Results 41 to 50 of about 4,610 (199)

Lines in supersingular quartics

, 2021
We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3.
Degtyarev, Alex
core   +1 more source

Multilevel Identification Friend or Foe of Objects and Analysis of the Applicability of Post-Quantum Cryptographic Algorithms for Information Security

Кібернетика та комп'ютерні технології, 2020
Introduction. Widespread use of unmanned aerial vehicles in the civilian and military spheres requires the development of new algorithms for identification friend or foe of targets, as used in the Armed Forces of Ukraine (AFU) devices of the "Parol ...
V. Korolyov, M. Ogurtsov, A. Khodzinsky
doaj   +1 more source

Distortion maps for supersingular genus two curves

Journal of Mathematical Cryptology, 2009
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g.
Galbraith Steven D., Pujolàs Jordi, Ritzenthaler Christophe, Smith Benjamin   +3 more
doaj   +1 more source

CODIMENSION TWO CYCLES IN IWASAWA THEORY AND ELLIPTIC CURVES WITH SUPERSINGULAR REDUCTION

Forum of Mathematics, Sigma, 2019
A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between analytic objects (a ...
ANTONIO LEI, BHARATHWAJ PALVANNAN
doaj   +1 more source

On the Search for Supersingular Elliptic Curves and Their Applications

Mathematics
Elliptic curves with the special quality known as supersingularity have gained much popularity in the rapidly developing field of cryptography. The conventional method of employing random search is quite ineffective in finding these curves.
Ismel Martinez-Diaz, Rashad Ali, Muhammad Kamran Jamil   +2 more
doaj   +1 more source

Equidistribution of Hecke points on the supersingular module

, 2012
For a fixed prime p, we consider the (finite) set of supersingular elliptic curves over $\bar{\mathbb{F}}$. Hecke operators act on this set. We compute the asymptotic frequence with which a given supersingular elliptic curve visits another under this ...
Menares, Ricardo
core   +1 more source

Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

Journal of Mathematical Cryptology, 2014
We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases
De Feo Luca, Jao David, Plût Jérôme
doaj   +1 more source

Rank parity for congruent supersingular elliptic curves [PDF]

Proceedings of the American Mathematical Society, 2017
A recent paper of Shekhar compares the ranks of elliptic curves E 1 E_1 and E 2 E_2 for which there is an isomorphism E 1 [ p ] ≃ E 2 [ p ] E_1[p] \simeq E_2[p]
openaire   +3 more sources

Computational problems in supersingular elliptic curve isogenies

Quantum Information Processing, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Galbraith, Steven D., Vercauteren, Frederik   +1 more
openaire   +3 more sources

Optimization of isogeny computation algorithms for post-quantum cryptography

Scientific African
Isogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves.
Mohammed El Baraka, Siham Ezzouak
doaj   +1 more source