Multivariate Polynomials and Low Degree Testing
The Complexity of Testing Monomials in Multivariate Polynomials
... of testing monomials in multivariate ...of polynomials to the study of those ...ΠΣ polynomials are obtained in this paper, laying a basis for further study along this ...
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Efficient Evaluation of Low Degree Multivariate Polynomials in Ring-LWE Homomorphic Encryption Schemes
... of polynomials over encrypted data and take advantage of the plaintext space polynomial ...evaluate multivariate linear polynomials over coefficient packed ...of low-degree ...
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Noisy Interpolating Sets for Low-Degree Polynomials
... for degree-d polynomials is a set of points S ⊆ F n such that if q(x 1 , ...a degree-d polynomial over F and we are given the set of values (q(s)) s∈S then we can reconstruct ...for degree-d ...
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Unconditional Pseudorandom Generators for Low-Degree Polynomials
... against low- degree polynomials over finite ...linear polynomials, known as small-bias generators, were first introduced by Naor and Naor (STOC ...against degree-d polynomials ...
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Homomorphic Secret Sharing for Low Degree Polynomials
... The above means that u elements are chosen from each of the b − p − v of the encrypted columns, and u + 1 elements are chosen from each of the remaining plaintext and en- crypted columns. Consider shifting any element ...
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Factorization of multivariate polynomials
... In an implementation one should try several different values for a and also try to factorize f(b, y) for random b if possible. This way, one can choose a univariate factorization with few factors and can detect ...
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11 Multivariate Polynomials
... Section 3.4 and Chapter 10 Ideals, Varieties, and Algorithms (Cox, Little, O’Shea): Chapters 1 & 2 Solving a linear system is the same as finding a solution to a system of degree-1 multivariate ...
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Zero-Knowledge for Multivariate Polynomials
... of multivariate quadratic equations over a finite ...for polynomials of any degree d, ...of polynomials: for example if the polynomials are sparse or ...
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Efficient Methods for Conversion and Solution of Sparse Systems of Low-Degree Multivariate Polynomials over GF(2) via SAT-Solvers
... of low-degree sparse multivariate equations into a conjunctive normal form satisfiability (CNF-SAT) problem, for which excellent heuristic algorithms have been developed in recent ...sparse ...
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Efficient Batch Zero-Knowledge Arguments for Low Degree Polynomials
... for low degree polynomial relations in these works proceed by masking an input variable u as f u = ux+u b , using a ran- dom challenge x and a random blinder u b ...the degree of the polynomial ...
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Efficient Batch Zero-Knowledge Arguments for Low Degree Polynomials
... for Low Degree ...of low-degree polynomial ...of low degree, and part of the witness is a satisfying assignment for the ...
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1 Formulating The Low Degree Testing Problem
... the low degree testing assumption, ...a degree d and access to an auxiliary proof, a probabilistic verifier can test whether f corresponds to a polynomial of degree at most d using a ...
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Multivariate Orthogonal Polynomials and Modified Moment Functionals
... Abstract. Multivariate orthogonal polynomials can be introduced by using a moment func- tional defined on the linear space of polynomials in several variables with real ...total degree 2, ...
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Multivariate Quadratic Polynomials in Public Key Cryptography
... that Multivariate Quadratic constructions only allows secure signature schemes so ...a low-end smart-card without a cryptographic ...of Multivariate Quadratic systems are outweighed by their ...
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On Functional Decomposition of Multivariate Polynomials with Differentiation and Homogenization
... for multivariate polynomials based on differentiation and ho- mogenization which are proposed by Ye, Dai, Lam (1999) and Faug`ere, Perret (2006, 2008, ...a degree proper functional decomposition for ...
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Multivariate Matching Polynomials of Cyclically Labelled Graphs
... The homomorphism property, Proposition 4.1, shows that tr N Sym (AB) = tr N Sym (BA), and that similar matrices have the same trace. Again by the homomorphism property, if two d × d matrices are similar, A = M BM −1 , ...
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Multivariate matching polynomials of cyclically labelled graphs
... A tree is a connected simple graph with no cycles, and a rooted tree is a tree in which some vertex of degree 1 has been specified to be the root, r. Given any rooted tree, let us label its edges by first ...
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Symbolic–numeric sparse interpolation of multivariate polynomials
... A key technique in this regard is the use of evaluation points at roots of unity, and the random choice of such roots. The use of roots of unity for interpolation is well-established, and adds numerical stability by ...
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Factoring Multivariate Polynomials over Finite Fields
... of testing the absolute irreducbility of an F q -irreducible polynomial, our algorithm uses the output of the partial factoring algorithm developed in the previous ...of polynomials f (x 1 , . . . , x n ) ∈ ...
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Factorization of Multivariate Polynomials by Extended Hensel Construction
... 5.3 E.H.C. from the left to the right In 3, we described the successive E.H.C.’s on the line segments L 1 ⇒ L 2 ⇒ · · · ⇒ L ρ . In each E.H.C., the Hensel lifting must be repeated until each coefficient w.r.t. x contains ...
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