ABSTRACT Mobile agents are autonomous software entities capable of migrating across heterogeneous platforms to perform distributed computational tasks with reduced communication overhead and improved operational flexibility. Despite these advantages, secure authentication of mobile agents remains a significant challenge in hostile and untrusted network environments due to threats such as impersonation, replay attacks, and man-in-the-middle attacks. This paper presents an efficient mobile agent authentication protocol based on the hardness of the Discrete Logarithm Problem (DLP) within group ring cryptographic structures. The proposed scheme utilizes the algebraic properties of group rings to provide secure key generation, authentication, and verification mechanisms while maintaining computational efficiency suitable for distributed and cloud-based systems. The protocol enables secure identity validation without revealing secret credentials, thereby strengthening confidentiality and integrity during agent migration. Security analysis demonstrates that the proposed protocol effectively resists major authentication attacks and provides enhanced cryptographic strength compared with existing lightweight authentication schemes. Performance evaluation further indicates reduced authentication time, lower communication overhead, and feasible computational cost, making the protocol suitable for dynamic multi-agent and distributed computing environments. The proposed approach offers a scalable and practical security solution for next-generation mobile agent systems.

Digital signatures serve as a crucial cryptographic primitive in an e-governance system for authenticating citizen-government interactions. Traditional methods (DSA, ECDSA) impose computational overhead on resource-limited endpoints and centralized verification servers. While complex-number cryptography provides theoretical efficiency through the Complex Discrete-Logarithm Problem (CDLP), prior works often fail to meet the requirements for real-world applications. This paper advances the knowledge in lightweight cryptography by introducing LDSEGoV, a lightweight digital signature scheme for e-governance infrastructure. The proposed method overcomes the shortcomings of previous methods by incorporating sound modular arithmetic for consistent verification, using NIST-approved hash functions. Furthermore, we provide a comprehensive security analysis, including formal proofs of existential unforgeability (EUF-CMA) for the proposed scheme in the Random Oracle Model. Additionally, the experimental results show a 6.5× improvement in signing performance and a 24.76× improvement in verification performance over ECDSA, with a 61% reduction in signature size. These results demonstrate computational efficiency suitable for e-governance authentication scenarios.

Fan graph encryption scheme using discrete logarithm problem

• The first functional implementation that integrates SDN, QKD, and IPsec technologies within a unified architecture, enabling dynamic establishment of IPsec tunnels protected with Quantum Key Distribution. • The proposed solution is based on the implementation of IPsec in accordance with QKD-related standards defined by ETSI, specifically adhering to the specifications ETSI GS QKD 004 and ETSI GS QKD 015. This approach ensures interoperability and alignment with current best practices for quantum secure network deployments. • Experimental results were obtained from a field-deployed QKD network operating over a hybrid quantum-classical infrastructure, providing empirical validation of the proposed approach in a production-grade environment laying a solid foundation for future large-scale deployments. The importance of digital communications makes protecting data in transit a critical priority. Internet Protocol Security (IPsec) plays a central role in this protection, by ensuring data confidentiality, integrity, and authenticity. However, quantum computing threatens the foundations of IPsec. Its ability to efficiently solve mathematical problems such as factoring and discrete logarithms could break the public-key cryptography used for IPsec key exchange. Quantum Key Distribution (QKD) is one of the most promising solutions to this problem, offering a security layer immune to both classical and quantum computational attacks. This work proposes a solution that integrates emerging quantum technologies into existing security and communication infrastructures to ensure long-term protection. We combine IPsec with Software-Defined Networking and QKD to build a novel network security infrastructure. It is designed to resist both classical and quantum threats. It is based on recent standardization efforts and operational tools for QKD integration. We demonstrate advanced capabilities such as rekeying and secure key transport on a field deployed QKD network operating within a shared quantum-classical production infrastructure.

