This book chapter is a part of the Springer Lecture Notes in Mathematics: Coding Theory and Applications V, Applications of Coding Theory in Quantum Computing and Cryptography
The improvements on quantum technology are threatening our daily cybersecurity, as a capable quantum computer can break all currently employed asymmetric cryptosystems. In preparation for the quantum-era the National Institute of Standards and Technology (NIST) has initiated in 2016 a standardization process for public-key encryption (PKE) schemes, key-encapsulation mechanisms (KEM) and digital signature schemes. In 2023, NIST made an additional call for post-quantum signatures. With this chapter we aim at providing a survey on code-based cryptography, focusing on PKEs and signature schemes. We cover the main frameworks introduced in code-based cryptography and analyze their security assumptions. We provide the mathematical background in a lecture notes style, with the intention of reaching a wider audience.
We give a decoding algorithm for a class of error-correcting codes, which can be used in the DHH-cryptosystem, which is a candidate for post-quantum cryptography, since it is of McEliece type. Furthermore, we implement the encryption and decryption algorithms for this cryptosystem and investigate its performance.
We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.
The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.
In this paper we present a modification of Reed-Solomon codes that beats the Guruwami-Sudan $1-\sqrt{R}$ decoding radius of Reed-Solomon codes at low rates $R$. The idea is to choose Reed-Solomon codes $U$ and $V$ with appropriate rates in a $\left( U\mid U+V\right)$ construction and to decode them with the Koetter-Vardy soft information decoder. We suggest to use a slightly more general version of these codes (but which has the same decoding performances as the $\left( U\mid U+V\right)$-construction) for code-based cryptography, namely to build a McEliece scheme. The point is here that these …
Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through intensive Monte Carlo simulations. However, several applications, like code-based cryptography, need guaranteed low values of the error rate, which are infeasible to assess through simulations, thus requiring the development of theoretical models for the error rate of these codes under iterative decoding. Some models of this type already exist, but become computat…
We surveyed 97 developers who had used cryptography in open-source projects, in the hope of identifying developer security and cryptography practices. We asked them about individual and company-level practices, and divided respondents into three groups (i.e., high, medium, and low) based on their level of knowledge. We found differences between the high-profile developers and the other two groups. For instance, high-profile developers have more years of experience in programming, have attended more security and cryptography courses, have more background in security, are highly concerned about …
Machine learning techniques have had a long list of applications in recent years. However, the use of machine learning in information and network security is not new. Machine learning and cryptography have many things in common. The most apparent is the processing of large amounts of data and large search spaces. In its varying techniques, machine learning has been an interesting field of study with massive potential for application. In the past three decades, machine learning techniques, whether supervised or unsupervised, have been applied in cryptographic algorithms, cryptanalysis, steganog…
Due to successful applications of data analysis technologies in many fields, various institutions have accumulated a large amount of data to improve their services. As the speed of data collection has increased dramatically over the last few years, an increasing number of users are growing concerned about their personal information. Therefore, privacy preservation has become an urgent problem to be solved. Differential privacy as a strong privacy preservation tool has attracted significant attention. In this survey, we focus on improving utility of between differentially private mechanisms thr…
With the advent of advanced technology, IoT introduces a vast number of devices connecting with each other and collecting a sheer volume of data. Thus, the demands of IoT security is paramount. Cryptography is being used to secure the networks for authentication, confidentiality, data integrity and access control. However, due to the resource constraint nature of IoT devices, the traditional cryptographic protocols may not be suited in all IoT environments. Researchers, as a result, have been proposing various lightweight cryptographic algorithms and protocols. In this paper, we discuss the st…
This survey provides a comparative overview of code-based signature schemes with respect to security and performance. Furthermore, we explicitly describe serveral code-based signature schemes with additional properties such as identity-based, threshold ring and blind signatures.
