630 research outputs found
Fast Arithmetics Using Chinese Remaindering
In this paper, some issues concerning the Chinese remaindering representation
are discussed. Some new converting methods, including an efficient
probabilistic algorithm based on a recent result of von zur Gathen and
Shparlinski \cite{Gathen-Shparlinski}, are described. An efficient refinement
of the NC division algorithm of Chiu, Davida and Litow
\cite{Chiu-Davida-Litow} is given, where the number of moduli is reduced by a
factor of
Adder Based Residue to Binary Number Converters for (2n - 1; 2n; 2n + 1)
Copyright © 2002 IEEEBased on an algorithm derived from the new Chinese remainder theorem I, we present three new residue-to-binary converters for the residue number system (2n-1, 2n, 2n+1) designed using 2n-bit or n-bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2n-bit adder based converter is faster and requires about half the hardware required by previous methods. For n-bit adder-based implementations, one new converter is twice as fast as the previous method using a similar amount of hardware, whereas another new converter achieves improvement in either speed, area, or dynamic range compared with previous convertersYuke Wang, Xiaoyu Song, Mostapha Aboulhamid and Hong She
Modular exponentiation via the explicit Chinese remainder theorem
In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabinâs algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms
EXPLORING CONFIDENTIALITY AND PRIVACY OF IMAGE IN CLOUD COMPUTING
With the increasing popularity of cloud computing, clients are storing their data in cloud servers and are using âsoftware as a serviceâ for computing services. However, clientsâ data may be sensitive, critical, and private, and processing such data with cloud servers may result in losing data privacy or compromising data confidentiality. Some cloud servers may be dishonest, while malicious entities may compromise others. In order to protect data privacy and confidentiality, clients need to be able to hide their actual data values and send the obfuscated values to cloud servers.
This thesis deals with the outsourcing of computing to cloud servers, in which clientsâ images can be computed and stored. This thesis proposes a technique that obfuscates images before sending them to servers, so these servers can perform computations on images without knowing the actual images. The proposed technique is expected to ensure data privacy and confidentiality. Servers will not be able to identify an individual whose images are stored and manipulated by the server. In addition, our approach employs an obfuscating technique to maintain the confidentiality of images, allowing cloud servers to compute obfuscated data accurately without knowing the actual data value, thus supporting privacy and confidentiality.
The proposed approach is based on the Rabin block cipher technique, which has some weaknesses, however. The main drawback is its decryption technique, which results in four values, and only one of these values represents the actual value of plain data. Another issue is that the blocking technique requires a private key for each block that requires a high-computing effort; requiring one private key for each block of data demands that a great number of keys be stored by the client. As a result, it decreases the robustness of the Rabin block cipher.
This thesis proposes additional techniques to overcome some of the weaknesses of the Rabin block cipher by introducing some new features, such as tokenization, a digit counter, and a set of blocks. The new technique increases the privacy of data and decreases the computational complexity by requiring fewer private keys. The new features have been implemented in image processing in order to demonstrate their applicability. However, in order to apply our approach to images, we must first apply some preprocessing techniques on images to make them applicable to being obfuscated by our proposed obfuscating system
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Data Compression Using a Multi-residue System (Mrs)
This work presents a novel technique for data compression based on multi-residue number systems. The basic theorem is that an under-determined system of congruences could be solved to accomplish data compression for a signal satisfying continuity of its information content and bounded in peak-to -peak amplitude by the product of relatively prime moduli,. This thesis investigates this property and presents quantitative results along with MATLAB codes. Chapter 1 is introductory in nature and Chapter 2 deals in more detail with the basic theorem. Chapter 3 explicitly mentions the assumptions made and chapter 4 shows alternative solutions to the Chinese remainder theorem. Chapter 5 explains the experiments in detail whose results are mentioned in chapter 6. Chapter 7 concludes with a summary and suggestions for future work
Montgomery Arithmetic from a Software Perspective
This chapter describes Peter L. Montgomery\u27s modular multiplication method and the various improvements to reduce the latency for software implementations on devices which have access to many computational units
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