The Quasigroup Block Cipher and its Analysis

This thesis discusses the Quasigroup Block Cipher (QGBC) and its analysis. We first present the basic form of the QGBC and then follow with improvements in memory consumption and security. As a means of analyzing the system, we utilize tools such as the NIST Statistical Test Suite, auto and crosscorrelation, then linear and algebraic cryptanalysis. Finally, as we review the results of these analyses, we propose improvements and suggest an algorithm suitable for low-cost FPGA implementation

Dynamic key scheduling algorithm for block ciphers using quasigroup string transformation

Cryptographic ciphers depend on how quickly the key affects the output of the ciphers (ciphertext). Keys are traditionally generated from small size input (seed) to a bigger size random key(s). Key scheduling algorithm (KSA) is the mechanism that generates and schedules all sub-keys for each round of encryption. Researches have suggested that sub-keys should be generated separately to avoid related-key attack. Similarly, the key space should be disproportionately large to resist any attack on the secret key. To archive that, some algorithms adopt the use of matrixes such as quasigroup, Hybrid cubes and substitution box (S-box) to generate the encryption keys. Quasigroup has other algebraic property called “Isotophism”, which literally means Different quasigroups that has the same order of elements but different arrangements can be generated from the existing one. This research proposed a Dynamic Key Scheduling Algorithm (KSA) using isotope of a quasigroup as the dynamic substitution table. A method of generating isotope from a non-associative quasigroup using one permutation with full inheritance is achieved. The generic quasigroup string transformation has been analyzed and it is found to be vulnerable to ciphertext only attack which eventually led to the proposal of a new quasigroup string transformation in this research to assess its strength as it has never been analyzed nor properly implemented before. Based on the dynamic shapeless quasigroup and the proposed new string transformation, a Dynamic Key Scheduling Algorithm (DKSA) is developed. To validate the findings, non-associativity of the generated isotopes has been tested and the generated isotopes appeared to be non-associative. Furthermore, the proposed KSA algorithm has been validated using the randomness test proposed and recommended by NIST, avalanche test and has achieved remarkable result of 94%, brute force and correlation assessment test with -0.000449 correlations. It was fully implemented in a modified Rijndael block cipher to validate it performance and it has produced a remarkable result of 3.35332 entropy

NaSHA

We propose the NaSHA-(m, k, r) family of cryptographic hash functions, based on quasigroup transformations. We use huge quasigroups defined by extended Feistel networks from small bijections and a novel design principle: the quasigroup used in every iteration of the compression function is different and depends on the processed message block. We present in all details of the implementations of NaSHA-(m, 2, 6) where m in {224, 256, 384, 512}

Abstracts of Ph.D. theses in mathematics

summary:Leischner, Pavel: Spatial imagination development of the secondary school pupils. Mašíček, Libor: Diagnostics and sensitivity of robust models. Duintjer Tebbens, Erik Jurjen: Modern methods for solving linear problems. Matonoha, Ctirad: Numerical realization of trust region methods. Duda, Jakub: Delta convexity, metric projection and negligible sets. Smrčka, Michael: Choquet's theory in function spaces. Hanika, Jiří: Search problems and bounded arithmetic. Pawlas, Zbyněk: Asymptotics in stochastic geometry. Bodlák, Karel: Methods of stereology and spatial statistics in applications. Čapek, Václav: M-smoothers Zvára, Petr: Prediction in non-linear autoregressive processes. Blanda, Jiří: Pricing of life insurance products Finfrle, Pavel: Model for calculation of liability value arising from life insurance. Finěk Václav: Orthonormal wavelets and their applications. Stanovský David : Left distributive left quasigroups. Koblížková, Michaela: Polyhedra and secondary school mathematics. Krýsl, Svatopluk: Invariant differential operators for projective contact geometries. Šmíd, Dalibor: Properties of invariant differential operators. Šmíd, Martin: Notes on approximation of stochastic programming problems. Komárková, Lenka: Change point problem for censored data. Kechlibar, Marian: Commutative algebra and cryptography

On free quasigroups and quasigroup representations

This work consists of three parts. The discussion begins with \emph{linear quasigroups}. For a unital ring $S$, an $S$-linear quasigroup is a unital $S$-module, with automorphisms $\rho$ and $\lambda$ giving a (nonassociative) multiplication $x\cdot y=x^\rho+y^\lambda$. If $S$ is the field of complex numbers, then ordinary characters provide a complete linear isomorphism invariant for finite-dimensional $S$-linear quasigroups. Over other rings, it is an open problem to determine tractably computable isomorphism invariants. The paper investigates this isomorphism problem for $\mathbb{Z}$-linear quasigroups. We consider the extent to which ordinary characters classify $\mathbb{Z}$-linear quasigroups and their representations of the free group on two generators. We exhibit non-isomorphic $\mathbb{Z}$-linear quasigroups with the same ordinary character. For a subclass of $\mathbb{Z}$-linear quasigroups, equivalences of the corresponding ordinary representations are realized by permutational intertwinings. This leads to a new equivalence relation on $\mathbb{Z}$-linear quasigroups, namely permutational similarity. Like the earlier concept of central isotopy, permutational similarity is intermediate between isomorphism and isotopy. The story progresses with a representation of the free quasigroup on a single generator. This provides the motivation behind the study of \emph{peri-Catalan numbers}. While Catalan numbers index the number of length $n$ magma words in a single generator, peri-Catalan numbers index the number of length $n$ reduced form quasigroup words in a single generator. We derive a recursive formula for the $n$-th peri-Catalan number. This is a new sequence in that it is not on the Online Encyclopedia of Integer Sequences

Quantifying Shannon's Work Function for Cryptanalytic Attacks

Attacks on cryptographic systems are limited by the available computational resources. A theoretical understanding of these resource limitations is needed to evaluate the security of cryptographic primitives and procedures. This study uses an Attacker versus Environment game formalism based on computability logic to quantify Shannon's work function and evaluate resource use in cryptanalysis. A simple cost function is defined which allows to quantify a wide range of theoretical and real computational resources. With this approach the use of custom hardware, e.g., FPGA boards, in cryptanalysis can be analyzed. Applied to real cryptanalytic problems, it raises, for instance, the expectation that the computer time needed to break some simple 90 bit strong cryptographic primitives might theoretically be less than two years.Comment: 19 page

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

Study of SMS security as part of an electronic voting system

This thesis report is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Computer Science and Engineering, 2006.Cataloged from PDF version of thesis report.Includes bibliographical references (page 48).E-voting is a new technology in voting system. Recently it was experimented in UK. Basically, this system is proposed to work via Short Message System (SMS). Using secure messaging system we are trying to develop the e-voting system here in our country. Our goal is to develop a system, which will be able to send SMS from a registered cell phone to a server located in the base polling station and cast a vote for a voter. The system must be secured so that while voting, no outside interference can be made to change the vote. So, there will be no tension of casting false vote. By the help of this system our voters will be able to cast their votes in a secure way and also the results will be available immediately when the vote casting finishes. This is going to be a pioneer change in our voting system. Some work on this proposed system has already been done. We wish to carry out the proposed system into further details. That is security aspects and implementation.B. Computer Science and Engineerin