The paper identifies and analyzes attacks aimed at Rainbow post-quantum electronic signature cryptanalysis. Today, due to advances in the quantum computers development, the need to present new standards for electronic signatures resistant to both quantum and classical cryptanalysis arisen. To solve the lack of such electronic signatures, NIST USA is running the NIST PQC competition. As part of this competition some electronic signatures designed to resist quantum cryptanalysis were presented, including Rainbow electronic signature. CZ-Rainbow and the compressed Rainbow algorithm were also presented along with the regular Rainbow algorithm. This paper analysis attacks on all three types of electronic signature. The possibility of a quantum attack against the Rainbow electronic signature, as well as the complexity of such an attack, defines the possibility of this electronic signature usage during the post-quantum period.
The paper identifies and analyzes attacks aimed at Rainbow post-quantum electronic signature cryptanalysis. Today, due to advances in the quantum computers development, the need to present new standards for electronic signatures resistant to both quantum and classical cryptanalysis arisen. To solve the lack of such electronic signatures, NIST USA is running the NIST PQC competition. As part of this competition some electronic signatures designed to resist quantum cryptanalysis were presented, including Rainbow electronic signature. CZ-Rainbow and the compressed Rainbow algorithm were also presented along with the regular Rainbow algorithm. This paper analysis attacks on all three types of electronic signature. The possibility of a quantum attack against the Rainbow electronic signature, as well as the complexity of such an attack, defines the possibility of this electronic signature usage during the post-quantum period.
Due to the development of quantum computers and quantum methods and algorithms, in order to ensure the security of information after the development of cryptographically relevant quantum computers, NIST conducted the NIST PQC competition. As a result of conducting three rounds of NIST PQC, NIST selected 4 candidates for standardization and four candidates for the fourth round (key encapsulation mechanisms BIKE, Classic McEliece, HQC, and SIKE (which the developers considered unreliable)). Due to the fact that selected algorithms are based on the use of lattices and to add diversity to this list through the use of general-purpose signatures, the process of standardizing additional digital signatures for quantum-resistant cryptography has been initiated. The following types of signatures are considered for the first round of this standardization process: code-based signatures, isogeny signatures, multivariate signatures, symmetric signatures, MPC-in-the-head, and NIST-defined "other" signatures. These "other" digital signatures are mostly based on new and promising post-quantum (quantum-resistant) problems. The purpose of the work is to analyze and compare candidates for quantum-resistant digital signatures, based on new and promising quantum-resistant problems, resistant to classical and quantum attacks and side-channel attacks. The paper provides comparison of four digital signatures classified by NIST as "other", namely: ALTEQ, eMLE-Sig 2.0, KAZ-SIGN, Xifrat1-Sign.I. For this purpose, the paper presents the basic principles of each of these digital signatures, their main parameters and available at the time of consideration attack vectors. The paper also provides unconditional criteria necessary for comparison. Digital signatures were compared according to such unconditional criteria as: possible lengths of the public key, possible lengths of the personal (secret) key, length of the result of cryptographic algorithm; and conclusions are made regarding the completeness of given comparison and the possibility of further research is highlighted.
Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.
An important feature of the post-quantum period in cryptography is the significant uncertainty regarding the source data for cryptanalysis and counteraction in terms of the capabilities of quantum computers, their mathematical and software, as well as the application of quantum cryptanalysis to existing cryptotransformations and cryptoprotocols. Mathematical methods of digital signature (DS) have been chosen as the main methods of NIST USA, which have undergone significant analysis and substantiation in the process of extensive research by cryptographers and mathematicians at the highest level. They are described in detail and studied at the first stage of the US NIST International Competition. In the second round, a number of decisions were made to merge some candidates for the post-quantum DS standard. 9 candidates were left for further research at the 2nd round: Crystals-Dilithium, Falcon, GeMSS, LUOV, MQDSS, Picnic, qTESLA, Rainbow and SPHINCS+. Three of them (Dilithium, Falcon, qTeSLA) are based on the stability of algebraic lattices (Lattice-based), four (GeMSS, LUOV, MQDSS, Rainbow) are based on multivariate transformations (MQ-transformations), one (SPHINCS+) is based on the stability of hash-function, one (Picnic) is based on the stability of the hash-function and block stream ciphers. During the 2nd round of the US NIST Competition the following finalist algorithms and alternative algorithms were selected as digital signatures according to the results of research on promising post-quantum cryptographic algorithms. As finalists algorithms such DS algorithms as Crystals-Dilithium, Falcon and Rainbow. Alternative algorithms are GeMSS, Picnic and SPHINCS+ were selected. This paper studies the peculiarities of construction of the digital signature algorithm considered as a candidate for the promising post-quantum standard of the NIST PQC competition – Picnic, also it analyzes the protection of the algorithm from known attacks. Data from the comparison of post-quantum algorithms such as digital signature are given. The description of the Picnic algorithm and its parameters are given.
