Abstract. In the digital age, cryptography is widely used in various important systems such as financial, military and government ones, medical records etc. The life of modern people is closely connected with the cryptography. We send messages via instant messengers without even considering in which way the security of communications and data is ensured. We buy things both online and transfer money with confidence in transaction security. The level of digitization of our society is constantly increasing, and the digital data needs a reliable protection, which makes cryptography a current topic. Cryptographic systems ensure our security and the basic properties of information, such as privacy, integrity, availability. However, with the beginning of the development of quantum computers, the field of cryptography has developed in a new direction. Quantum cryptography is a science that studies the methods of communication systems protection. It is based on the idea that patterns of quantum physics (physical properties described by the laws of quantum optics, quantum electrodynamics, or quantum field theory) are inviolable. The current state of development and usage of powerful quantum computers, as well as their mathematical and software, is strictly confidential and securely protected. Only clear-cut information about quantum computers and their usage in cryptography is provided. NIST has announced an open competition to select quantum-resistant public-key cryptographic algorithms. After the third round, CRYSTALS-KYBER, CRYSTALS Dilithium, FALCON, and SPHINCS+ were proposed to be standardized. NIST has already recommended moving from the sizes of keys and algorithms that provide 80 security bits to the sizes of keys and algorithms that provide 112 or 128 security bits in order to protect against classic attacks. Post-quantum cryptography, which with its complexities still requires a more detailed study, challenge science once more. However, it is unknown when the changes will occur and when the quantum era will begin, as well as what consequences they will have. It is only possible to predict how many advantages will have quantum calculations compared to usual, and how different the new quantum models will be from classic ones.
Abstract. In the digital age, cryptography is widely used in various important systems such as financial, military and government ones, medical records etc. The life of modern people is closely connected with the cryptography. We send messages via instant messengers without even considering in which way the security of communications and data is ensured. We buy things both online and transfer money with confidence in transaction security. The level of digitization of our society is constantly increasing, and the digital data needs a reliable protection, which makes cryptography a current topic. Cryptographic systems ensure our security and the basic properties of information, such as privacy, integrity, availability. However, with the beginning of the development of quantum computers, the field of cryptography has developed in a new direction. Quantum cryptography is a science that studies the methods of communication systems protection. It is based on the idea that patterns of quantum physics (physical properties described by the laws of quantum optics, quantum electrodynamics, or quantum field theory) are inviolable. The current state of development and usage of powerful quantum computers, as well as their mathematical and software, is strictly confidential and securely protected. Only clear-cut information about quantum computers and their usage in cryptography is provided. NIST has announced an open competition to select quantum-resistant public-key cryptographic algorithms. After the third round, CRYSTALS-KYBER, CRYSTALS Dilithium, FALCON, and SPHINCS+ were proposed to be standardized. NIST has already recommended moving from the sizes of keys and algorithms that provide 80 security bits to the sizes of keys and algorithms that provide 112 or 128 security bits in order to protect against classic attacks. Post-quantum cryptography, which with its complexities still requires a more detailed study, challenge science once more. However, it is unknown when the changes will occur and when the quantum era will begin, as well as what consequences they will have. It is only possible to predict how many advantages will have quantum calculations compared to usual, and how different the new quantum models will be from classic ones.
