Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations

In this paper we propose a definition and construction of a new family of one-way candidate functions ${\cal R}_N:Q^N \to Q^N$, where $Q=\{0,1,...,s-1\}$ is an alphabet with $s$ elements. Special instances of these functions can have the additional property to be permutations (i.e. one-way permutations). These one-way functions have the property that for achieving the security level of $2^n$ computations in order to invert them, only $n$ bits of input are needed. The construction is based on quasigroup string transformations. Since quasigroups in general do not have algebraic properties such as associativity, commutativity, neutral elements, inverting these functions seems to require exponentially many readings from the lookup table that defines them (a Latin Square) in order to check the satisfiability for the initial conditions, thus making them natural candidates for one-way functions.Comment: Submitetd to conferenc

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

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

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

A Key Scheduling Algorithm Based on Dynamic Quasigroup String Transformation and All-Or-Nothing Key Derivation Function

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. 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 meant for secret keys. 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 “Isotopism”, which literally means Different quasigroups that has the same order of elements but different arrangements. This paper proposed a Dynamic Key Scheduling Algorithm (KSA) using Isotope of a quasigroup as the dynamic substitution table. The proposed algorithm is a modification and upgrade to Allor-nothing Key Derivation Function (AKDF). To minimize the complexity of the algorithm, a method of generating Isotope from a non-associative quasigroup using one permutation is achieved. 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 will be validated using the Randomness test proposed and recommended by NIST, Avalanche and Correlation Assessment test

Breaking Another Quasigroup-Based Cryptographic Scheme

In their paper ``A Quasigroup Based Random Number Generator for Resource Constrained Environments , the authors Matthew Battey and Abhishek Parakh propose the pseudo random number generator LOQG PRNG 256. We show several highly efficient attacks on LOQG PRNG 256

A Random Number Generator Using Ring Oscillators and SHA-256 as Post-Processing

Today, cryptographic security depends primarily on having strong keys and keeping them secret. The keys should be produced by a reliable and robust to external manipulations generators of random numbers. To hamper different attacks, the generators should be implemented in the same chip as a cryptographic system using random numbers. It forces a designer to create a random number generator purely digitally. Unfortunately, the obtained sequences are biased and do not pass many statistical tests. Therefore an output of the random number generator has to be subjected to a transformation called post-processing. In this paper the hash function SHA-256 as post-processing of bits produced by a combined random bit generator using jitter observed in ring oscillators (ROs) is proposed. All components – the random number generator and the SHA-256, are implemented in a single Field Programmable Gate Array (FPGA). We expect that the proposed solution, implemented in the same FPGA together with a cryptographic system, is more attack-resistant owing to many sources of randomness with significantly different nominal frequencies

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing