We introduce Ouroboros (The Ouroboros symbol is an ancient symbol which represents the notion of cyclicity in many civilizations), a new Key Exchange protocol based on coding theory. The protocol gathers the best prop...
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ISBN:
(纸本)9783319598796;9783319598789
We introduce Ouroboros (The Ouroboros symbol is an ancient symbol which represents the notion of cyclicity in many civilizations), a new Key Exchange protocol based on coding theory. The protocol gathers the best properties of the recent MDPC-McEliece and HQC protocols for the Hamming metric: simplicity of decoding and security reduction, based on a double cyclic structure. This yields a simple, secure and efficient approach for key exchange. We obtain the same type of parameters (and almost the same simple decoding) as for MDPC-McEliece, but with a security reduction to decoding random quasi-cyclic codes in the Random Oracle Model.
Group algebras have been used in the context of coding theory since the beginning of the latter, but not in its full power. The article of Ferraz and Polcino Milies entitled Idempotents in group algebras and minimal a...
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Group algebras have been used in the context of coding theory since the beginning of the latter, but not in its full power. The article of Ferraz and Polcino Milies entitled Idempotents in group algebras and minimal abelian codes (Finite Fields Appl 13(2): 382-393, 2007) gave origin tomany thesis and papers linking these two subjects. In these works, the techniques of group algebras are mainly brought into play for the computing of the idempotents that generate the minimal codes and the minimum weight of such codes. In this paper I present a survey on the main results proceeding from applications of that seminal work.
The P300-based brain-computer interface (BCI) speller relies on eliciting and detecting specific brain responses to target stimulus events, termed event-related potentials (ERPs). In a visual speller, ERPs are elicite...
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ISBN:
(纸本)9781509041176
The P300-based brain-computer interface (BCI) speller relies on eliciting and detecting specific brain responses to target stimulus events, termed event-related potentials (ERPs). In a visual speller, ERPs are elicited when the user's desired character, i.e. the "target," is flashed on a computer screen. The P300 speller is currently limited by its relatively slow typing speed due to the need for repetitive data measurements that are necessary to achieve reasonable signal-to-noise ratios. In addition, refractory effects limit the ability to elicit ERPs with every target stimulus event presentation. In this paper, we present a new method to design the stimulus presentation paradigm for the P300 speller by exploiting an information-theoretic approach to maximize the information content that is presented to the user while also mitigating refractory effects. We present results with real-time BCI use which demonstrate significant performance improvements with our performance-based paradigm compared to the conventional stimulus presentation paradigm.
Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theoryuntil now....
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ISBN:
(纸本)1466567805;9781466567801
Although several books cover the coding theory of wireless communications and the hardware technologies and coding techniques of optical CDMA, no book has been specifically dedicated to optical coding theoryuntil now. Written by renowned authorities in the field, Optical coding theory with Prime gathers together in one volume the fundamentals and developments of optical coding theory, with a focus on families of prime codes, supplemented with several families of non-prime codes. The book also explores potential applications to coding-based optical systems and networks. Learn How to Construct and Analyze Optical Codes The authors use a theorem-proof approach, breaking down theories into digestible form so that readers can understand the main message without searching through tedious proofs. The book begins with the mathematical tools needed to understand and apply optical coding theory, from Galois fields and matrices to Gaussian and combinatorial analytical tools. Using a wealth of examples, the authors show how optical codes are constructed and analyzed, and detail their performance in a variety of applications. The book examines families of 1-D and 2-D asynchronous and synchronous, multilength, and 3-D prime codes, and some non-prime codes. Get a Working Knowledge of Optical coding theory to Help You Design Optical Systems and Networks Prerequisites include a basic knowledge of linear algebra and coding theory, as well as a foundation in probability and communications theory. This book draws on the authors extensive research to offer an authoritative reference on the emerging field of optical coding theory. In addition, it supplies a working knowledge of the theory and optical codes to help readers in the design of coding-based optical systems and networks. For more on the technological aspects of optical CDMA, see Optical Code Division Multiple Access: Fundamentals and Applications (CRC Press 2005).
Storage systems are experiencing a historical paradigm shift from hard disk to nonvolatile memories due to its advantages such as higher density, smaller size and non-volatility. On the other hand, Solid Storage Disk ...
