scholarly journals A New Class of Q-Ary Codes for the McEliece Cryptosystem

Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 11
Author(s):  
Jürgen Freudenberger ◽  
Johann-Philipp Thiers
Keyword(s):  
Channel Model ◽  
Low Complexity ◽  
Code Construction ◽  
Mceliece Cryptosystem ◽  
Weight One ◽  
Information Set ◽  
Maximum Distance Separable Codes ◽  
Channel Errors ◽  
Simple Product ◽  
The One

The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model. With this one Mannheim error channel, errors are limited to weight one. We investigate the channel capacity of this channel and discuss its relation to the McEliece system. The proposed codes are based on a simple product code construction and have a low complexity decoding algorithm. For the one Mannheim error channel, these codes achieve a higher error correction capability than maximum distance separable codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding.

scholarly journals Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography

Cryptography ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 33
Author(s):  
Johann-Philipp Thiers ◽  
Jürgen Freudenberger
Keyword(s):  
Error Correction ◽  
Low Complexity ◽  
Concatenated Codes ◽  
Mds Codes ◽  
Gaussian Integers ◽  
Work Factor ◽  
Code Construction ◽  
Error Correction Capability ◽  
Weight One ◽  
Information Set

The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.

scholarly journals Reliability profile of an information source: The most basic version

2020 ◽  
Vol 63 (1) ◽  
pp. 107-121
Author(s):  
Adam Nedeljkovic
Keyword(s):  
Information Sources ◽  
Information Source ◽  
Prima Facie ◽  
The Other ◽  
Interesting Connection ◽  
Explanatory Coherence ◽  
Information Set ◽  
The One ◽  
Basic Version ◽  
Formal Theories

The aim of this paper is an attempt at analyses and reconciliation of some prima facie confronted theories of reliability in the context of formal theories of coherence. Formal coherentists attempted to show that there is an epistemologically interesting connection between coherence of an information set and reliability of information sources. Amongst these authors there are divisions and differences concerning the nature of coherence, as well as the nature of reliability. On the one side, we have before us probabilistic coherentists who support a statistical understanding of reliability. On the other side we have supporters of explanatory coherence who see reliability as a dispostition. There are two goals that we shall attempt to achieve in this paper: to present and explain some ideas of reliability, without going into fine detailes and depths of theories in which they were formulated and to show that those ideas about reliability are not that irreconcilable as they might appear, but that they together can form something that we shall call ?reliability profile of an information source?, ?the most basic version?, or shorter: RPISbasic.

scholarly journals Neural Network Approach to MPPT Control and Irradiance Estimation

2020 ◽  
Vol 10 (15) ◽  
pp. 5051
Author(s):  
Žarko Zečević ◽  
Maja Rolevski
Keyword(s):  
Neural Network ◽  
Computational Complexity ◽  
Low Complexity ◽  
Maximum Power ◽  
Photovoltaic Module ◽  
Neural Network Approach ◽  
Point Tracking ◽  
The Neural Network ◽  
Power Point ◽  
The One

Photovoltaic (PV) modules require maximum power point tracking (MPPT) algorithms to ensure that the amount of power extracted is maximized. In this paper, we propose a low-complexity MPPT algorithm that is based on the neural network (NN) model of the photovoltaic module. Namely, the expression for the output current of the NN model is used to derive the analytical, iterative rules for determining the maximal power point (MPP) voltage and irradiance estimation. In this way, the computational complexity is reduced compared to the other NN-based MPPT methods, in which the optimal voltage is predicted directly from the measurements. The proposed algorithm cannot instantaneously determine the optimal voltage, but it contains a tunable parameter for controlling the trade-off between the tracking speed and computational complexity. Numerical results indicate that the relative error between the actual maximum power and the one obtained by the proposed algorithm is less than 0.1%, which is up to ten times smaller than in the available algorithms.

scholarly journals Performance Analysis of Identification Codes

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1067
Author(s):  
Sencer Derebeyoğlu ◽  
Christian Deppe ◽  
Roberto Ferrara
Keyword(s):  
Performance Analysis ◽  
Computational Cost ◽  
Identification Code ◽  
Code Construction ◽  
Reed Solomon Codes ◽  
Trade Offs ◽  
The One ◽  
The Cost

In this paper, we analyze the construction of identification codes. Identification codes are based on the question: “Is the message I have just received the one I am interested in?”, as opposed to Shannon’s transmission, where the receiver is interested in not only one, but any, message. The advantage of identification is that it allows rates growing double exponentially in the blocklength at the cost of not being able to decode every message, which might be beneficial in certain applications. We focus on a special identification code construction based on two concatenated Reed-Solomon codes and have a closer look at its implementation, analyzing the trade-offs of identification with respect to transmission and the trade-offs introduced by the computational cost of identification codes.

