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Subquadratic zero-knowledge

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[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
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*Zero*-

*knowledge*proofs are a well developed field of cryptography. ... This article presents a general and practical

*zero*-

*knowledge*protocol with an explanation of relevant theoretical results. ... Hence

*zero*-

*knowledge*schemes developed in this way are referred to as arguments rather than proofs. A perfect

*zero*-

*knowledge*argument protocol is described in [6] . ...

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Subquadratic Computational Complexity Schemes for Extended Binary Field Multiplication Using Optimal Normal Bases

2007
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IEEE transactions on computers
*

Index Terms Finite field,

doi:10.1109/tc.2007.1076
fatcat:7kxswgs3nrgnloqjl7unqc46ea
*subquadratic*computational complexity multiplication, normal basis, optimal normal basis. ... Based on a recently proposed Toeplitz matrix-vector product approach, a*subquadratic*computational complexity scheme is presented for multiplications in binary extended finite fields using Type I and II ... To the best of our*knowledge*, this is the first*subquadratic*computational complexity scheme for Type II ONB multiplication. ...##
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On Formal Specification of Maple Programs
[chapter]

2012
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Lecture Notes in Computer Science
*

Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-

doi:10.1007/978-3-642-31374-5_33
fatcat:fkcz4vgspvcz3lxafmnqbg7y3m
*zero*: x(t) = 0 ∀t . (8) Proof. ... Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-*zero*: x(t) = 0 ∀t . (8) Proof. ...##
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Discriminative Parameter Estimation for Random Walks Segmentation: Technical Report
[article]

2013
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arXiv
*
pre-print

Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-

arXiv:1306.1083v1
fatcat:dq56intjw5dunjypdo7ny5pona
*zero*: x(t) = 0 ∀t . (8) Proof. ... Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-*zero*: x(t) = 0 ∀t . (8) Proof. ... As an example, the function x α , with 1 ≤ α < 2, is (0, ε)-*subquadratic*at infinity for every ε > 0. Similarly, the Hamiltonian is (k, k + ε)-*subquadratic*for every ε > 0. ...##
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A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields

2007
*
IEEE transactions on computers
*

To the best of our

doi:10.1109/tc.2007.19
fatcat:tzzv5soclzdwlanxbxgtfrpvua
*knowledge*, this is the first time that*subquadratic*space complexity parallel multipliers are proposed for dual, weakly dual, and triangular bases. ... A recursive design algorithm is also proposed for efficient construction of the proposed*subquadratic*space complexity multipliers. ... Omitted. } ELSE {// Padding Print sentences for padding*zeroes*after the last elements of matrix T 's first row and first column, respectively; Print the sentence for padding a*zero*after the last element ...##
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Design of a Distributed Reachability Algorithm for Analysis of Linear Hybrid Automata
[article]

2007
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arXiv
*
pre-print

Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-

arXiv:0710.3764v1
fatcat:5ph5e2c4indvlensmj4ihur4ta
*zero*: x(t) = 0 ∀t . (8) Proof. Condition (??) ... Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-*zero*: x(t) = 0 ∀t . (8) Proof. Condition (??) ... As an example, the function x α , with 1 ≤ α < 2, is (0, ε)-*subquadratic*at infinity for every ε > 0. Similarly, the Hamiltonian is (k, k + ε)-*subquadratic*for every ε > 0. ...##
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Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time

2016
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European Symposium on Algorithms
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ACM 62 (2015) Art. 13]

doi:10.4230/lipics.esa.2016.52
dblp:conf/esa/KarppaKKC16
fatcat:aeu2t4zknzgghhg6g7vuplxlce
*subquadratic*-time algorithm for finding outlier correlations in binary data. ... Our derandomized algorithm gives deterministic*subquadratic*scaling essentially for the same parameter range as Valiant's randomized algorithm, but the precise constants we save over quadratic scaling ... Furthermore, we seek to do this without a priori*knowledge*of q. ...##
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Grammatic -- a tool for grammar definition reuse and modularity
[article]

2009
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arXiv
*
pre-print

Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-

arXiv:0901.2461v1
fatcat:y4gdqmyq2nex7agj4w4fjyh5ui
*zero*: x(t) = 0 ∀t . (8) Proof. ... Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-*zero*: x(t) = 0 ∀t . (8) Proof. ... As an example, the function x α , with 1 ≤ α < 2, is (0, ε)-*subquadratic*at infinity for every ε > 0. Similarly, the Hamiltonian is (k, k + ε)-*subquadratic*for every ε > 0. ...##
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Dynamic Time Warping in Strongly Subquadratic Time: Algorithms for the Low-Distance Regime and Approximate Evaluation

