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Subquadratic zero-knowledge

J. Boyar, G. Brassard, R. Peralta
[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science  
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] .  ... 
doi:10.1109/sfcs.1991.185350 dblp:conf/focs/BoyarBP91 fatcat:anr556awszdv5hu2r6y2i5win4

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

Haining Fan, M. Anwar Hasan
2007 IEEE transactions on computers  
Index Terms Finite field, 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.  ... 
doi:10.1109/tc.2007.1076 fatcat:7kxswgs3nrgnloqjl7unqc46ea

On Formal Specification of Maple Programs [chapter]

Muhammad Taimoor Khan, Wolfgang Schreiner
2012 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-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.  ... 
doi:10.1007/978-3-642-31374-5_33 fatcat:fkcz4vgspvcz3lxafmnqbg7y3m

Discriminative Parameter Estimation for Random Walks Segmentation: Technical Report [article]

Pierre-Yves Baudin, Danny Goodman, Puneet Kumar, Noura Azzabou (MIRCEN, UPMC), Pierre G. Carlier, Nikos Paragios (INRIA Saclay - Ile de France, LIGM, ENPC, MAS), M. Pawan Kumar
2013 arXiv   pre-print
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.  ...  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.  ... 
arXiv:1306.1083v1 fatcat:dq56intjw5dunjypdo7ny5pona

A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields

Haining Fan, M. Anwar Hasan
2007 IEEE transactions on computers  
To the best of our 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  ... 
doi:10.1109/tc.2007.19 fatcat:tzzv5soclzdwlanxbxgtfrpvua

Design of a Distributed Reachability Algorithm for Analysis of Linear Hybrid Automata [article]

Sumit Kumar Jha
2007 arXiv   pre-print
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 (??)  ...  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.  ... 
arXiv:0710.3764v1 fatcat:5ph5e2c4indvlensmj4ihur4ta

Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time

Matti Karppa, Petteri Kaski, Jukka Kohonen, Padraig Ó Catháin, Marc Herbstritt
2016 European Symposium on Algorithms  
ACM 62 (2015) Art. 13] 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.  ... 
doi:10.4230/lipics.esa.2016.52 dblp:conf/esa/KarppaKKC16 fatcat:aeu2t4zknzgghhg6g7vuplxlce

Grammatic -- a tool for grammar definition reuse and modularity [article]

Andrey Breslav
2009 arXiv   pre-print
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.  ...  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.  ... 
arXiv:0901.2461v1 fatcat:y4gdqmyq2nex7agj4w4fjyh5ui

Dynamic Time Warping in Strongly Subquadratic Time: Algorithms for the Low-Distance Regime and Approximate Evaluation

William Kuszmaul, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
For an arbitrary metric space Σ with distances normalized so that the smallest non-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.  ... 
doi:10.4230/lipics.icalp.2019.80 dblp:conf/icalp/Kuszmaul19 fatcat:xe4lwksimzdolibymqsnw6jdua

Communication Complexity of Byzantine Agreement, Revisited [article]

Ittai Abraham, T-H. Hubert Chan, Danny Dolev, Kartik Nayak, Rafael Pass, Ling Ren, Elaine Shi
2020 arXiv   pre-print
A few existing works have shown how to achieve 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.  ... 
arXiv:1805.03391v4 fatcat:cxhb6mf5xvb3tfft2b6bytzwbm

Towards a Theory of Domains for Harmonic Functions and its Symbolic Counterpart [article]

van Chiên Bui, Gérard Duchamp, Quoc Hoàn Ngo, Vincel Hoang Ngoc Minh, Vu Nguyen Dinh
2021 arXiv   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 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 • ).  ... 
arXiv:2110.13743v1 fatcat:gortyezxvnev7fzd4tjhqwxznq

New Subquadratic Algorithms for Constructing Lightweight Hadamard MDS Matrices (Full Version) [article]

Tianshuo Cong, Ximing Fu, Xuting Zhou, Yuli Zou, Haining Fan
2020 IACR Cryptology ePrint Archive  
To the best of our 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.  ... 
dblp:journals/iacr/CongFZZF20 fatcat:rr3xircr45gsba7ymgnzb5e54a

Patchiness in assemblages of epiphytic macroalgae on Posidonia coriacea at a hierarchy of spatial scales

MA Vanderklift, PS Lavery
2000 Marine Ecology Progress Series  
Bank at which the study was conducted Some of the selected 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.  ... 
doi:10.3354/meps192127 fatcat:gvyemeyzijgyleoaql64pajcsq

Page 7288 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 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.  ... 

Quality Measures of Parameter Tuning for Aggregated Multi-Objective Temporal Planning [article]

Mostepha Redouane Khouadjia, Marc Schoenauer, Johann Dréo
2013 arXiv   pre-print
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 . 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.  ... 
arXiv:1305.2265v1 fatcat:njdxb7bt5rg3boioej2mfu6q54
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