Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete Logarithm Problem. In other words, many once-secure protocols have to be replaced by still-secure alternatives. Instead of relying, for example, on the RSA protocol, the Diffie-Hellman key-exchange or the (Elliptic Curve) Digital Signature Algorithm, many researchers moved their attention to the design and analysis of primitives which are yet to be broken by quantum algorithms. The urgency of the threat imposed by quantum computers led the U.S. National Institute of Standards and Technology (NIST) to open calls for both Post-Quantum Public-Keys Exchange Algorithms and Post-Quantum Digital Signature Algorithms. In this brief survey we focus on the round 3 finalists and alternate candidates for Digital Signatures: CRYSTALS-DILITHIUM, FALCON, Rainbow, SPHINCS+, GeMSS, Picnic.
Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete Logarithm Problem. In other words, many once-secure protocols have to be replaced by still-secure alternatives. Instead of relying, for example, on the RSA protocol, the Diffie-Hellman key-exchange or the (Elliptic Curve) Digital Signature Algorithm, many researchers moved their attention to the design and analysis of primitives which are yet to be broken by quantum algorithms. The urgency of the threat imposed by quantum computers led the U.S. National Institute of Standards and Technology (NIST) to open calls for both Post-Quantum Public-Keys Exchange Algorithms and Post-Quantum Digital Signature Algorithms. In this brief survey we focus on the round 3 finalists and alternate candidates for Digital Signatures: CRYSTALS-DILITHIUM, FALCON, Rainbow, SPHINCS+, GeMSS, Picnic.
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.
The rapid advancement of quantum computing poses a fundamental threat to classical cryptographic mechanisms that underpin modern digital security. Shor’s algorithm can efficiently solve integer factorization and discrete logarithm problems, thereby breaking widely used public-key cryptosystems such as RSA, ECC, and Diffie–Hellman. Grover’s algorithm also reduces the effective security of symmetric encryption and hash functions by half. This paper provides a systematic analysis of the impact of quantum attacks on current cryptographic infrastructures, including TLS, digital signatures, and blockchain. We then review the state of post-quantum cryptography (PQC) as standardized by NIST, focusing on three leading candidates: CRYSTALS-Kyber for key encapsulation, and CRYSTALS-Dilithium and FALCON for digital signatures. Through simulation using the Open Quantum Safe (liboqs) library on a standard x86_64 platform, we measure key generation time, encryption/signing speed, decryption/verification latency, and key/signature sizes. Our results show that Kyber-768 achieves key generation in <0.1 ms and produces public keys of about 1.2 KB, while Dilithium-3 generates signatures of ~2.7 KB with verification times under 0.3 ms. Compared to RSA-2048 and ECDSA-P256, PQC algorithms offer competitive performance at the cost of larger key and signature sizes. Based on these findings, we propose a hybrid transition roadmap that combines classical and PQC algorithms in parallel, minimizing risk while maintaining backward compatibility. The paper concludes that organizations should begin immediate preparations for the post-quantum era, especially for data requiring long-term confidentiality.
The advent of quantum computing poses a significant existential threat to current public-key cryptographic systems, most notably RSA and Elliptic Curve Cryptography (ECC), which rely on the presumed hardness of integer factorization and discrete logarithm problems. Shor's algorithm, a quantum algorithm, can efficiently solve these problems, rendering classical asymmetric primitives insecure. This paper addresses the imperative need for post-quantum cryptography (PQC) by exploring lattice-based constructs as robust alternatives for asymmetric primitives. We provide a comprehensive overview of the fundamental mathematical problems underlying lattice-based cryptography, such as the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Learning With Errors (LWE), and Ring Learning With Errors (RLWE). The paper surveys prominent lattice-based schemes, including NTRU, CRYSTALS-Kyber, and CRYSTALS-Dilithium, analyzing their security foundations, performance characteristics, and the extent to which they offer a viable "post-quantum RSA." We delve into the methodology of constructing these primitives, discuss their resilience against both classical and quantum attacks, and evaluate their practical implications for key sizes, computational efficiency, and deployment challenges. Our analysis highlights that lattice-based cryptography, particularly the NIST-standardized schemes, presents a strong candidate for securing digital communications in the quantum era, offering provable security rooted in worst-case to average-case reductions for lattice problems.
Quantum computing challenges the mathematical problems anchoring the security of the classical public key algorithms. For quantum-resistant public key algorithms, the National Institute of Standards and Technology (NIST) has undergone a multi-year standardization process and selected the post-quantum cryptography (PQC) public key digital signatures of Dilithium, Falcon, and SPHINCS+. Finding common ground to compare these algorithms can be difficult because of their design differences, including the fundamental math problems (lattice-based vs. hash-based). We use a visualization model to show the key/signature size vs. security trade-offs for all PQC algorithms. Our performance analyses compare the algorithms’ computational loads in the execution time. Building on the individual algorithms’ analyses, we analyze the communication costs and implementation overheads when integrated with Public Key Infrastructure (PKI) and with Transport Layer Security (TLS) and Transmission Control Protocol (TCP)/Internet Protocol (IP). Our results show that the lattice-based algorithms of Dilithium and Falcon induce lower computational overheads than the hash-based algorithms of SPHINCS+. In addition, the lattice-based PQC can outperform the classical algorithm with comparable security strength; for example, Dilithium 2 and Falcon 512 outperform RSA 4096 in the TLS handshake time duration.
The National Institute of Standards and Technology (NIST) has recently concluded the third round of its Post Quantum Cryptography Standardization Process, selecting four finalist algorithms for standardization: CRYSTALS Kyber, CRYSTALS-Dilithium, FALCON, and SPHINCS+. These algorithms are designed to withstand attacks from both classical and quantum computers, ensuring the long-term security of digital communications. This paper presents a comprehensive comparative analysis of the security margins and practical deployment readiness of these finalist algorithms. CRYSTALS-Kyber, a key encapsulation mechanism based on the hardness of the Module Learning With Errors problem, offers strong security and efficient performance. CRYSTALS-Dilithium, a digital signature algorithm based on module lattices, provides robust security guarantees and relatively straightforward implementation. FALCON, a lattice-based digital signature algorithm utilizing the Fast Fourier Transform, offers compact signatures and fast verification but faces implementation challenges due to its reliance on floating-point arithmetic. SPHINCS+, a hash-based signature scheme, stands out as a conservative choice with security based solely on the well-established security of hash functions. The analysis reveals that while each algorithm has its strengths, they also face unique challenges in terms of side-channel vulnerabilities, formal security proofs, and performance trade-offs. The practical deployment of these algorithms requires careful consideration of specific security requirements, performance needs, and resource constraints. Ongoing research efforts aim to enhance the algorithms' resistance against advanced attacks, optimize their performance across diverse platforms, and develop standardized and secure hybrid cryptographic systems. The transition to post-quantum cryptography will involve challenges such as interoperability with legacy systems, the need for clear standards and regulatory guidance, and the costs associated with software and hardware updates. Continued engagement with the cryptographic community and monitoring of the evolving security landscape will be crucial for ensuring a secure and effective migration to post-quantum cryptography.
The emergence of quantum computing is a serious threat to the principles of modern crypto-logical mathematics. The classical public-key cryptography, including Rivest-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC), and Diffie-Hellman are very safe against classical adversaries yet become susceptible to quantum algorithms, including the Shor algorithm, which can easily solve the underlying mathematical problems. This weakness is jeopardizing confidentiality and integrity of the world-wide systems of communication, money transactions, and essential structures, and requires the immediate creation of safe alternatives. The current literature on post-quantum cryptography (PQC) has covered various classes of algorithm, such as lattice-based, code-based, multivariate schemes, and isogeny-based schemes. Although lattice-based approaches like Nth Degree Truncated Polynomial Ring Unit (NTRU) and FrodoKEM can be highly theoretically resistant, they can be computationally and memory-intensive. Cryptosystems based on code such as Classic McEliece are secure but not practicable because they have huge public key sizes. Multivariate schemes like Rainbow, and isogeny-based schemes like Super singular Isogeny Key Encapsulation (SIKE) have been attacked recently by cryptanalytic attacks, and broken completely. Such restrictions open the necessity to find more efficient and secure quantum-resistant solutions.This research study postulates a hybrid post-quantum cryptographic (PQC) system that combines CRYSTALS-Kyber for encryption with CRYSTALS-Dilithium for digital signatures both of which are approved through the National Institute of Standards and Technology (NIST) PQC standardization program. The model will be such that it ensures quantum resistance but at the same time it will be scalable, efficient and compatible with the existing infrastructures. The test outcomes indicate that the hybrid PQC model is 35-45 percent faster to encrypt and decrypt, signature performance is enhanced by up to 40 percent, and the throughput is 20 times higher (98.7 Mbps) than the same base PQC scheme including Nth Degree Truncated Polynomial Ring Unit (NTRU), McEliece and Rainbow. These enhancements affirm that the suggested model provides a viable trade-off between the security, speed, and efficiency in terms of key size, which makes it a viable and a sound base to ensure secure communication in the quantum age.