Post-quantum digital signature schemes aim to remain secure against quantum adversaries, yet their practical security may be affected by physical attacks. This work studies the use of Grover’s algorithm in a Cold Boot Attack scenario against the RYDE post-quantum digital signature scheme. We construct a quantum oracle adapted to the RYDE key derivation process and analyze the corresponding Grover operator. Furthermore, we estimate the required quantum resources, including the number of quantum registers and quantum gates. This study provides insight on the feasibility of quantum-assisted attacks on seed-based post-quantum digital signature schemes.
Post-quantum digital signature schemes aim to remain secure against quantum adversaries, yet their practical security may be affected by physical attacks. This work studies the use of Grover’s algorithm in a Cold Boot Attack scenario against the RYDE post-quantum digital signature scheme. We construct a quantum oracle adapted to the RYDE key derivation process and analyze the corresponding Grover operator. Furthermore, we estimate the required quantum resources, including the number of quantum registers and quantum gates. This study provides insight on the feasibility of quantum-assisted attacks on seed-based post-quantum digital signature schemes.
Post-quantum digital signature algorithms are being developed as an alternative to classical schemes, capable of ensuring cryptographic security even in the presence of quantum computing power. The results of the analysis and research of the FULEECA, WAVE, BISCUIT, and RYDE post-quantum digital signature algorithms, which are based on different cryptographic approaches to ensuring resistance in quantum computing environments — from code and rank schemes to multilateral quadratic constructions — providing multi-level resistance to a wide range of attacks, are presented. The analysis showed that all the algorithms considered have high potential for use in post-quantum systems, meeting key requirements for security, performance, and efficiency. At the same time, each algorithm has its own requirements for resources, key and signature sizes, implementation features, and cryptographic resistance to classical and quantum attacks. The results provide a basis for further comparative analysis, as well as for formulating recommendations for the application of each of the algorithms depending on the specifics of the information system, the level of threats, and the limitations of the implementation environment.
The advent of quantum computers poses a direct threat to the security of traditional digital signature schemes, which are based on the Rivest–Shamir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) cryptosystems. Shor's algorithm allows solving the Discrete Logarithm Problem (DLP) in polynomial time, whereas Grover's algorithm significantly reduces the effort required for brute-force attacks on symmetric hash functions and ciphers. Although many post-quantum solutions have been proposed, such as lattice-based schemes (e.g., CRYSTALS-Dilithium, Falcon) or hash-based schemes (e.g., SPHINCS+), they still have some limitations to overcome, such as large public keys, bulky signatures, high computational costs, and difficulties in integrating into existing Public Key Infrastructures (PKIs). In this paper, we propose a new type of hard problem, defined over a finite prime field, in which the generator is kept secret to prevent any direct Shor attack and is only subject to a limited influence from Grover. Based on this newly proposed hard problem, we construct a post-quantum digital signature scheme that is both Shor-resistant and Grover-resistant, secure against classical attacks, and fully compatible with current PKI infrastructures. Compared with existing post-quantum digital signature schemes, our solution significantly optimizes the size of public keys and signatures while increasing the speed of signing and verification. The newly proposed hard problem cannot be solved by known classical or quantum algorithms, thus ensuring long-term security. Performance evaluation results show that the scheme provides an optimal balance between performance and security, opening up a cost-effective implementation path for the post-quantum cryptography era.
Quantum computing represents one of the most disruptive technological advancements of the 21st century, with profound implications for modern cryptographic systems. Traditional digital signature algorithms—such as RSA, DSA, and Elliptic Curve Cryptography (ECC)—derive their security from mathematical problems like integer factorization and discrete logarithms, which are computationally infeasible for classical computers. However, the advent of quantum algorithms, particularly Shor’s and Grover’s algorithms, poses a direct threat to these cryptographic assumptions by drastically reducing the time required to solve such problems. This development renders existing Digital Signature infrastructures potentially obsolete once large-scale quantum computers become operational. To counter this threat, researchers have proposed a range of post-quantum cryptographic (PQC) algorithms, including lattice-based, hash-based, and multivariate polynomial-based signature schemes, which are designed to resist quantum attacks. This paper critically examines the extent of quantum vulnerability in current Digital Signature systems and evaluates the comparative performance, efficiency, and security trade-offs of post-quantum alternatives. The study aims to provide a structured understanding of the ongoing transition toward quantum-resistant digital authentication and to propose a roadmap for secure implementation in future cryptographic environments.
