# Questions tagged [multivariate-cryptography]

A generic term for asymmetric cryptographic primitives based on multivariate polynomials over a finite field

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### Post-quantum secure trapdoor function

I am looking for examples post-quantum secure trapdoor functions. Ideally, the inversion knowing the trapdoor should be "simple" in the sense that it can be computed by a circuit in NC^1.
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### Is it possible to solve a linear polynomial in a finite field

Say that in $\mathbb{F}_{999,999,000,001}$ I have an equation $0 = ax - b$ where $a$ and $b$ are random values from the field. Is it possible to solve this equation for $x$ using the Extended ...
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### Question about Mesquite signature size?

I have a question regarding William Wang's paper Shorter Signatures from MQ. According to him the (maximum) signature size is:  2\kappa + 3\kappa\cdot \lceil\tau\log\frac{M}{\tau}\rceil + \tau\cdot\...
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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 $F_{q^{\... 3 votes 1 answer 230 views ### Multivariate cryptography - easily invertible quadratic map I am reading through multivariate cryptography and in every source I have seen, the secret map$P$is described as "easily invertible" or "easy to invert". What exactly does it mean "easily ... 2 votes 1 answer 122 views ### Why does solving the underlying polynomial system "break" the multivariate cryptosystem I was wondering why exactly does solving a polynomial system (directly or indirectly) "break" a multivariate cryptosystem as a digital signature. I realize that the exact reason differs from system ... 1 vote 0 answers 44 views ### Dedekind sum is a product of sawtooth function [closed] "The Dedekind sum is a product of a sawtooth function." This sentence does not make sense to me. A sawtooth is a kind of wave for sound generation. But in the realms of cryptography, the Dedekind sum ... 1 vote 0 answers 46 views ### Algorithms for solving systems of quadratic multivariate polynomials What are the best algorithms for solving systems of$k$polynomials equations where these are quadratic multivariate polynomials on$k$variables? I've encountered such systems on my research and I'm ... 4 votes 0 answers 228 views ### Solving not so much overdetermined system of multivariate polynomial equations I'm studying algorithms solving multivariate equations. I'm stuck in solving overdetermined set of quadratic equations. Concretely, with the number$n$of variables, the number of equations is$m=\...
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 ...