Quadratic compact knapsack public-key cryptosystem

AbstractKnapsack-type cryptosystems were among the first public-key cryptographic schemes to be invented. Their NP-completeness nature and the high speed in encryption/decryption made them very attractive. However, these cryptosystems were shown to be vulnerable to the low-density subset-sum attacks or some key-recovery attacks. In this paper, additive knapsack-type public-key cryptography is reconsidered. We propose a knapsack-type public-key cryptosystem by introducing an easy quadratic compact knapsack problem. The system uses the Chinese remainder theorem to disguise the easy knapsack sequence. The encryption function of the system is nonlinear about the message vector. Under the relinearization attack model, the system enjoys a high density. We show that the knapsack cryptosystem is secure against the low-density subset-sum attacks by observing that the underlying compact knapsack problem has exponentially many solutions. It is shown that the proposed cryptosystem is also secure against some brute-force attacks and some known key-recovery attacks including the simultaneous Diophantine approximation attack and the orthogonal lattice attack

CRYSTALS-Dilithium: A lattice-based digital signature scheme

In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes

A tight security reduction in the quantum random oracle model for code-based signature schemes

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes

Lattice Sieving With G6K

Recent advances in quantum computing threaten the cryptography we use today. This has led to a need for new cryptographic algorithms that are safe against quantum computers. The American standardization organization NIST has now chosen four quantum-safe algorithms in their process of finding new cryptographic standards. Three out of the four algorithms are based on the hardness of finding a shortest vector in a lattice. The biggest threat to such schemes is lattice reduction. One of the best tools used for lattice reduction is the G6K framework. In this thesis, we study sieving algorithms and lattice reduction strategies implemented in G6K. After an introduction to cryptography, we go over the necessary preliminary lattice theory, important concepts, and related problems. Further, we look at lattice reduction where we study different approaches with a main focus on lattice sieving. We then explore the G6K framework, before finally performing some experiments using G6K. The results we get often depend on what type of lattice we are working on. Our experiments show that it is still possible to improve G6K for solving the shortest vector problem for some lattice types.Masteroppgave i informatikkINF399MAMN-INFMAMN-PRO

Overview of blockchain technology cryptographic security

This thesis work is aimed at developing understanding of the hash functions and algorithms being used in blockchain technologies Bitcoin in comparison to Ethereum and private blockchain hash functions. This study attempts to answer one fundamental research question: “What considerations are important in assessing blockchain cryptographic security, with an emphasis on hash functions”. The study was carried out qualitatively using a desk research approach and combining this approach with using two public blockchains-based cryptocurrencies; Ethereum and Bitcoin as case studies. The research aims to provide a holistic view of blockchain cryptographic security comparing Bitcoin and Ethereum as use cases, and thus providing a consolidated document which students studying cryptography can access to obtain a better understanding of what is involved in blockchain security. From an academic perspective, the research aims at providing a model which can be used in assessing what is important to consider in the cryptographic security of blockchains. Three main categories of factors considered were presented in the proposed model which were strategical factors, complexity attributes and technical drivers. This results in a base crucial metrics such as absence of secret seeds, efficiency of verification, preimage collision resistance, fixed output size, low collision probability, and even distribution of preimages in output