Related papers: Pairings on hyperelliptic curves
Pairing-based cryptographic schemes require so-called pairing-friendly elliptic curves, which have special properties. The set of pairing-friendly elliptic curves that are generated by given polynomials form a complete family. Although a…
In this study, we introduce a new approach to curve pairs by using integral curves. We consider the direction curve and donor curve to study curve couples such as involute-evolute curves, Mannheim partner curves and Bertrand partner curves.…
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
The development of secure cryptographic protocols and the subsequent attack mechanisms have been placed in the literature with the utmost curiosity. While sophisticated quantum attacks bring a concern to the classical cryptographic…
An algorithm is given to compute a normal form for hyperelliptic curves. The elliptic case has been treated in a previous paper. In this paper the hyperelliptic case is treated.
We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function.
We present e cient algorithms for computing isogenies between hyperelliptic curves, leveraging higher genus curves to enhance cryptographic protocols in the post-quantum context. Our algorithms reduce the computational complexity of isogeny…
We introduce the notion of isolated genus two curves. As there is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap, the discrete log problem (DLP) cannot be efficiently…
The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Cryptography (ECC). In this paper, we present an attack to the…
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
Computing endomorphism rings of supersingular elliptic curves is an important problem in computational number theory, and it is also closely connected to the security of some of the recently proposed isogeny-based cryptosystems. In this…
We give a method to construct deep holes for elliptic curve codes. For long elliptic curve codes, we conjecture that our construction is complete in the sense that it gives all deep holes. Some evidence and heuristics on the completeness…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…
The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
In the study of hyperelliptic curve cryptography, presentations of semi-reduced divisors on a hyperelliptic curve play important roles. In this note, we give an interpretation for such presentations from view points of Gr\"obner bases. As…
We give several algorithms addressing computations of intersections of conjugate subgroups.
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
Recently, Edwards curves have received a lot of attention in the cryptographic community due to their fast scalar multiplication algorithms. Then, many works on the application of these curves to pairing-based cryptography have been…