Post-quantum cryptography is one of the key areas of development of modern means of information protection inconnection with the active progress of quantum technologies. Classical cryptographic algorithms, such as RSA and ECC,become vulnerable due to the Shor algorithm, which threatens the long-term security of information systems. The articleprovides an in-depth review of the current state of post-quantum cryptographic algorithms based on the results of the NationalInstitute of Standards and Technology (NIST) selection, and also analyzes the approaches proposed in recent scientificpublications. The characteristics of the Kyber, Dilithium, Falcon, and SPHINCS+ algorithms are considered in detail - theirsecurity parameters, performance, cryptographic strength, requirements for hardware resources, and possibilities of applicationin practical systems. Special attention is paid to the issues of integrating post-quantum algorithms into existing cryptographicprotocols, in particular, into public-key systems, public-key infrastructure, and secure communication channels. The keyproblems of implementing post-quantum cryptography in information infrastructures are considered, including: increased keysizes and cryptographic parameters, computational delays, compatibility with existing software and hardware solutions, and theneed to revise key management policies. The prospects for implementing post-quantum solutions in Ukraine are separatelyanalyzed, and practical recommendations are offered for a phased migration to such algorithms for state and corporate systems,taking into account the requirements for long-term data confidentiality and protection of critical information infrastructure.Keywords: post-quantum cryptography, quantum attacks, NIST PQC, Kyber, Dilithium, Falcon, SPHINCS+,cryptoresistance. References1. NIST. (n.d.). Post-Quantum Cryptography Standardization Project. https://csrc.nist.gov/projects/postquantum-cryptography.2. NIST. (2024). NIST releases first 3 finalized post-quantum encryption standards. https://www.nist.gov/newsevents.3. Dam, D. T., Mavroeidis, V., & Vishi, K. (2023). A survey of post-quantum cryptography: Start of a newquantum era. Cryptography, 7(3). https://doi.org/10.3390/cryptography7030040.4. Kokare, Priyanka & Vora, Deepali & Patil, Shruti & Kotecha, Ketan & Khairnar, Vaishali & Choudhury,Tanupriya & Kulkarni, Ambarish. (2024). Post Quantum Cryptography: A survey of Past and Future.https://www.researchgate.net/publication/382398375_Post_Quantum_Cryptography_A_survey_of_Past_and_Future.5. Chen, L., Jordan, S., Liu, Y.-K., Moody, D., Peralta, R., Perlner, R., Smith-Tone, D. (2016). Report on PostQuantum Cryptography. NIST IR 8105. https://doi.org/10.6028/NIST.IR.8105.6. Bos, J. W., et al. (2017). CRYSTALS-Kyber: A CCA-Secure Module-Lattice-Based KEM. https://pqcrystals.org/kyber/data/kyber-specification-round3.pdf.7. Ducas, L., et al. (2018). CRYSTALS-Dilithium: Digital Signatures from Module Lattices. https://pqcrystals.org/dilithium/data/dilithium-specification-round3.pdf.8. Pöppelmann, T., Oder, T., & Güneysu, T. (2015). High-Speed Ideal Lattice-Based Cryptography on 8-bit AVRMicrocontrollers. IACR Cryptology ePrint Archive, Report 2015/382. https://eprint.iacr.org/2015/382.pdf.9. Cloudflare. (2023). Post-Quantum Cryptography Support in TLS and Web Infrastructure.https://blog.cloudflare.com/tag/post-quantum-cryptography/.10. ETSI. (2020). Quantum-Safe Cryptography – An Overview. https://www.etsi.org/technologies/quantum-safecryptography.11. NCSC UK. (2020). Preparing for Quantum-Safe Cryptography. https://www.ncsc.gov.uk/whitepaper/preparing-for-quantum-safe-cryptography.12. Keyfactor & Ponemon Institute. (2023). State of Machine Identity Management Report. Keyfactor, Inc.https://www.keyfactor.com.13. Shor, P. (1994). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the35th Annual Symposium on Foundations of Computer Science.14. Bernstein, D., & Lange, T. (2017). Post-Quantum Cryptography. Springer. https://doi.org/10.1007/978-3-540-88702-7.15. Grover, L. (1996). A fast quantum mechanical algorithm for database search. STOC '96.https://doi.org/10.1145/237814.237866.16. Mosca, M. (2018). Cybersecurity in an era with quantum computers: Will we be ready? IEEE Security &Privacy, 16(5), 38–41. https://doi.org/10.1109/MSP.2018.3761723.17. Prest, T. (2020). Efficient implementation issues in Falcon. https://falcon-sign.info.18. SPHINCS+ Team. (n.d.). SPHINCS+ Specification. https://sphincs.org/data/sphincs+-specification.pdf.
