This article describes a polynomial attack on the new multilinear map over the integers presented by Coron, Lepoint and Tibouchi at Crypto 2015 (CLT15). This version is a fix of the first multilinear map over the integers presented by the same authors at Crypto 2013 (CLT13) and broken by Cheon et al. at Eurocrypt 2015. The attack essentially downgrades CLT15 to its original version CLT13, and l...

It is shown that any weakly-skew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natural read-once property. A 2 size lower bound is proven for ordered syntactically multilinear ABPs computing an...

Since its introduction, pseudorandom functions (PRFs) have become one of the main building blocks of cryptographic protocols. In this work, we revisit two recent extensions of standard PRFs, namely multilinear and aggregate PRFs, and provide several new results for these primitives. In the case of aggregate PRFs, one of our main results is a proof of security for the Naor-Reingold PRF with resp...

This paper reports new results regarding the usefulness of colour measurements in flotation process. Colour measurements coming simultaneously from RGB-camera and a spectrophotometer (and from the same measurement point) are compared. The measured variables are used to construct a partial least squares (PLS) model and a multilinear regression (MLR) model for the prediction of the zinc content i...

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect t...

Deene the MOD m-degree of a boolean function F to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments ~ x, F(~ x) = 0 ii P(~ x) = 0. By exploring the periodic property of the binomial coeecients modulo m, two new lower bounds on the MOD m-degree of the MOD l and :MOD m functions are proved, where m is any composite integer and l has ...

This paper discusses the interpretation of multilinear representations of speech utterances using a computational linguistic model. The model uses a feature-based finite state automaton representation of phonotactic constraints and axioms of event logic to provide a multilinear representation with a temporal interpretation. The asynchronous nature of the features in multilinear representations ...

By means of the new software MOLGEN-QSPR, a multilinear regression model for the boiling points of lower fluoroalkanes is established. The model is based exclusively on simple descriptors derived directly from molecular structure and nevertheless describes a broader set of data more precisely than previous attempts that used either more demanding (quantum chemical) descriptors or more demanding...

An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over +,× where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression.