Примена на квазигрупи во криптокодирање и блок-вериги

Abstract

In this doctoral dissertation, the research is focused in two directions. The first one is the application of quasigroups for designing error-correcting cryptocodes. Random codes based on quasigroups (RCBQ) are considered. These codes are proposed for the first time by D. Gligoroski, S. Markovski and Lj. Kocarev and they are a combination of cryptographic algorithms and error-corecting codes and depend on several parameters. The speed of the decoding process is one of the biggest problems for these codes. In order to increase the speed of the decoding process, A. Popovska-Mitroviќ, S. Markovski and V. Bakeva define a new coding/ decoding algorithm called Cut-Decoding algorithm. Then the same authors proposed a modification of this algorithm and the modified coding/decoding algorithm is called 4-Sets-Cut-Decoding algorithm. In this doctoral dissertation the performance of RCBQ for transmission through Gaussian channel are considered. Especially, we investigate their performances for image transmission and compare the results obtained with Cut-Decoding algorithm and 4-Sets-Cut-Decoding algorithm. Also, a filter for visually enhance of the damage caused by errors that occur when images are transmitted through the Gaussian channel is defined. To get an even faster decoding process, we define encoding/decoding algorithms, called Fast-Cut-Decoding and Fast-4-Sets-Cut-Decoding algorithm. Performances of various RCBQ decoding algorithms (Cut-Decoding, Fast-Cut-Decoding, 4-Sets-Cut-Decoding and Fast-4-Sets-Cut-Decoding algorithms) for code with rate R = 1/4 and R = 1/8 and different values of SNR in Gaussian channel are analyzed. Also, in order to improve the quality of audio files transmitted through the Gaussian channel we define a filter. Furthermore, the performance of cryptcodes based on quasigroups for transmission through the channel with burst errors are studied. For simulation a channel with burst errors, Gilbert-Elliott model is used. We define new burst algorithms (Burst-Cut-Decoding and Burst-4-Sets-Cut-Decoding algorithms), which improve the decoding process in channels with burst errors. We analyze the performances of different RCBQ decoding algorithms (Cut-Decoding, Burst-Cut-Decoding, 4- Sets-Cut-Decoding and Burst-4-Sets-Cut-Decoding algorithms) for transmission of ordinary messages and images for code with rate R = 1/4 and R = 1/8 and different combinations of transition probabilities from good to bad and from bad to bad state. In order to adopt the fast RCBQ algorithms ffor transmission through a burst channel, we define two new encoding/decoding algorithms - called called FastBCut- Decoding and FastB-4-Sets-Cut-Decoding algorithms. In these algorithms we apply interleaving on the obtained codewords and deinterleaving on the received messages on the output of the channel, after dividing in two (or four) parts. The performance of FastB-Cut-Decoding and FastB-4-Sets-Cut-Decoding algorithms for code for rate R = 1/4 and R = 1/8, for transmission through Gilbert-Elliot channel are analyzed. The experiments were made for different combinations of transition probabilities from good to bad and from bad to bad state. The second direction of research in this thesis is application of quasigroups in Blockchain to speed up transmission and reduce storage space. Initially, research was done on Blockchain technology. The basic concepts used in this technology, the way how the blockchain works, its basic features, as well as its application in BigData and the Internet of Things are discussed. One of the main problems in blockchains is the speed of transmission. Network coding as a technique that improves network power and provides high security is one of the solutions to this problem. In order to provide a faster and simpler decoding process in network coding, we define a new algorithm for network coding based on quasigroups, that increase the conductivity in the “butterfly” communications network. This algorithm is simpler and faster than the algorithms used in linear network coding. On the other side, Blockchain establishes a cryptographically secure structure for storing hash-chain transactions. One of the main limitations of this technology is the size of the storage space because each node must keep a copy of the main book of all transactions. As the number of transactions increases, so does the amount of storage required to store them, which limits the scalability of this system. One way to reduce the space required for storage is reducing the size of the transaction stored in the Blockchain blocks and reduce transaction storage costs. In this dissertation, we propose an algorithm for reducing the storage space in the blockchain using Shamir’s secret sharing scheme.