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Storage systems are experiencing a historical paradigm shift from hard disk to nonvolatile memories due to its advantages such as higher density, smaller size and non-volatility. On the other hand, Solid Storage Disk (SSD) also poses critical challenges to application and system designers. The first challenge is called endurance. Endurance means flash memory can only experience a limited number of program/erase cycles, and after that the cell quality degradation can no longer be accommodated by the memory system fault tolerance capacity. The second challenge is called reliability, which means flash cells are sensitive to various noise and disturbs, i.e., data may change unintentionally after experiencing noise/disturbs. The third challenge is called security, which means it is impossible or costly to delete files from flash memory securely without leaking information to possible eavesdroppers. In this dissertation, we first study noise modeling and capacity analysis for NAND flash memories (which is the most popular flash memory in market), which gains us some insight on how flash memories are working and their unique noise. Second, based on the characteristics of content-replication codewords in flash memories, we propose a joint decoder to enhance the flash memory reliability. Third, we explore data representation schemes in flash memories and optimal rewriting code constructions in order to solve the endurance problem. Fourth, in order to make our rewriting code more practical, we study noisy write-efficient memories and Write-Once Memory (WOM) codes against inter-cell interference in NAND memories. Finally, motivated by the secure deletion problem in flash memories, we study coding schemes to solve both the endurance and the security issues in flash memories. This work presents a series of information theory and coding theory research studies on the aforesaid three critical issues, and shows that how coding theory can be utilized to address these challenges.
This dissertation leverages the connection between coding theory and classical sparse recovery problems like sparse Fourier and Hadamard transform computations to understand properties of existing recovery algorithms ...
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This dissertation leverages the connection between coding theory and classical sparse recovery problems like sparse Fourier and Hadamard transform computations to understand properties of existing recovery algorithms under various signal models, propose improvements, and adopt them to interesting applications in theoretical computer science like pattern matching. In the first part of the dissertation, we begin by demonstrating the relationship between an extended Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm and the iterative hard decision decoding of product codes. We show that the FFAST algorithm is analogous to an iterative decoder for a carefully defined product code whose thresholds can be computed by an extension of Justensen's analysis to d-dimensional product codes. Interpreting the FFAST algorithm as decoding of a product code also provides insight into the performance of the FFAST algorithm when non-zero coefficients are not randomly chosen but are bursty such as what may be encountered in many practical applications like spectrum sensing. Recoverability results are guaranteed for the finite length case and we provided thresholds for the 1 and 2 burst cases asymptotically. It is further observed that the FFAST algorithm performs better for bursty signals in comparison to those for randomly chosen non-zero coefficients. We then consider the problem of computing the Walsh-Hadamard Transform (WHT) of an N = 2n dimensional signal whose WHT is K-sparse, when the sparsity parameter K scales sub-linearly in N. We propose improvements to the algorithm by Scheibler et al. by introducing a two error correcting code at each check node. Further, through density evolution analysis and simulations we show that the proposed modification substantially improves the space and time complexity of the algorithm, sometimes achieving as much as a 70% reduction. We conclude by considering the substring/pattern matching problem of querying a string (or a database)
Title: Homomorphic encryption and coding theory Author: Veronika Půlpánová Department: Department of algebra Supervisor: RNDr. Michal Hojsík, Ph.D., Department of algebra Abstract: The current mainstrea...
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Title: Homomorphic encryption and coding theory Author: Veronika Půlpánová Department: Department of algebra Supervisor: RNDr. Michal Hojsík, Ph.D., Department of algebra Abstract: The current mainstream in fully homomorphic encryption is the appro- ach that uses the theory of lattices. The thesis explores alternative approaches to homomorphic encryption. First we present a code-based homomorphic encrypti- on scheme by Armknecht et. al. and study its properties. Then we describe the family of cryptosystems commonly known as Polly Cracker and identify its pro- blematic aspects. The main contribution of this thesis is the design of a new fully homomorphic symmetric encryption scheme based on Polly Cracker. It proposes a new approach to overcoming the complexity of the simple Polly Cracker - based cryptosystems. It uses Gröbner bases to generate zero-dimensional ideals of po- lynomial rings over finite fields whose factor rings are then used as the rings of ciphertexts. Gröbner bases equip these rings with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem. Keywords: Fully homomorphic encryption, Polly Cracker, coding theory, zero- dimensional ideals
This article examines the process of creating and researching a virtual laboratory for training students in coding theory. General information about the virtual laboratories is presented. A methodology for conducting ...
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This article examines the process of creating and researching a virtual laboratory for training students in coding theory. General information about the virtual laboratories is presented. A methodology for conducting comprehensive scientific research is presented, as well as a specialized method for designing and developing the virtual laboratory, including the system's architecture. The article also presents brief information about the developed system. The results of the experimental research, including a pedagogical experiment aimed at evaluating the influence of the virtual laboratory on the students' success rate, as well as an analysis of the statistical data on their activity, are discussed in detail. In addition, a survey was conducted to assess the satisfaction of students with the use of the laboratory.
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