Application of Quasigroups in Cryptography and Data Communications

In the past decade, quasigroup theory has proven to be a fruitfull field for production of new cryptographic primitives and error-corecting codes. Examples include several finalists in the flagship competitions for new symmetric ciphers, as well as several assimetric proposals and cryptcodes. Since the importance of cryptography and coding theory for secure and reliable data communication can only grow within our modern society, investigating further the power of quasigroups in these fields is highly promising research direction. Our team of researchers has defined several research objectives, which can be devided into four main groups: 1. Design of new cryptosystems or their building blocks based on quasigroups - we plan to make a classification of small quasigroups based on new criteria, as well as to identify new optimal 8–bit S-boxes produced by small quasigroups. The results will be used to design new stream and block ciphers. 2. Cryptanalysis of some cryptosystems based on quasigroups - we will modify and improve the existing automated tools for differential cryptanalysis, so that they can be used for prove the resistance to differential cryptanalysis of several existing ciphers based on quasigroups. This will increase the confidence in these ciphers. 3. Codes based on quasigroups - we will designs new and improve the existing error correcting codes based on combinatorial structures and quasigroups. 4. Algebraic curves over finite fields with their cryptographic applications - using some known and new tools, we will investigate the rational points on algebraic curves over finite fields, and explore the possibilities of applying the results in cryptography

A Quasigroup Based Random Number Generator for Resource Constrained Environments

This paper proposes a pseudo random number generator (PRNG) based on quasigroups. The proposed PRNG has low memory requirements, is autonomous and the quality of the output stream of random numbers is better than other available standard PRNG implementations (commercial and open source) in majority of the tests. Comparisons are done using the benchmark NIST Statistical Test Suite and compression tools. Results are presented for quality of raw stream of random numbers and for encryption results using these random numbers

A Family of Block Ciphers Based on Multiple Quasigroups

A family of block ciphers parametrized by an optimal quasigroup is proposed in this paper. The proposed cipher uses sixteen $4\times 4$ bits S-boxes as an optimal quasigroup of order 16. Since a maximum of $16!$ optimal quasigroups of order 16 can be formed, the family consists of $C^{16!}_1$ cryptosystems. All the sixteen S-boxes have the highest algebraic degree and are optimal with the lowest linearity and differential characteristics. Therefore, these S-boxes are secure against linear and differential attacks. The proposed cipher is analyzed against various attacks, including linear and differential attacks, and we found it to be resistant to these attacks. The proposed cipher is implemented in C++, compared its performance with existing quasigroup based block ciphers, and we found that our proposal is more efficient than existing quasigroup based proposals. We also evaluated our cipher using various statistical tests of the NIST-STS test suite, and we found it to pass these tests. We also established in this study that the randomness of our cipher is almost the same as that of the AES-128

Joint Schemes for Physical Layer Security and Error Correction

The major challenges facing resource constraint wireless devices are error resilience, security and speed. Three joint schemes are presented in this research which could be broadly divided into error correction based and cipher based. The error correction based ciphers take advantage of the properties of LDPC codes and Nordstrom Robinson code. A cipher-based cryptosystem is also presented in this research. The complexity of this scheme is reduced compared to conventional schemes. The securities of the ciphers are analyzed against known-plaintext and chosen-plaintext attacks and are found to be secure. Randomization test was also conducted on these schemes and the results are presented. For the proof of concept, the schemes were implemented in software and hardware and these shows a reduction in hardware usage compared to conventional schemes. As a result, joint schemes for error correction and security provide security to the physical layer of wireless communication systems, a layer in the protocol stack where currently little or no security is implemented. In this physical layer security approach, the properties of powerful error correcting codes are exploited to deliver reliability to the intended parties, high security against eavesdroppers and efficiency in communication system. The notion of a highly secure and reliable physical layer has the potential to significantly change how communication system designers and users think of the physical layer since the error control codes employed in this work will have the dual roles of both reliability and security