This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying code-based cryptography. Here, we briefly describe the first scheme of code based public key cryptosystems given by R. J. McEliece in 1978 and its improved version given by H. Niederreiter in 1986. We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD). Successf…
We introduce a new family of rank metric codes: Low Rank Parity Check codes (LRPC), for which we propose an efficient probabilistic decoding algorithm. This family of codes can be seen as the equivalent of classical LDPC codes for the rank metric. We then use these codes to design cryptosystems à la McEliece: more precisely we propose two schemes for key encapsulation mechanism (KEM) and public key encryption (PKE). Unlike rank metric codes used in previous encryption algorithms -notably Gabidulin codes - LRPC codes have a very weak algebraic structure. Our cryptosystems can be seen as an equi…
Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The strength of computing machinery has made these techniques theoretically susceptible to attack and hence recently there has been an active line of research to develop cryptosystems and key exchange protocols using noncommutative cryptographic platforms. This line of investigation has been given the broad title of noncommutative algebraic cryptography. This wa…
Subcodes of Lambda-Gabidulin Codes for Compact-Ciphertext Cryptography
University of Yaounde I（雅温得第一大学）；National Advanced School of Engineering of Yaoundé, University of Yaounde I（雅温得国立高等工程学院，雅温得第一大学）；The University of Bamenda（班达马大学）；Université Cheikh Anta Diop de Dakar（达喀尔谢赫安塔·迪奥普大学）；Higher Teacher Training College, University of Yaounde I（雅温得第一大学高等师资培训学院）
The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards. We discuss the chronology of attacks on Elliptic Curve Discrete Logarithm Problem and investigate their countermeasures to highlight the evolved selection criteria of cryptographically safe elliptic curves. Further, two popular deterministic and random approaches for selection of Short Weierstrass elliptic curve for cryptography are evaluated from computational, security and…
Side-channel attacks have become a severe threat to the confidentiality of computer applications and systems. One popular type of such attacks is the microarchitectural attack, where the adversary exploits the hardware features to break the protection enforced by the operating system and steal the secrets from the program. In this paper, we systematize microarchitectural side channels with a focus on attacks and defenses in cryptographic applications. We make three contributions. (1) We survey past research literature to categorize microarchitectural side-channel attacks. Since these are hardw…
Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups. Moreover, the non-virtually nilpotent ones exhibit an exponential growth rate. These properties make them suitable for use in group-based cryptography, which was proposed in 2004 by Eick and Kahrobaei. Since then, many cryptosystems have been created that employ polycyclic groups. These include key exchanges such as non-commutative ElGamal, authentication schemes …
Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today's world as the information to be sent might be of invaluable importance to both the sender and the receiver. Various cryptographic techniques ensure that even if an intruder intercepts the sent information, he is not able to decipher it thus render ending it useless for the intruder. Cryptography can be grouped into two types, that is Symmetric key cryptography and Asymmetric key cryptography. Symmetric key cryptography uses the…
In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisenträger-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] gives rise to interesting questions about number fields. We extend these attacks and survey related open problems in number theory, including spectral distortion of an algebraic number and its relationship to Mahler measure, the monogenic property for the ring of integers of a number field, and the size of elements of small order modulo q.
Fighting against computer malware require a mandatory step of reverse engineering. As soon as the code has been disassemblied/decompiled (including a dynamic analysis step), there is a hope to understand what the malware actually does and to implement a detection mean. This also applies to protection of software whenever one wishes to analyze them. In this paper, we show how to amour code in such a way that reserse engineering techniques (static and dymanic) are absolutely impossible by combining malicious cryptography techniques developped in our laboratory and new types of programming (k-ary…
Quantum-resistant cryptography is cryptography that aims to deliver cryptographic functions and protocols that remain secure even if large-scale fault-tolerant quantum computers are built. NIST will soon announce the first selected public-key cryptography algorithms in its Post-Quantum Cryptography (PQC) standardization which is the most important current effort in the field of quantum-resistant cryptography. This report provides an overview to security experts who do not yet have a deep understanding of quantum-resistant cryptography. It surveys the computational model of quantum computers; t…
Traditional and lightweight cryptography primitives and protocols are insecure against quantum attacks. Thus, a real-time application using traditional or lightweight cryptography primitives and protocols does not ensure full-proof security. Post-quantum Cryptography is important for the Internet of Things (IoT) due to its security against Quantum attacks. This paper offers a broad literature analysis of post-quantum cryptography for IoT networks, including the challenges and research directions to adopt in real-time applications. The work draws focus towards post-quantum cryptosystems that ar…
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem such new settings secure, we first need to understand and analyze the complexity of the underlying problem, in this case the problem of decoding a random interleaved code. A simple approach to decode such codes, would be to randomly choose a vector in the row span of the received matrix and run a classical information set decoding algorithm on this erroneous…
