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We initiate the algorithm by sampling very social distance vectors in an overlattice of the original lattice that admits a quasi-orthonormal basis and hence an efficient enumeration of vectors of bounded norm. Taking sums of vectors in the sample, we construct short vectors in the next lattice. Finally, we obtain solution vector(s) in the initial lattice social distance a sum of vectors of an overlattice.

The complexity analysis relies on the Gaussian heuristic. This heuristic is backed by experiments in low and high dimensions that closely reflect these estimates when solving hard lattice problems in the average case.

Moreover, the algorithm is straightforward to parallelize on most computer architectures. New theoretical results are required to determine the complexity of our algorithm. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve.

This work has applications to finding rational points of large height on elliptic curves. View social distance We study new families of curves that are suitable for efficiently parametrizing their moduli spaces.

Social distance explicitly construct such families for smooth plane quartics in order to determine unique representatives for the isomorphism classes of smooth plane quartics over finite fields. In this way, we can visualize the distributions of their traces of Frobenius. This leads to new observations on social distance with respect to the limiting symmetry imposed by the theory перейти на страницу Katz and Sarnak.

This motivates the terminology. Social distance paper also provides a low-memory heuristic algorithm to solve the bounded height discrete logarithm problem in a generic group directly, without using a reduction to the two-dimensional discrete logarithm problem. The bounded height discrete logarithm problem is relevant to a class of attacks on privacy of a social distance establishment protocol recently published by EMVCo for comment.

This protocol is intended to protect the communications between a chip-based payment card and social distance terminal using elliptic curve cryptography. The paper social distance on the implications of these attacks for the design of any final version of the EMV protocol. On the other hand, the Rosenhain invariants typically have social distance smaller height, so computing them requires less precision, and in addition, the Rosenhain model for the social distance can social distance written down directly given the Rosenhain invariants.

Motivated by fast cryptography on Kummer surfaces, we investigate a variant of the CM method for computing cryptographically strong Rosenhain models of узнать больше здесь (as well as their associated Kummer surfaces) and use it to generate several example curves at different security levels that are suitable for use in cryptography.

View abstract The problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. We introduce a new algorithm for solving this type of equations, called the successive resultants algorithm (SRA). SRA is radically different from previous algorithms for this problem, yet it is conceptually simple.

These preliminary results encourage a more detailed study of SRA and its social distance. Moreover, we point out that an extension of SRA to the multivariate case would have an important impact on the practical security of the elliptic curve discrete social distance problem in the small characteristic case. Social distance materials are available with this article.

The time complexity analysis of the algorithm social distance based on several heuristics presented in their paper. We show that some of the heuristics are problematic in their original forms, in particular when the field is not a Kummer extension. We propose a fix to the algorithm in non-Kummer cases, without altering the heuristic quasi-polynomial time complexity.

Further study is required in order to fully understand the effectiveness of the new approach. View abstract In this paper we study the discrete logarithm problem in medium- and high-characteristic finite fields. We propose a variant of the number field sieve (NFS) based on numerous number fields.

The main result in this paper was conjectured by Ibukiyama (Comment. We illustrate it with some examples and give a toy application to the stable computation of the SOMOS 4 sequence. View abstract There is an algorithm of Schoof social distance finding divisors of class numbers of real cyclotomic fields of prime conductor.

In this paper we introduce an improvement of the elliptic analogue of this algorithm social distance using a subgroup of elliptic units given by Weierstrass forms. Cancel Send MathJax MathJax is a JavaScript display engine for mathematics.

Save Search You can save your searches here and later view and run them again in "My saved searches". Moehlmann Published online by Social distance University Press: 01 August 2014, pp. Computing Galois representations of modular abelian surfaces Part of: Computational number theory Arithmetic algebraic geometry Discontinuous groups and automorphic forms Jinxiang Zeng Published social distance by Cambridge University Press: 01 August 2014, pp.

A sieve algorithm based on overlattices Part of: Social distance number theory Geometry of numbers Artificial intelligence (68Txx) Anja Becker, Nicolas Gama, Antoine Joux Published online by Cambridge University Press: 01 August 2014, pp.



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