Abstract It is viewed as revolutionary technology, offering incredible potential in terms of computing power within different scientific and industrial sectors. Quantum computers provide remarkable computing power; however, they also present significant security risks to existing public-key cryptography systems used to secure digital communication, online banking systems, government, medical applications, cloud computing systems, and IoT systems. Security of commonly used encryption schemes like RSA, DH, and ECC depends on mathematical problems that are impossible for classical computers to solve but can be easily resolved with the help of powerful enough quantum computers by using Shor’s algorithm. Furthermore, Grover’s algorithm makes exhaustive search attacks much faster, thus effectively lowering the security level of symmetric encryption schemes since it provides the speed-up for brute-force attacks. Post-Quantum Cryptography (PQC) turned out to be an effective and scalable method to protect digital data from attacks using quantum computing. In contrast to quantum cryptography, which requires a special quantum communication channel, PQC uses classical cryptographic algorithms that cannot be broken down by either classical or quantum computer due to certain mathematical problems. This research paper offers an extensive exploration of post-quantum cryptography through the analysis of the development of quantum computing, weaknesses of current cryptographic techniques, and mathematics behind quantum-resistant algorithms. Moreover, this paper explores the major classes of PQC techniques such as lattice-based, code-based, hash-based, multivariate, and isogeny-based cryptography and provides details about their security and application. Moreover, the report gives an overview of the NIST Post-Quantum Cryptography Standardization Project and analyzes recent standardizations of quantum-proof algorithms to be utilized in future digital infrastructures. Keywords: Post-Quantum Encryption, Quantum Security, Quantum-Proof Public-Key Cryptography, Lattice-Based Security Protocols, ML-KEM Key Encapsulation Mechanism, ML-DSA Digital Signature Algorithm, NIST Post-Quantum Cryptography, Contemporary Cybersecurity, Secure Communications, Cryptographic Algorithms.
As quantum computing advances, current cryptographic protocols are increasingly vulnerable to quantum attacks, particularly those based on Public Key Infrastructure (PKI) like RSA or Elliptic Curve Cryptography (ECC). This paper presents a comprehensive review of Post-Quantum Cryptography (PQC) as a solution to protect digital systems in the quantum era. We provide an in-depth analysis of various quantum-resistant cryptographic algorithms, including lattice-based, code-based, hash-based, isogeny-based, and multivariate approaches. The review highlights the National Institute of Standards and Technology (NIST) PQC standardization process, highlighting key algorithms, such as CRYSTALS–Kyber, CRYSTALS–Dilithium, Falcon, and SPHINCS+, and discusses the strengths, vulnerabilities, and implementation challenges of the leading algorithms. In addition, we explore transition strategies for organizations, emphasizing hybrid cryptography to ensure backward compatibility during migration. This study offers key insights into the future of cryptographic standards and the critical steps necessary to prepare for the transition from classical to quantum-resistant systems.
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.
The advent of quantum computing will pose a substantial threat to the security of classical cryptographic methods, which could become vulnerable to quantum-based attacks. In response to this impending challenge, the field of post-quantum cryptography has emerged, aiming to develop algorithms that can withstand the computational power of quantum computers. This study addressed the pressing concern of classical cryptographic methods becoming vulnerable to quantum-based attacks due to the rise of quantum computing. The emergence of post-quantum cryptography has led to the development of new resistant algorithms. Our research focused on four quantum-resistant algorithms endorsed by America’s National Institute of Standards and Technology (NIST) in 2022: CRYSTALS-Kyber, CRYSTALS-Dilithium, FALCON, and SPHINCS+. This study evaluated the security, performance, and comparative attributes of the four algorithms, considering factors such as key size, encryption/decryption speed, and complexity. Comparative analyses against each other and existing quantum-resistant algorithms provided insights into the strengths and weaknesses of each program. This research explored potential applications and future directions in the realm of quantum-resistant cryptography. Our findings concluded that the NIST algorithms were substantially more effective and efficient compared to classical cryptographic algorithms. Ultimately, this work underscored the need to adapt cryptographic techniques in the face of advancing quantum computing capabilities, offering valuable insights for researchers and practitioners in the field. Implementing NIST-endorsed quantum-resistant algorithms substantially reduced the vulnerability of cryptographic systems to quantum-based attacks compared to classical cryptographic methods.
A significant topic of contemporary cryptography research and standardization is the development of public key crypto systems that resist attacks from quantum computers. Protocols and applications should start investigating the use of quantum-resistant key exchange and encryption to protect the confidentiality of current communications against future quantum computers utilizing post-quantum cryptography for a particular key exchange. Since they operate harder and need fewer steps compared to conventional computers, quantum algorithms are more secure and robust. Attackers who use quantum computers have powerful computing capabilities, and a quantum allows for simple cryptographic system breaking. Security algorithms that are quantum secure are resistant to attacks from conventional, as well as quantum computers. This work has surveyed, summarized, and analysed previous research to provide readers of this study an integrated understanding of quantum cryptography. It also discusses quantum attacks, which could be used in place of more conventional cryptography techniques, such as quantum key distribution, which takes advantage of quantum mechanics' properties to ensure secure exchanges of the secret keys, and various quantum algorithms. With quantum computation becoming a very real threat, this should motivate more people to show an early interest in the future of cryptography.