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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.
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...
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...
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...
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...

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