing Optimizations for Isogeny-Based Cryptosystems
IET Information SecurityIn isogeny-based cryptography, bilinear pairings are regarded as a powerful tool in various applications, including key compression, public key validation, and torsion basis generation. However, in most isogeny-based protocols, the performance of pairing
Shiping Cai, Kaizhan Lin, Chang-An Zhao
doaj +1 more source
Transactions on Cryptographic Hardware and Embedded Systems, 2018 We present high-speed implementations of the post-quantum supersingular isogeny Diffie-Hellman key exchange (SIDH) and the supersingular isogeny key encapsulation (SIKE) protocols for 32-bit ARMv7-A processors with NEON support.
Hwajeong Seo +3 more
doaj +1 more source
On the Security of Supersingular Isogeny Cryptosystems [PDF]
, 2016 We study cryptosystems based on supersingular isogenies. This is an active area of research in post-quantum cryptography. Our first contribution is to give a very powerful active attack on the supersingular isogeny encryption scheme. This attack can only be prevented by using a (relatively expensive) countermeasure.
Steven D. Galbraith +3 more
openaire +4 more sources