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Algebraic properties of polar codes from a new polynomial formalism
TLDR
We show that there is a way to define a nontrivial (partial) order onmonomials so that the monomials generating a polar code devised for a binary-input symmetric channel always form a decreasing set. Expand
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On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations
We extend the notion of regular sequence ([Mac16]) to overdetermined system of algebraic equations. We study generic properties of Grobner bases and analyse precisely the behavior of the F5 [Fau02]Expand
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On the complexity of solving quadratic Boolean systems
TLDR
We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. Expand
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On the complexity of the F5 Gröbner basis algorithm
TLDR
We study the complexity of Grobner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. Expand
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Complexity of Gröbner basis computation for Semi-regular Overdetermined sequences over F_2 with solutions in F_2
We present complexity results for solving "typical"overdetermined algebraic systems over GF(2) with solutions in GF(2) using Grobner bases. They are useful for instance to predictthe complexity of anExpand
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Asymptotic Behaviour of the Degree of Regularity of Semi-Regular Polynomial Systems
We compute the asymptotic expansion of the degree of regularity for overdetermined semi-regular sequences of algebraic equations. This degree implies bounds for the generic complexity of GröbnerExpand
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Weak Keys for the Quasi-Cyclic MDPC Public Key Encryption Scheme
TLDR
We analyze a new key recovery attack against the Quasi-Cyclic MDPC McEliece scheme and give under certain hypothesis an algorithm that is able to solve a key equation relating the public key to the private key. Expand
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BIG QUAKE BInary Goppa QUAsi–cyclic Key Encapsulation
TLDR
The present proposal is a key encapsulation scheme based on a Niederreiter–like public key encryption scheme using binary quasi–cyclic Goppa codes. Expand
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Cryptanalysis of the McEliece Public Key Cryptosystem Based on Polar Codes
TLDR
Polar codes discovered by Arikan form a very powerful family of codes attaining many information theoretic limits in the fields of error correction and source coding. Expand
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An Algebraic Attack on Rank Metric Code-Based Cryptosystems
TLDR
In this paper, starting from Ourivski and Johansson's algebraic modelling of the problem into a system of polynomial equations, we show how to augment this system with easily computed equations so that the augmented system is solved much faster via Groebner bases. Expand
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