Chinese remainder theorem: applications in computing, coding, cryptography
TL;DR: Introduction and philosophy Chinese remainder algorithm in modular computations in algorithmics in bridging computation in coding theory in cryptography tutorial in information theory tutorial in algebra list of mathematical symbols.
Abstract: Introduction and philosophy Chinese remainder algorithm in modular computations in algorithmics in bridging computations in coding theory in cryptography tutorial in information theory tutorial in algebra list of mathematical symbols.
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02 May 1999
TL;DR: A new trapdoor mechanism is proposed and three encryption schemes are derived : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA, which are provably secure under appropriate assumptions in the standard model.
Abstract: This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
7,008 citations
Cites methods from "Chinese remainder theorem: applicat..."
...The Chinese Remainder Theorem [6] can be used to efficiently reduce the decryption workload of the three cryptosystems....
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Proceedings Article•
16 Mar 2016TL;DR: Chronos, a system that enables a single WiFi access point to localize clients to within tens of centimeters, demonstrates that Chronos's accuracy is comparable to state-of-the-art localization systems, which use four or five access points.
Abstract: We present Chronos, a system that enables a single WiFi access point to localize clients to within tens of centimeters. Such a system can bring indoor positioning to homes and small businesses which typically have a single access point.
The key enabler underlying Chronos is a novel algorithm that can compute sub-nanosecond time-of-flight using commodity WiFi cards. By multiplying the time-of-flight with the speed of light, a MIMO access point computes the distance between each of its antennas and the client, hence localizing it. Our implementation on commodity WiFi cards demonstrates that Chronos's accuracy is comparable to state-of-the-art localization systems, which use four or five access points.
669 citations
01 Jan 2008
TL;DR: This book presents an introduction to the principles of the fast Fourier transform, which covers FFTs, frequency domain filtering, and applications to video and audio signal processing.
Abstract: This manuscript describes a number of algorithms that can be used to quickly evaluate a polynomial over a collection of points and interpolate these evaluations back into a polynomial. Engineers define the “Fast Fourier Transform” as a method of solving the interpolation problem where the coefficient ring used to construct the polynomials has a special multiplicative structure. Mathematicians define the “Fast Fourier Transform” as a method of solving the evaluation problem. One purpose of the document is to provide a mathematical treatment of the topic of the “Fast Fourier Transform” that can also be understood by someone who has an understanding of the topic from the engineering perspective.
The manuscript will also introduce several new algorithms that solve the fast multipoint evaluation problem over certain finite fields and require fewer finite field operations than existing techniques. The document will also demonstrate that these new algorithms can be used to multiply polynomials with finite field coefficients with fewer operations than Schonhage's algorithm in most circumstances.
A third objective of this document is to provide a mathematical perspective of several algorithms which can be used to multiply polynomials of size which is not a power of two. Several improvements to these algorithms will also be discussed.
Finally, the document will describe several applications of the “Fast Fourier Transform” algorithms presented and will introduce improvements in several of these applications. In addition to polynomial multiplication, the applications of polynomial division with remainder, the greatest common divisor, decoding of Reed-Solomon error-correcting codes, and the computation of the coefficients of a discrete Fourier Series will be addressed.
272 citations
Cites methods from "Chinese remainder theorem: applicat..."
...Otherwise, [19] provides the following alternative method of computing a with less effort than (1....
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TL;DR: It is proved that the proposed EPOM achieves the goal of secure integer number processing without resulting in privacy leakage of data to unauthorized parties.
Abstract: In this paper, we propose a toolkit for efficient and privacy-preserving outsourced calculation under multiple encrypted keys (EPOM). Using EPOM, a large scale of users can securely outsource their data to a cloud server for storage. Moreover, encrypted data belonging to multiple users can be processed without compromising on the security of the individual user’s (original) data and the final computed results. To reduce the associated key management cost and private key exposure risk in EPOM, we present a distributed two-trapdoor public-key cryptosystem, the core cryptographic primitive. We also present the toolkit to ensure that the commonly used integer operations can be securely handled across different encrypted domains. We then prove that the proposed EPOM achieves the goal of secure integer number processing without resulting in privacy leakage of data to unauthorized parties. Last, we demonstrate the utility and the efficiency of EPOM using simulations.
194 citations
TL;DR: A well-rounded treatment of known families of almost difference sets is given, relations between some difference sets and some almost difference Sets are established, and the numerical multiplier group of some families ofalmost difference sets are determined.
Abstract: Almost difference sets have interesting applications in cryptography and coding theory. We give a well-rounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost difference sets, and four classes of binary sequences of period n/spl equiv/0 (mod 4) with optimal autocorrelation. We have also obtained two classes of relative difference sets and four classes of divisible difference sets (DDSs). We also point out that a result due to Jungnickel (1982) can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation.
186 citations