A Note on Attribute-Based Group Homomorphic Encryption

Group Homomorphic Encryption (GHE), formally defined by Armknecht, Katzenbeisser and Peter, is a public-key encryption primitive where the decryption algorithm is a group homomorphism. Hence it supports homomorphic evaluation of a single algebraic operation such as modular addition or modular multiplication. Most classical homomorphic encryption schemes such as as Goldwasser-Micali and Paillier are instances of GHE. In this work, we extend GHE to the attribute-based setting. We introduce and formally define the notion of Attribute-Based GHE (ABGHE) and explore its properties. We then examine the algebraic structure on attributes induced by the group operation in an ABGHE. This algebraic stricture is a bounded semilattice. We consider some possible semilattices and how they can be realized by an ABGHE supporting inner product predicates. We then examine existing schemes from the literature and show that they meet our definition of ABGHE for either an additive or multiplicative homomorphism. Some of these schemes are in fact Identity-Based Group Homomorphic Encryption (IBGHE) schemes i.e. instances of ABGHE whose class of access policies are point functions. We then present a possibility result for IBGHE from indistinguishability obfuscation for any group for which a (public-key) GHE scheme exists

Adaptive Encryption Techniques In Wireless Communication Channels With Tradeoffs Between Communication Reliability And Security

Encryption is a vital process to ensure the confidentiality of the information transmitted over an insecure wireless channel. However, the nature of the wireless channel tends to deteriorate because of noise, interference and fading. Therefore, a symmetrically encrypted transmitted signal will be received with some amount of error. Consequently, due to the strict avalanche criterion (sac), this error propagates during the decryption process, resulting in half the bits (on average) after decryption to be in error. In order to alleviate this amount of error, smart coding techniques and/or new encryption algorithms that take into account the nature of wireless channels are required. The solution for this problem could involve increasing the block and key lengths which might degrade the throughput of the channel. Moreover, these solutions might significantly increase the complexity of the encryption algorithms and hence to increase the cost of its implementation and use. Two main approaches have been folloto solve this problem, the first approach is based on developing an effective coding schemes and mechanisms, in order to minimize and correct the errors introduced by the channel. The second approach is more focused on inventing and implementing new encryption algorithms that encounter less error propagation, by alleviating the sac effect. Most of the research done using these two approaches lacked the comprehensiveness in their designs. Some of these works focused on improving the error performance and/or enhancing the security on the cost of complexity and throughput. In this work, we focus on solving the problem of encryption in wireless channels in a comprehensive way that considers all of the factors in its structure (error performance, security and complexity). New encryption algorithms are proposed, which are modifications to the standardized encryption algorithms and are shown to outperform the use of these algorithms in wireless channels in terms of security and error performance with a slight addition in the complexity. We introduce new modifications that improve the error performance for a certain required security level while achieving the highest possible throughput. We show how our proposed algorithm outperforms the use of other encryption algorithms in terms of the error performance, throughput, complexity, and is secure against all known encryption attacks. In addition, we study the effect of each round and s-box in symmetric encryption algorithms on the overall probability of correct reception at the receiver after encryption and the effect on the security is analyzed as well. Moreover, we perform a complete security, complexity and energy consumption analysis to evaluate the new developed encryption techniques and procedures. We use both analytical computations and computer simulations to evaluate the effectiveness of every modification we introduce in our proposed designs

Patterns and Signals of Biology: An Emphasis On The Role of Post Translational Modifications in Proteomes for Function and Evolutionary Progression

After synthesis, a protein is still immature until it has been customized for a specific task. Post-translational modifications (PTMs) are steps in biosynthesis to perform this customization of protein for unique functionalities. PTMs are also important to protein survival because they rapidly enable protein adaptation to environmental stress factors by conformation change. The overarching contribution of this thesis is the construction of a computational profiling framework for the study of biological signals stemming from PTMs associated with stressed proteins. In particular, this work has been developed to predict and detect the biological mechanisms involved in types of stress response with PTMs in mitochondrial (Mt) and non-Mt protein. Before any mechanism can be studied, there must first be some evidence of its existence. This evidence takes the form of signals such as biases of biological actors and types of protein interaction. Our framework has been developed to locate these signals, distilled from “Big Data” resources such as public databases and the the entire PubMed literature corpus. We apply this framework to study the signals to learn about protein stress responses involving PTMs, modification sites (MSs). We developed of this framework, and its approach to analysis, according to three main facets: (1) by statistical evaluation to determine patterns of signal dominance throughout large volumes of data, (2) by signal location to track down the regions where the mechanisms must be found according to the types and numbers of associated actors at relevant regions in protein, and (3) by text mining to determine how these signals have been previously investigated by researchers. The results gained from our framework enable us to uncover the PTM actors, MSs and protein domains which are the major components of particular stress response mechanisms and may play roles in protein malfunction and disease