Post-Quantum Cryptography (PQC) is a rapidly developing field that addresses the potential threat quantum computers pose to the security of current cryptographic algorithms. With the rapid advancement of quantum computing technologies, it has become imperative to identify and standardize new cryptographic techniques that can withstand attacks from quantum computers. This paper explores the motivation behind PQC and provides an overview of the experimental research conducted in the field. It highlights the vulnerabilities of traditional cryptographic algorithms, such as RSA and ECC, to quantum attacks and emphasizes the need for transitioning to quantum-resistant alternatives. The experiments conducted in the PQC domain encompass the evaluation and analysis of candidate algorithms submitted to the NIST PQC competition. These experiments involve comprehensive security assessments, performance evaluations, and code audits to ensure the suitability and effectiveness of the proposed algorithms in real-world scenarios. This paper provides guidelines for organizations and practitioners adopting PQC. It discusses considerations for selecting and implementing post-quantum cryptographic algorithms, including security levels, algorithmic characteristics, performance tradeoffs, and integration challenges. It also outlines the importance of a smooth transition from classical to post-quantum cryptographic systems and highlights the need for standardization efforts to ensure interoperability and compatibility.
The advent of quantum computing poses a significant threat to current cryptographic systems, particularly public-key algorithms such as RSA and ECC, which are vulnerable to quantum attacks like Shor's algorithm. Post-Quantum Cryptography (PQC) aims to develop and standardize quantum-resistant cryptographic algorithms to secure digital communications in the quantum era. This paper examines the current landscape of PQC, focusing on the evaluation and standardization efforts led by organizations such as the National Institute of Standards and Technology (NIST). We analyze the major families of quantum-resistant algorithms, including lattice-based, hash-based, code-based, multivariate, and isogeny-based cryptography, discussing their security guarantees, performance trade-offs, and implementation challenges. Furthermore, we review NIST's PQC standardization process, highlighting selected finalists and alternate candidates, and explore the ongoing transition challenges in adopting these algorithms across industries. Finally, we discuss future directions for PQC research, including hybrid cryptographic systems and the need for continued cryptanalysis to ensure long-term security. This work provides a comprehensive overview of the progress and challenges in deploying quantum-resistant cryptography to safeguard against emerging quantum threats.
In recent years, there has been steady progress in the creation of quantum computers. If large-scale quantum computers are implemented, they will threaten the security of many widely used public-key cryptosystems. Key-establishment schemes and digital signatures based on factorization, discrete logarithms, and elliptic curve cryptography will be most affected. Symmetric cryptographic primitives such as block ciphers and hash functions will be broken only slightly. As a result, there has been an intensification of research on finding public-key cryptosystems that would be secure against cryptanalysts with both quantum and classical computers. This area is often called post-quantum cryptography (PQC), or sometimes quantum-resistant cryptography. The goal is to design schemes that can be deployed in existing communication networks and protocols without significant changes. The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through an open competition. New public-key cryptography standards will define one or more additional digital signatures, public-key encryption, and key-establishment algorithms. It is assumed that these algorithms will be able to protect confidential information well in the near future, including after the advent of quantum computers. After three rounds of evaluation and analysis, NIST has selected the first algorithms that will be standardized as a result of the PQC standardization process. The purpose of this article is to review and analyze the state of NIST's post-quantum cryptography standardization evaluation and selection process. The article summarizes each of the 15 candidate algorithms from the third round and identifies the algorithms selected for standardization, as well as those that will continue to be evaluated in the fourth round of analysis. Although the third round is coming to an end and NIST will begin developing the first PQC standards, standardization efforts in this area will continue for some time. This should not be interpreted as meaning that users should wait to adopt post-quantum algorithms. NIST looks forward to the rapid implementation of these first standardized algorithms and will issue future guidance on the transition. The transition will undoubtedly have many complexities, and there will be challenges for some use cases such as IoT devices or certificate transparency.