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CHAMP: Cayley HAshing with Matrix Products
Alexander Demin, Alexey Ovchinnikov, Vladimir Shpilrain
Cayley hash functions hash binary strings by representing the bits of the message as elements of a semigroup and multiplying the corresponding elements. This gives Cayley hash func…
Practical Algebraic Parameter Estimation for Noisy Data via Gaussian Process Regression
Oren Bassik, Alexander Demin, Alexey Ovchinnikov
Parameter estimation for ordinary differential equation (ODE) models is a fundamental task that is often complicated by the limitations of conventional optimization-based methods.…
Redactable blockchains and polynomial equations
Alexander Demin, Alexey Ovchinnikov, Vladimir Shpilrain
We develop new tools for constructing redactable authenticated data structures with post-quantum security. In our construction, inverting the proposed one-way function means solvin…
Groebner.jl: Fast Gröbner Tracing in Julia
Alexander Demin
A standard way to control expression swell in computer algebra is to use multi-modular or evaluation-interpolation methods. In computations involving Gröbner bases, these technique…
Fast Rational Univariate Representation via Gaussian Elimination
Alexander Demin, Fabrice Rouillier
In this note, we present RationalUnivariateRepresentationjl (https://newrur.gitlabpages.inria.fr/RationalUnivariateRepresentation.jl/), a Julia package for computing rational un…