Abstract Traditional threshold signature schemes, which are based on number-theoretic problems, are vulnerable to attacks in quantum computing environments. Moreover, these schemes incur high communication and computational costs among nodes, which pose significant challenges for meeting the stringent requirements of interactive security and real-time performance in power grid load regulation systems. To address these challenges, this paper introduces a post-quantum threshold signature scheme based on CRYSTALS-Dilithium (CDTS) specifically designed for power grid load regulation systems. Constructed within the Fiat-Shamir framework and integrating a CRYSTALS-Dilithium-based threshold signature, this scheme effectively ensures the system’s fault tolerance and security in the face of quantum computing threats. In terms of efficiency, the CDTS scheme significantly reduces computational overheads through the introduction of rejection sampling techniques and the optimization of the number-theoretic transform algorithm. To further enhance the scheme’s adaptability to the dynamic nature of power grid load regulation, an innovative dynamic threshold adjustment mechanism is proposed. This mechanism monitors load changes in real-time within a $$\Delta T$$ Δ T time window, allowing for flexible adjustments to the threshold parameters. Security analysis confirms that the proposed scheme satisfies the security requirements of power grid load regulation systems, making it a robust solution for ensuring secure and efficient load regulation in the quantum era. We conducted rigorous experimental comparisons under the same security level (NIST Level 3) and system scale ( $$th=5, n=10$$ t h = 5 , n = 10 ), the sizes of the public key (1.32 KB), private key (2.01 KB), and signature (2.45 KB) of the CDTS scheme are almost identical to those of the original Dilithium scheme. This data demonstrates that the threshold construction we proposed is nearly lossless in terms of storage efficiency, significantly outperforming the exponential overhead growth typically brought by traditional scheme. Through rigorous software testing and verification, we evaluated the performance of the CDTS scheme by randomly generating a 59-byte message and iteratively executing the signing process 10,000 times. The results indicate that the CDTS scheme achieves a complete signature and verification process in an average of 506.73 microseconds. This efficiency makes the CDTS scheme highly feasible for practical applications, particularly in environments requiring rapid and secure transaction processing.
Abstract Traditional threshold signature schemes, which are based on number-theoretic problems, are vulnerable to attacks in quantum computing environments. Moreover, these schemes incur high communication and computational costs among nodes, which pose significant challenges for meeting the stringent requirements of interactive security and real-time performance in power grid load regulation systems. To address these challenges, this paper introduces a post-quantum threshold signature scheme based on CRYSTALS-Dilithium (CDTS) specifically designed for power grid load regulation systems. Constructed within the Fiat-Shamir framework and integrating a CRYSTALS-Dilithium-based threshold signature, this scheme effectively ensures the system’s fault tolerance and security in the face of quantum computing threats. In terms of efficiency, the CDTS scheme significantly reduces computational overheads through the introduction of rejection sampling techniques and the optimization of the number-theoretic transform algorithm. To further enhance the scheme’s adaptability to the dynamic nature of power grid load regulation, an innovative dynamic threshold adjustment mechanism is proposed. This mechanism monitors load changes in real-time within a ΔT Δ T time window, allowing for flexible adjustments to the threshold parameters. Security analysis confirms that the proposed scheme satisfies the security requirements of power grid load regulation systems, making it a robust solution for ensuring secure and efficient load regulation in the quantum era. We conducted rigorous experimental comparisons under the same security level (NIST Level 3) and system scale ( th=5,n=10 t h = 5 , n = 10 ), the sizes of the public key (1.32 KB), private key (2.01 KB), and signature (2.45 KB) of the CDTS scheme are almost identical to those of the original Dilithium scheme. This data demonstrates that the threshold construction we proposed is nearly lossless in terms of storage efficiency, significantly outperforming the exponential overhead growth typically brought by traditional scheme. Through rigorous software testing and verification, we evaluated the performance of the CDTS scheme by randomly generating a 59-byte message and iteratively executing the signing process 10,000 times. The results indicate that the CDTS scheme achieves a complete signature and verification process in an average of 506.73 microseconds. This efficiency makes the CDTS scheme highly feasible for practical applications, particularly in environments requiring rapid and secure transaction processing.
To overcome the issue of traditional blind signature schemes being vulnerable to quantum computing attacks during interactions over the consumer electronic Internet of Things (CIoT), a new blind signature scheme called CDBS has been developed. The post quantum digital signature technique CRYSTALS-Dilithium, which was standardized by NIST, serves as the foundation for the quantum-resistant blind signature scheme, CDBS, presented in this study. This system is appropriate for a variety of internet application scenarios, including e-ticketing, anonymous payments, and privacy protection, because it integrates the idea of blind signatures, which is not included in typical digital signature schemes. This scheme is designed to resist quantum computing attacks and is based on the post-quantum digital signature algorithm CRYSTALS-Dilithium, which NIST has selected. The whole technique utilizes the Fiat-Shamir signature structure, which consists of five stages: key creation, blinding, signing, unblinding, and verification. The security of the proposed scheme is dependent on the resolution of the Module Learning with Errors (MLWE) problem and the Short Integer Solution (SIS) problem. Additionally, the scheme must satisfy the criteria of correctness, blindness, and unforgeability. According to the test results, the CRYSTALS-Dilithium scheme requires an average of 401.89 μ s for a single round of verification and signing. The CDBS technique takes an average of 657.65 ls for one round of signing and verification since the blinding and unblinding modules are added on top of the original algorithm, increasing the algorithm’s complexity. The software testing results indicate that the average time required to complete a single full blind signature and verification operation is 657.65 microseconds. The suggested system offers a framework for expanding the CRYSTALS-Dilithium digital signature algorithm.
