The Niederreiter cryptosystem and Quasi-Cyclic codes

McEliece and Niederreiter cryptosystems are robust and versatile cryptosystems. These cryptosystems work with any linear error-correcting codes. They are popular these days because they can be quantum-secure. In this paper, we study the Niederreiter cryptosystem using quasi-cyclic codes. We prove, if these quasi-cyclic codes satisfy certain conditions, the corresponding Niederreiter cryptosystem is resistant to the hidden subgroup problem using quantum Fourier sampling. Our proof requires the classification of finite simple groups

Quantum algorithm for the Boolean hidden shift problem

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a whole range of underlying groups. In a way, this distinguishes it from the hidden subgroup problem where more stringent requirements about the existence of a periodic subgroup have to be made. And yet, the hidden shift problem proves to be rich enough to capture interesting features of problems of algebraic, geometric, and combinatorial flavor. We present a quantum algorithm to identify the hidden shift for any Boolean function. Using Fourier analysis for Boolean functions we relate the time and query complexity of the algorithm to an intrinsic property of the function, namely its minimum influence. We show that for randomly chosen functions the time complexity of the algorithm is polynomial. Based on this we show an average case exponential separation between classical and quantum time complexity. A perhaps interesting aspect of this work is that, while the extremal case of the Boolean hidden shift problem over so-called bent functions can be reduced to a hidden subgroup problem over an abelian group, the more general case studied here does not seem to allow such a reduction.Comment: 10 pages, 1 figur

Cryptanalysis of the McEliece Cryptosystem on GPGPUs

The linear code based McEliece cryptosystem is potentially promising as a so-called post-quantum public key cryptosystem because thus far it has resisted quantum cryptanalysis, but to be considered secure, the cryptosystem must resist other attacks as well. In 2011, Bernstein et al. introduced the Ball Collision Decoding (BCD) attack on McEliece which is a significant improvement in asymptotic complexity over the previous best known attack. We implement this attack on GPUs, which offer a parallel architecture that is well-suited to the matrix operations used in the attack and decrease the asymptotic run-time. Our implementation executes the attack more than twice as fast as the reference implementation and could be used for a practical attack on the original McEliece parameters

Post-quantum blockchain for internet of things domain

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonIn the evolving realm of quantum computing, emerging advancements reveal substantial challenges and threats to existing cryptographic infrastructures, particularly impacting blockchain technologies. These are pivotal for securing the Internet of Things (IoT) ecosystems. The traditional blockchain structures, integral to myriad IoT applications, are susceptible to potential quantum computations, emphasizing an urgent need for innovations in post-quantum blockchain solutions to reinforce security in the expansive domain of IoT. This PhD thesis delves into the crucial exploration and meticulous examination of the development and implementation of post-quantum blockchain within the IoT landscape, focusing on the incorporation of advanced post-quantum cryptographic algorithms in Hyperledger Fabric, a forefront blockchain platform renowned for its versatility and robustness. The primary aim is to discern viable post-quantum cryptographic solutions capable of fortifying blockchain systems against impending quantum threats enhancing security and reliability in IoT applications. The research comprehensively evaluates various post-quantum public-key generation and digital signature algorithms, performing detailed analyses of their computational time and memory usage to identify optimal candidates. Furthermore, the thesis proposes an innovative lattice-based digital signature scheme Fast-Fourier Lattice-based Compact Signature over NTRU (Falcon), which leverages the Monte Carlo Markov Chain (MCMC) algorithm as a trapdoor sampler to augment its security attributes. The research introduces a post-quantum version of the Hyperledger Fabric blockchain that integrates post-quantum signatures. The system utilizes the Open Quantum Safe (OQS) library, rigorously tested against NIST round 3 candidates for optimal performance. The study highlights the capability to manage IoT data securely on the post-quantum Hyperledger Fabric blockchain through the Message Queue Telemetry Transport (MQTT) protocol. Such a configuration ensures safe data transfer from IoT sensors directly to the blockchain nodes, securing the processing and recording of sensor data within the node ledger. The research addresses the multifaceted challenges of quantum computing advancements and significantly contributes to establishing secure, efficient, and resilient post-quantum blockchain infrastructures tailored explicitly for the IoT domain. These findings are instrumental in elevating the security paradigms of IoT systems against quantum vulnerabilities and catalysing innovations in post-quantum cryptography and blockchain technologies. Furthermore, this thesis introduces strategies for the optimization of performance and scalability of post-quantum blockchain solutions and explores alternative, energy-efficient consensus mechanisms such as the Raft and Stellar Consensus Protocol (SCP), providing sustainable alternatives to the conventional Proof-of-Work (PoW) approach. A critical insight emphasized throughout this thesis is the imperative of synergistic collaboration among academia, industry, and regulatory bodies. This collaboration is pivotal to expedite the adoption and standardization of post-quantum blockchain solutions, fostering the development of interoperable and standardized technologies enriched with robust security and privacy frameworks for end users. In conclusion, this thesis furnishes profound insights and substantial contributions to implementing post-quantum blockchain in the IoT domain. It delineates original contributions to the knowledge and practices in the field, offering practical solutions and advancing the state-of-the-art in post-quantum cryptography and blockchain research, thereby paving the way for a secure and resilient future for interconnected IoT systems

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

A Distinguisher for High Rate McEliece Cryptosystems

International audienceThe Goppa Code Distinguishing (GD) problem consists in distinguishing the matrix of a Goppa code from a random matrix. The hardness of this problem is an assumption to prove the security of code-based cryptographic primitives such as McEliece's cryptosystem. Up to now, it is widely believed that the GD problem is a hard decision problem. We present the first method allowing to distinguish alternant and Goppa codes over any field. Our technique can solve the GD problem in polynomial-time provided that the codes have sufficiently large rates. The key ingredient is an algebraic characterization of the key-recovery problem. The idea is to consider the rank of a linear system which is obtained by linearizing a particular polynomial system describing a key-recovery attack. Experimentally it appears that this dimension depends on the type of code. Explicit formulas derived from extensive experimentations for the rank are provided for "generic" random, alternant, and Goppa codes over any alphabet. Finally, we give theoretical explanations of these formulas in the case of random codes, alternant codes over any field of characteristic two and binary Goppa codes