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Nearly Linear-Time Zero-Knowledge Proofs for Correct Program Execution
Zero-knowledge proofs succinct arguments of knowledge TinyRAM
2018/5/2
There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We constru...
Linear-Time Zero-Knowledge Proofs for Arithmetic Circuit Satisfiability
Zero-knowledge arithmetic circuit ideal linear commitments
2017/9/14
We give computationally efficient zero-knowledge proofs of knowledge for arithmetic circuit satisfiability over a large field. For a circuit with N addition and multiplication gates, the prover only u...
Linear-Time Non-Malleable Codes in the Bit-Wise Independent Tampering Model
Non-malleable codes Bit-Wise Independent Tampering Model
2016/4/22
Non-malleable codes were introduced by Dziembowski et al. (ICS 2010) as coding schemes that protect a message against tampering attacks. Roughly speaking, a code is non-malleable if decoding an advers...
Computing theta functions in quasi-linear time in genus 2 and above
number theory hyperelliptic curves theta functions
2016/2/24
We outline an algorithm to compute θ(z, τ ) in genus 2 in quasi-optimal time, borrowing
ideas from the algorithm for theta constants and the one for θ(z, τ ) in genus 1. Our
implementation shows a l...
Rate-1, Linear Time and Additively Homomorphic UC Commitments
commitment asymptotic efficiency universal composability
2016/2/23
We propose the first UC commitment scheme for binary
strings with the optimal properties of rate approaching 1 and linear time
(in the amortised sense, using a small number of seed OTs). On top of
...
Linear Time Approximation Schemes for Geometric Maximum Coverage
Maximum coverage Geometric set cover Polynomial-time approximation scheme
2016/1/22
We study approximation algorithms for the following geo-metric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a × b rectangles such that ...
Computing Jacobi's \theta in quasi-linear time
number theory elliptic curve cryptosystem theta function
2015/12/21
Jacobi’s θ function has numerous applications in mathematics and computer science; a
naive algorithm allows the computation of θ(z, τ ), for z, τ verifying certain conditions, with
precision P in O(...
MEAN SQUARED ERROR REDUCTION FOR GMM ESTIMATORS OF LINEAR TIME SERIES MODELS
GMM LINEAR TIME SERIES MODELS
2015/9/22
In this paper we analyze Generalized Method of Moments (GMM) estimators for time
series models as advocated by Hansen and Singleton. It is well known that these estimators
achieve efficiency bo...
Subharmonic functions and performance bounds on linear time-invariant feedback systems
Harmonic function linear the performance of the single output system a linear control system the harmonic function
2015/8/13
In this paper we study multi-input multi-output (MIMO) linear time-invariant (LTI) control systems. We show that some well known constraints on the performance of single-input single-output (SISO) lin...
Linear Time-of-Arrival Estimation in a Multipath Environment by Inverse Correlation Method
Linear Time-of-Arrival Estimation Multipath Environment Inverse Correlation Method
2015/6/26
The Maximum Likelihood Estimator (MLE) is most often used to estimate the signal time delay in a multipath en vironment. There are various implementations of the MLE which can be divided into the time...
Guaranteed Error Bounds for Model Reduction of Linear Time-Varying Systems
Time-Varying Systems Model Reduction
2015/6/19
New techniques are presented for the model reduction of linear time-varying and linear periodically-varying systems, including the formulation and proof of guaranteed upper bounds for the error. The c...
Error Bounds for Balanced Model Reduction of Linear Time-Varying Systems
Time-Varying Systems Model Reduction
2015/6/19
Error-bounds are developed for balanced truncation of linear time-varying systems, leading to an extension of the `twice the sum of the tail' formulae, well-known in the time-invariant case. The appro...
Constructing Lyapunov-Krasovskii Functionals for Linear Time Delay Systems
Linear Time Delay Systems Lyapunov-Krasovskii
2015/6/19
We present an algorithmic methodology for constructing Lyapunov-Krasovskii (L-K) functionals for linear time-delay systems, using the sum of squares decomposition of multivariate polynomials to solve ...
Positive Forms and Stability of Linear Time-Delay Systems
Time-Delay Systems Positive Forms and Stability
2015/6/19
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that stability implies that there exists a quadratic Lyapunov fun...
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Ly...