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Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
NSA Solving Multivariate Quadratic Equations
2017/12/25
In August 2015 the cryptographic world was shaken by a sudden and surprising announcement by the US National Security Agency (NSA) concerning plans to transition to post-quantum algorithms. Since this...
Asymptotically faster quantum algorithms to solve multivariate quadratic equations
FXL Grover reversibility
2017/12/19
Asymptotically faster quantum algorithms to solve multivariate quadratic equations.
Solving Quadratic Equations with XL on Parallel Architectures - extended version
block Wiedemann sparse solver multivariate quadratic systems
2016/5/3
Solving a system of multivariate quadratic equations (MQ) is an NP-complete problem whose complexity estimates are relevant to many cryptographic scenarios. In some cases it is required in the best kn...
Algorithms to solve massively under-defined systems of multivariate quadratic equations
under-defined multivariate quadratic equations oil and vinegar signature scheme
2009/6/12
It is well known that the problem to solve a set of randomly chosen multivariate
quadratic equations over a finite field is NP-hard. However, when the number of
variables is much larger than the num...
Taxonomy of Public Key Schemes based on the problem of Multivariate Quadratic equations
Public Key Schemes Multivariate Quadratic equations
2009/1/20
Multivariate quadratic systems can be used to construct both secure and effi-
cient public key schemes. In this article, we introduce the necessary mathematical
tools to deal with multivariate quadr...
Another Look at Square Roots and Traces (and Quadratic Equations) in Fields of Even Characteristic
Binary fields Polynomial basis Square root extraction
2008/9/8
We discuss irreducible polynomials that can be used to speed
up square root extraction in fields of characteristic two. We call such
polynomials square root friendly. The obvious applications are to...