2019
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International Colloquium on Automata, Languages and Programming
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For an arbitrary metric space Σ with distances normalized so that the smallest non-

doi:10.4230/lipics.icalp.2019.80
dblp:conf/icalp/Kuszmaul19
fatcat:xe4lwksimzdolibymqsnw6jdua
*zero*distance is one, we present an algorithm which computes dtw(x, y) for two strings x and y over Σ in time O(n · dtw ... to a conditional lower bound of Bringmann and Künnemann pertaining to edit distance over {0, 1}, we obtain a conditional lower bound for computing DTW over a three letter alphabet (with distances of*zero*... To the best of our*knowledge*, however, they are the first such algorithms to run in strongly*subquadratic*time. ...##
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Communication Complexity of Byzantine Agreement, Revisited
[article]

2020
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arXiv
*
pre-print

A few existing works have shown how to achieve

arXiv:1805.03391v4
fatcat:cxhb6mf5xvb3tfft2b6bytzwbm
*subquadratic*BA under an adaptive adversary. ... Lastly, we show that some setup assumption is necessary for achieving*subquadratic*multicast-based BA. ... Then, there exists a proof system that satisfies perfect completeness, non-erasure computational*zero*-*knowledge*, and perfect*knowledge*extraction. ...##
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Towards a Theory of Domains for Harmonic Functions and its Symbolic Counterpart
[article]

2021
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arXiv
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pre-print

the extension of this "polylogarithmic calculus" and the world of harmonic sums, we propose a local theory, adapted to a full calculus on indices of Harmonic Sums based on the Taylor expansions, around

arXiv:2110.13743v1
fatcat:gortyezxvnev7fzd4tjhqwxznq
*zero*... (i) First point says that every function analytic at*zero*can be represented around*zero*as Li S (z) for some S ∈ C x 1 . ... In order to gain more indexing series and to describe the local situation at*zero*, we reshape and define a new domain of Li around*zero*to Dom loc (Li • ). ...##
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New Subquadratic Algorithms for Constructing Lightweight Hadamard MDS Matrices (Full Version)
[article]

2020
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IACR Cryptology ePrint Archive
*

To the best of our

dblp:journals/iacr/CongFZZF20
fatcat:rr3xircr45gsba7ymgnzb5e54a
*knowledge*,*subquadratic*multipliers have not been used to construct MDS matrices. ... We firstly propose*subquadratic*Hadamard matrix-vector product formulae (HMVP), and provide two new XOR count metrics. ... Section 2 briefly introduces some basic concepts such as background*knowledge*of MDS matrices and*subquadratic*TMVP formulae. ...##
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Patchiness in assemblages of epiphytic macroalgae on Posidonia coriacea at a hierarchy of spatial scales

2000
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Marine Ecology Progress Series
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Bank at which the study was conducted Some of the selected

doi:10.3354/meps192127
fatcat:gvyemeyzijgyleoaql64pajcsq
*subquadrats*fell on bare sand. As there were no epiphytes in these samples, all values were*zero*. ... The quadrat was 50 X 50 Cm, divided into a grid of 10 X 10 cm*subquadrats*. Divers deployed the quadrat 5 times, and collected seagrass from 5 randomly selected*subquadrats*. ...##
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Page 7288 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
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Mathematical Reviews
*

(English summary)

*Knowledge*discovery and learning. Ann. Math. Artif. Intell. 39 (2003), no. 3, 211-221. ...*Subquadratic*optimization algorithms in computational geometry rely on the monotonicity of the optimized function. ...##
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Quality Measures of Parameter Tuning for Aggregated Multi-Objective Temporal Planning
[article]

2013
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arXiv
*
pre-print

Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-

arXiv:1305.2265v1
fatcat:njdxb7bt5rg3boioej2mfu6q54
*zero*: x(t) = 0 ∀t . Proof. ... Set: δ := lim inf x→0 2N (x) x −2 . (7) If γ < −λ < δ, the solution u is non-*zero*: x(t) = 0 ∀t . (8) Proof. ... As an example, the function x α , with 1 ≤ α < 2, is (0, ε)-*subquadratic*at infinity for every ε > 0. Similarly, the Hamiltonian is (k, k + ε)-*subquadratic*for every ε > 0. ...
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