The conventional cryptography solutions are ill-suited to strict memory, size and power limitations of resource-constrained devices, so lightweight cryptography solutions have been specifically developed for this type of applications. In this domain of cryptography, the term lightweight never refers to inadequately low security, but rather to establishing the best balance to maintain sufficient security. This paper presents the first comprehensive survey evaluation of lightweight block ciphers in terms of their speed, cost, performance, and balanced efficiency in hardware implementation, and f…
Quantum computing and quantum communications are exciting new frontiers in computing and communications. Indeed, the massive investments made by the governments of the US, China, and EU in these new technologies are not a secret and are based on the expected potential of these technologies to revolutionize communications, computing, and security. In addition to several field trials and hero experiments, a number of companies such as Google and IBM are actively working in these areas and some have already reported impressive demonstrations in the past few years. While there is some skepticism a…
The security of public-key cryptosystems is mostly based on number theoretic problems like factorization and the discrete logarithm. There exists an algorithm which solves these problems in polynomial time using a quantum computer. Hence, these cryptosystems will be broken as soon as quantum computers emerge. Code-based cryptography is an alternative which resists quantum computers since its security is based on an NP-complete problem, namely decoding of random linear codes. The McEliece cryptosystem is the most prominent scheme to realize code-based cryptography. Many codeclasses were propose…
In this paper the author present a new technique of using QR Codes (commonly known as 'Quick Respond Codes') in the field of Cryptography. QR Codes are mainly used to convey or store messages because they have higher or large storage capacity than any other normal conventional 'barcodes'. In this paper the primary focus will be on storing messages in encrypted format with a password and send it to the required destination hiding in a QR Code, without being tracked or decrypted properly by any hacker or spyware. Since QR Codes have fast response time and have large storage capacity, QR Codes ca…
Public-key cryptography algorithms, especially elliptic curve cryptography (ECC) and elliptic curve digital signature algorithm (ECDSA) have been attracting attention from many researchers in different institutions because these algorithms provide security and high performance when being used in many areas such as electronic-healthcare, electronic-banking, electronic-commerce, electronic-vehicular, and electronic-governance. These algorithms heighten security against various attacks and at the same time improve performance to obtain efficiencies (time, memory, reduced computation complexity, a…
Although practised as an art and science for ages, cryptography had to wait until the mid-twentieth century before Claude Shannon gave it a strong mathematical foundation. However, Shannon's approach was rooted is his own information theory, itself inspired by the classical physics of Newton and Einstein. But our world is ruled by the laws of quantum mechanics. When quantum-mechanical phenomena are taken into account, new vistas open up both for codemakers and codebreakers. Is quantum mechanics a blessing or a curse for the protection of privacy? As we shall see, the jury is still out!
In this paper, through considering lightweight cryptography, we present a comparative realization of MDS matrices used in the VLSI implementations of lightweight cryptography. We verify the MixColumn/MixNibble transformation using MDS matrices and propose reliability approaches for thwarting natural and malicious faults. We note that one other contribution of this work is to consider not only linear error detecting codes but also recomputation mechanisms as well as fault space transformation (FST) adoption for lightweight cryptographic algorithms. Our intention in this paper is to propose reli…
The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density parity-check (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to extend the maximum reconciliation distance between the two remote parties. Key reconciliation over multiple dimensions has been shown to further improve the error-correction performance of multi-edge LDPC …
The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present cryptographic schemes (symmetric and asymmetric), differences between quantum and classical computing, challenges in quantum computing, quantum algorithms (Shor's and Grover's), public key encryption schemes affected, symmetric schemes affected, the impact on hash functions, and post quantum cryptography. Specifically, the section of Post-Quantum Cryptography deal…
The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST post-quantum cryptography standardization process. However, similar approaches have been less fortunate in the context of code-based digital signatures, since no secure and efficient signature scheme based on these codes is available to date. The main limitation of previous attempts in this line of research has been the use of sparse signatures, which produces…
We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in cryptography. We believe that the encoding of cryptographic algorithms is an important step in that direction, and it is the main reason why in this paper we present a software implementation of finding the inverse element, the operation which is essentially related to both ECC (Elliptic Curve Cryptography) and the RSA schemes of digital signature.
This paper presents a survey of key distribution schemes for wireless sensor networks. This survey includes the new approach of key distribution using the piggy bank method. Different Network architectures and different key pre-distribution schemes are described. The survey includes the use of the piggy bank approach to cryptography in which part of the key is pre-distributed and the remainder is varied in the application.
