On the first fall degree of summation polynomials-Reference-Cited by-同舟云学术

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On the first fall degree of summation polynomials

Published:2019-10-01 Issue:3-4 Volume:13 Page:229-237
ISSN:1862-2976
Container-title:Journal of Mathematical Cryptology
language:
Short-container-title:

Author:

Kousidis Stavros^ORCID,Wiemers Andreas

Abstract

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Computer Science Applications

Link

https://www.degruyter.com/document/doi/10.1515/jmc-2017-0022/pdf

Reference28 articles.

1. Inverting HFE systems is quasi-polynomial for all fields;Advances in Cryptology—CRYPTO 2011,2011

2. Last fall degree, HFE, and Weil descent attacks on ECDLP;Advances in Cryptology—CRYPTO 2015

3. Summation polynomials and the discrete logarithm problem on elliptic curves;Preprint,2004

4. Notes on summation polynomials;Preprint,2015

5. Inverting HFE is quasipolynomial;Advances in Cryptology—CRYPTO,2006

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