Some Notes on Code-Based Cryptography

This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma