منابع مشابه
On Border Basis and Gröbner Basis Schemes
Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing zero-dimensional ideals when the coefficients are inexact. And in this situation they show a clear advantage with respect to Gröbner bases which, neverthele...
متن کاملComplexity of Gröbner basis detection and border basis detection
Gröbner basis detection (GBD) is defined as follows: given a set of polynomials, decide whether there exists and if “yes” find a term order such that the set of polynomials is a Gröbner basis. This problem was proposed by Gritzmann and Sturmfels (1993) and it was shown to be NP-hard by Sturmfels and Wiegelmann. We investigate the computational complexity of this problem when the given set of po...
متن کاملComparison Between XL and Gröbner Basis Algorithms
This paper compares the XL algorithm with known Gröbner basis algorithms. We show that to solve a system of algebraic equations via the XL algorithm is equivalent to calculate the reduced Gröbner basis of the ideal associated with the system. Moreover we show that the XL algorithm is also a Gröbner basis algorithm which can be represented as a redundant variant of a Gröbner basis algorithm F4. ...
متن کاملBlock Ciphers Sensitive to Gröbner Basis Attacks
We construct and analyze Feistel and SPN ciphers that have a sound design strategy against linear and differential attacks but for which the encryption process can be described by very simple polynomial equations. For a block and key size of 128 bits, we present ciphers for which practical Gröbner basis attacks can recover the full cipher key requiring only a minimal number of plaintext/ciphert...
متن کاملGröbner Basis Based Cryptanalysis of SHA-1
Recently, Wang proposed a new method to cryptanalyze SHA-1 and found collisions of 58-round SHA-1. However many details of Wang’s attack are still unpublished, especially, 1) How to find differential paths? 2) How to modify messages properly? For the first issue, some results have already been reported. In our article, we clarify the second issue and give a sophisticated method based on Gröbner...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Collectanea mathematica
سال: 2009
ISSN: 0010-0757
DOI: 10.1007/bf03191213