Distributed systems are widely used in modern environments such as cloud platforms, Internet of Things (IoT) networks, smart grids, and blockchain-based systems. These platforms often require digital signatures to maintain trust between devices or users. When many signatures are shared at once, the size of the communication grows, and processing takes more time. This becomes a problem in applications where quick message verification is important. Classical digital signature schemes, such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA), are not safe against quantum attacks. Post-quantum cryptography offers better protection, but it often increases communication size and computation cost. This paper introduces a quantum-resistant model that supports signature aggregation and constant-time verification. The method is based on lattice-based techniques, using structures similar to CRYSTALS-Dilithium. By combining several signatures into a single aggregated form, the model reduces the time needed for verification and the overall communication overhead. The design is suitable for real-time applications, offering strong accuracy and faster message handling. Simulation results show that the proposed method performs better than recent approaches in multiple areas. The model achieves a low authentication time, high verification accuracy, reduced message size, and improved throughput. These benefits help meet the needs of distributed systems where speed, accuracy, and security must work together. The architecture is designed to be flexible for use in real-world deployments. Future directions include support for multi-party signing, adaptive quantum-safe policies, and integration with quantum co-processors. This research supports the development of secure and efficient communication frameworks that remain effective even in the presence of future quantum threats.
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.
As quantum computing advances, modern cryptographic standards face an existential threat, necessitating a transition to post-quantum cryptography (PQC). The National Institute of Standards and Technology (NIST) has selected CRYSTALS-Kyber and CRYSTALS-Dilithium as standardized PQC algorithms for secure key exchange and digital signatures, respectively. This study conducts a comprehensive performance analysis of these algorithms by benchmarking execution times across cryptographic operations such as key generation, encapsulation, decapsulation, signing, and verification. Additionally, the impact of AVX2 optimizations is evaluated to assess hardware acceleration benefits. Our findings demonstrate that Kyber and Dilithium achieve efficient execution times, outperforming classical cryptographic schemes such as RSA and ECDSA at equivalent security levels. Beyond technical performance, the real-world deployment of PQC introduces challenges in telecommunications networks, where large-scale infrastructure upgrades, interoperability with legacy systems, and regulatory constraints must be addressed. This paper examines the feasibility of PQC adoption in telecom environments, highlighting key transition challenges, security risks, and implementation strategies. Through industry case studies, we illustrate how telecom operators are integrating PQC into 5G authentication, subscriber identity protection, and secure communications. Our analysis provides insights into the computational trade-offs, deployment considerations, and standardization efforts shaping the future of quantum-safe cryptographic infrastructure.
ABSTRACT The rapid advancement of quantum computing presents a significant threat to classical cryptographic systems, particularly RSA, whose security is based on the hardness of integer factorization. Shor’s algorithm demonstrates that large RSA keys can be efficiently broken in a quantum environment, raising concerns about the long-term reliability of traditional digital signatures. To address this, post-quantum cryptography (PQC) has emerged as a promising solution, with lattice-based schemes such as CRYSTALS-Dilithium3 gaining attention for their quantum resistance and efficiency. This study presents a comparative security and performance analysis of RSA and CRYSTALS-Dilithium3 digital signatures in the post-quantum era. The evaluation considers signature size, signing and verification speed, tamper detection capability, and resilience against classical and quantum attack models. Results highlight that RSA offers compact signature sizes but fails to provide integrity protection once subjected to simulated quantum attacks, while Dilithium3 ensures robust tamper detection, forward security, and cross-format verification across multiple document types. Despite larger signature sizes, Dilithium3 demonstrates superior verification speed and scalability, making it a viable candidate for post-quantum digital infrastructures. The findings emphasize the need for transitioning from classical to quantum-resistant cryptographic systems to ensure secure digital communication in the emerging quantum age. Keywords: Post-Quantum Cryptography, RSA, CRYSTALS-Dilithium3, Digital Signatures, Quantum Attacks, Tamper Detection, Performance Analysis
With the advancement in quantum computing technology, the number theory-based hard problems underlying traditional searchable encryption algorithms are now vulnerable to efficient quantum attacks. To address this challenge, this paper proposes Dilithium-PAEKS (Dilithium-Public Authenticated Encryption with Keyword Search), a searchable encryption scheme based on the post-quantum cryptographic algorithm CRYSTALS-Dilithium. By transforming the verification relationship of digital signatures into a matching relationship between trapdoors and ciphertexts, the scheme not only meets the functional requirements of searchable encryption but also demonstrates quantum resistance. The implementation enhances algorithm efficiency through keyword-based signatures and dynamic matching testing mechanisms. The security of the scheme is defined by the MLWE and MSIS hard problems, with proofs of keyword ciphertext indistinguishability and trapdoor indistinguishability under the random oracle model. Additionally, the scheme provides strong resistance against both outside and insider keyword guessing attacks through sender–receiver binding mechanisms and trapdoor indistinguishability properties. Experimental results show that, compared to the post-quantum schemes CP-Absel and LB-FSSE, the proposed scheme demonstrates superior overall computational efficiency while maintaining stronger quantum resistance than the traditional scheme SM9-PAEKS.