Public key cryptography plays a pivotal role in maintaining digital security and privacy, with its foundations built on the hardness of certain mathematical problems. However, the emergence of quantum computing threatens the security of current cryptographic systems, making the adoption of post-quantum cryptography (PQC) an urgent necessity. Digital signature schemes are essential components in secure communications, providing authentication, non-repudiation, and data integrity. This paper examines the state of post-quantum digital signature schemes across various cryptographic approaches, including lattice-based, code-based, multivariate polynomial-based, hash-based, symmetric-key-based, and isogeny-based systems, alongside advancements in Multi-Party Computation in the Head (MPC-in-the-head) schemes. The paper then explores application-specific signatures such as blind, undeniable, threshold, chameleon, aggregate, and ring signatures, explaining their main use cases and the existing post-quantum cryptographic classifications that support these constructions individually. Software implementations of selected prominent PQC digital signature schemes were carried out, and their performance was systematically analysed using metrics such as bandwidth consumption, latency, and computational efficiency. These results provide key observations regarding the suitability of different schemes for both resource-constrained and high-performance environments. Subsequently, a detailed literature review of implementations on embedded and hardware platforms is presented, focusing on ARM-based devices and FPGA accelerators to evaluate deployment feasibility beyond general-purpose processors. Based on the software and implementation-level findings, a comparative analysis across software, embedded, and hardware platforms is conducted to highlight architectural influences on performance, scalability, and practicality. Furthermore the cryptanalytic attacks on post-quantum digital signature schemes across various PQC classifications are examined in this paper, taking into account both classical and quantum adversarial models. To evaluate realistic security constraints, implementation-oriented vulnerabilities such as side-channel and fault-based attacks are also examined. In addition, the applicability of post-quantum digital signature schemes within TLS, IoT, and related practical deployment scenarios is analysed. The study also discusses possible directions for further investigation, focusing on the requirement for effective and expandable PQC systems that can satisfy changing cybersecurity requirements. In order to protect sensitive data in the digital era, this study emphasizes the need for implementing quantum-secure systems by fusing theoretical understandings with real-world applications.
Grover’s algorithm represents a cornerstone quantum attack against symmetric cryptography, offering a quadratic speedup for exhaustive key search. While its theoretical properties are well established, the practical robustness of Grover’s algorithm under non-ideal oracle execution remains insufficiently quantified, particularly in security-relevant contexts. This work presents a comprehensive quantitative analysis of Grover’s robustness against intermittent oracle failures, modeling realistic execution imperfections that may arise in practical quantum attack scenarios. Using a reduced two-dimensional representation of amplitude amplification, we define and measure a practical reliability threshold beyond which Grover’s success probability collapses abruptly. Our results demonstrate that this threshold decreases exponentially with problem size, scaling as p∗(n)∝2−n/2, implying that cryptographically relevant problem sizes require unrealistically high oracle reliability to preserve quantum advantage. For n=40, the oracle must fail less than once every ∼800,000 iterations to preserve practical advantage, a requirement that becomes exponentially more stringent for larger key sizes. These findings do not contradict Grover’s theoretical correctness but highlight critical robustness limitations that must be explicitly considered when assessing quantum threats to symmetric cryptography. We provide actionable insights for post-quantum security assessment by translating abstract quantum assumptions into concrete reliability requirements, demonstrating that the practical feasibility of Grover-based attacks may be significantly lower than commonly assumed under realistic hardware constraints.
Abstract Due to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a quantum computer (post-quantum cryptography algorithms). The security of many well-known post-quantum cryptosystems based on lattice theory depends on the complexity of solving the shortest vector problem (SVP). In this paper, a model of quantum oracle developed from Grover’s algorithm is described to implement a hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used for attacks on cryptosystems whose security depends on solving the SVP. Upper bounds for the number of qubits and the depth of the circuit were obtained for two implementations of the proposed quantum oracle model: minimizing the number of qubits and minimizing the circuit depth. The complexity of implementing the proposed quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed.