Questions tagged [multivariate-cryptography]

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What are the security implications of knowing the private polynomial $\mathcal{F}$

First, affine transformations $S,T$ are defined by $S=A_1+v_s, T=A_2+v_t$. Let the private polynomial function $\mathcal{F}$ be known. The short description of the public key map is $P(X) = T \circ \...
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Help with cryptanalysis of branching in schemes based on Multivariate Public Key Cryptography

I'm familiarized with the structure of branching found in Multivariate Cryptography, as it allows us to partition a $n$-tuple over $F_{q}$ into a $k$-tuple where the $i$-th element is in $F_{q^{\...
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114 views

Multivariate cryptography - easily invertible quadratic map

I am reading through multivariate cryptography and in every source I have seen, the secret map $P$ is described as "easily invertible" or "easy to invert". What exactly does it mean "easily ...
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Why does solving the underlying polynomial system “break” the multivariate cryptosystem

I was wondering why exactly does solving a polynomial system (directly or indirectly) "break" a multivariate cryptosystem as a digital signature. I realize that the exact reason differs from system ...
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33 views

Dedekind sum is a product of sawtooth function [closed]

"The Dedekind sum is a product of a sawtooth function." This sentence does not make sense to me. A sawtooth is a kind of wave for sound generation. But in the realms of cryptography, the Dedekind sum ...
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Algorithms for solving systems of quadratic multivariate polynomials

What are the best algorithms for solving systems of $k$ polynomials equations where these are quadratic multivariate polynomials on $k$ variables? I've encountered such systems on my research and I'm ...
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129 views

Solving not so much overdetermined system of multivariate polynomial equations

I'm studying algorithms solving multivariate equations. I'm stuck in solving overdetermined set of quadratic equations. Concretely, with the number $n$ of variables, the number of equations is $m=\...
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1answer
111 views

Multivariate Cryptography: Security of the affine transform T

In this question, I'd like to discuss the security of the last transformation $T$ employed in the construction of a MV-scheme. MVCrypto is based on solving a system of polynomial equations, but ...
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Associative Multivariate Permutation

Popular multivariate schemes are constructed by having a several easy-to-invert functions/maps as parivate key, and their composition as the public key. When signing, the hash, or a padded form of ...