scholarly journals On automorphism groups of low complexity subshifts

2015 ◽  
Vol 36 (1) ◽  
pp. 64-95 ◽  
Author(s):  
SEBASTIÁN DONOSO ◽  
FABIEN DURAND ◽  
ALEJANDRO MAASS ◽  
SAMUEL PETITE
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Polynomial Complexity ◽  
Automorphism Groups ◽  
Low Complexity ◽  
Topological Dynamics ◽  
Main Technique ◽  
Shift Map ◽  
The One ◽  
A Finite Group

In this article, we study the automorphism group$\text{Aut}(X,{\it\sigma})$of subshifts$(X,{\it\sigma})$of low word complexity. In particular, we prove that$\text{Aut}(X,{\it\sigma})$is virtually$\mathbb{Z}$for aperiodic minimal subshifts and certain transitive subshifts with non-superlinear complexity. More precisely, the quotient of this group relative to the one generated by the shift map is a finite group. In addition, we show that any finite group can be obtained in this way. The class considered includes minimal subshifts induced by substitutions, linearly recurrent subshifts and even some subshifts which simultaneously exhibit non-superlinear and superpolynomial complexity along different subsequences. The main technique in this article relies on the study of classical relations among points used in topological dynamics, in particular, asymptotic pairs. Various examples that illustrate the technique developed in this article are provided. In particular, we prove that the group of automorphisms of a$d$-step nilsystem is nilpotent of order$d$and from there we produce minimal subshifts of arbitrarily large polynomial complexity whose automorphism groups are also virtually$\mathbb{Z}$.

Error Probability Analysis of Time-Hopping Biorthogonal Pulse Position Modulation UWB Systems with a RAKE Receiver over Indoor Multi-Path Fading Channels

2012 ◽  
Vol 433-440 ◽  
pp. 2011-2018
Author(s):  
Hao Zhang ◽  
Wei Shi ◽  
Ting Ting Lv ◽  
T. Aaron Gulliver
Keyword(s):  
Fading Channels ◽  
Error Probability ◽  
Channel Model ◽  
Rake Receiver ◽  
Low Complexity ◽  
Probability Analysis ◽  
Ultra Wideband ◽  
Pulse Position Modulation ◽  
Probability Of Error ◽  
Time Hopping

This paper presents the error probability analysis of Time-Hopping Biorthogonal Pulse Position Modulation (TH-BPPM) ultra-wideband (UWB) systems with a RAKE receiver over indoor multi-path fading channels. UWB signals suffer from severe multi-path interference when employed in an indoor fading environment. A RAKE receiver can be used to improve the performance of UWB systems. TH-BPPM has attracted much attention in recent years due to its many advantages, such as low probability of error and low complexity. In this paper, the IEEE 802.15.3a indoor channel model is employed to analyze the performance of TH-BPPM UWB systems with different RAKE receivers. The bit error rate (BER) of ARake, PRake, and SRake TH-BPPM UWB systems is derived. The results indicate that ARake has the best performance, SRake is better than PRake when the number of fingers is same.

scholarly journals Low complexity full duplex MIMO systems: Analog canceler architectures, beamforming design, and future directions

2021 ◽  
Vol 2 (2) ◽  
pp. 109-127
Author(s):  
George C. Alexandropoulos
Keyword(s):  
Communication Systems ◽  
Mimo Systems ◽  
Multiple Input Multiple Output ◽  
Low Complexity ◽  
Full Duplex ◽  
Hardware Complexity ◽  
Algorithmic Solution ◽  
Input Multiple Output ◽  
The One ◽  
Rate Optimization

The hardware complexity of the analog Self-Interference (SI) canceler in conventional full duplex Multiple Input Multiple Output (MIMO) designs mostly scales with the number of transmit and receive antennas, thus exploiting the benefits of analog cancellation becomes impractical for full duplex MIMO transceivers, even for a moderate number of antennas. In this paper, we provide an overview of two recent hardware architectures for the analog canceler comprising of reduced number of cancellation elements, compared to the state of the art, and simple multiplexers for efficient signal routing among the transceiver radio-frequency chains. The one architecture is based on analog taps and the other on AUXiliary (AUX) Transmitters (TXs). In contrast to the available analog cancellation architectures, the values for each tap or each AUX TX and the configuration of the multiplexers are jointly designed with the digital transceiver beamforming filters according to desired performance objectives. We present a general optimization framework for the joint design of analog SI cancellation and digital beamforming, and detail an example algorithmic solution for the sum-rate optimization objective. Our representative computer simulation results demonstrate the superiority, both in terms of hardware complexity and achievable performance, of the presented low complexity full duplex MIMO schemes over the relative available ones in the literature. We conclude the paper with a discussion on recent simultaneous transmit and receive operations capitalizing on the presented architectures, and provide a list of open challenges and research directions for future FD MIMO communication systems, as well as their promising applications.

scholarly journals Low Complexity Channel Model for Mobility Investigations in 5G Networks

2020 ◽  
Author(s):  
Umur Karabulut ◽  
Ahmad Awada ◽  
Ingo Viering ◽  
Andre Noll Barreto ◽  
Gerhard P. Fettweis
Keyword(s):  
Channel Model ◽  
Low Complexity ◽  
5G Networks
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