The integration of communication technologies has made authentication a crucial security element in the cyberphysical power system (CPPS) scenario. Since it offers a range of security services, such as credentials privacy, session-key (SK) security, and safe mutual authentication, authentication plays a significant role in the CPPS context. In this article, the threat of quantum attacks to the security of CPPS is analyzed. The attacks are developed based on the principles of quantum computing, and they can easily compromise SK security under the wellaccepted traditional difficulty problems of discrete logarithms and large integer factorization. A new efficient and secure authenticated post-quantum key agreement scheme is proposed for CPPS, leveraging ring learning with errors (RLWE) problem to achieve the security functionalities, for example, SK security. In the RLWE problem, a number-theoretic transform method is investigated to improve the efficiency of the proposed scheme. Moreover, the Indistinguishability under Chosen Ciphertext Attack security of the proposed scheme in this paper is formally proven in the random oracle model through the construction of a security game. Furthermore, security analysis shows the proposed scheme can ensure data confidentiality, SK security, forward secrecy, resistance to eavesdropping attacks, and quantum attack resistance under the RLWE problem. The proposed scheme reduces the computation and communication overheads for CPPS devices. Additionally, the proposed scheme offers more security functionalities than the existing schemes. Cite this article as: X. Li, Y. Zhu, X. Yuan, Z. Zhou and C. Jiang, “Secure authenticated post-quantum key agreement scheme based on ring learning with errors for cyber-physical power system,” Electrica, 2026, 26, 0182, doi: 10.5152/electrica.2026.25182.

The emergence of quantum computing has introduced both opportunities and threats to modern secure communication systems. Classical cryptographic algorithms, which rely on computational complexity, are vulnerable to quantum algorithms capable of solving problems such as integer factorization and discrete logarithms efficiently. This paper explores the role of quantum computing in secure communication, focusing on quantum cryptographic techniques such as Quantum Key Distribution (QKD) and Quantum Secure Direct Communication (QSDC). A comprehensive review of existing literature is presented, followed by an analysis of methodologies used in quantum-secure communication systems. The study evaluates the advantages, limitations, and practical challenges of implementing quantum communication technologies. Finally, future research directions and the integration of quantum technologies into next-generation communication networks are discussed.

The accelerating adoption of federated learning as a distributed machine learning paradigm has opened a new dimension of data privacy in interconnected industrial systems. While federated learning allows participating clients to retain raw data locally and transmit only model parameter updates for global training, it remains vulnerable to inference attacks mounted by an honest-but-curious aggregation server. Countermeasures that exist today either demand a trusted third party for key generation, impose computationally expensive operations such as discrete logarithm evaluation every training round, or fail to accommodate the dynamic participation patterns—dropouts and rejoins—that are unavoidable in large-scale industrial deployments. This paper introduces a general-purpose, efficient, and provably private cross-silo federated learning protocol specifically designed to address these shortcomings. The approach pairs a novel double-layer encryption mechanism with Shamir’s threshold secret sharing, arranging the protocol so that secret sharing is invoked only at the key-establishment phase and upon client re-entry rather than at every round. The result is a scheme that achieves cryptographic privacy guarantees without the ciphertext-expansion cost of homomorphic encryption and without the accuracy penalty associated with differential privacy. The framework is applied concretely to the detection of False Data Injection Attacks (FDIA) in multi-area power transmission grids, using IEEE 14-bus and IEEE 118-bus benchmark datasets. Empirical evaluation demonstrates that the proposed federated model attains 93.4% classification accuracy on the 14-bus case and 91.8% on the 118-bus case after fifty communication rounds, staying within two percentage points of a fully centralised ensemble baseline while providing stronger and more principled privacy assurances

Blockchain-based systems increasingly require authentication mechanisms that simultaneously preserve user privacy, support accountability, and enable efficient credential revocation. However, most existing anonymous authentication schemes rely on pairing-based cryptography which introduce high computational overhead and limit deploy ability on widely adopted blockchain platforms such as Ethereum. This paper presents BAAR, a Blockchain-based Anonymous and Revocable authentication framework designed entirely within the discrete logarithm setting over the secp256k1 elliptic curve. BAAR integrates Pedersen vector commitments, Schnorr-based zero-knowledge proofs, and a Merkle-tree-based dynamic accumulator to support anonymous and unlinkable authentication with selective attribute disclosure and public, auditable revocation. Authentication and proof verification are performed off-chain, while the blockchain maintains only a compact revocation state, significantly reducing on-chain computation and gas costs. A formal security analysis demonstrates unforgeability, unlinkability, attribute privacy, and revocation soundness under standard cryptographic assumptions in the random oracle model. A prototype implementation on Ethereum confirms that BAAR achieves low gas consumption, logarithmic-time revocation, and scalable performance with respect to both the number of users and attributes. These results indicate that BAAR provides a practical balance between strong privacy guarantees and deploy ability, making it suitable for real-world blockchain-based identity and access-control systems.

In real-world applications, anonymity, confidentiality, and unforgeability play pivotal roles in secure communication, especially in the scenarios where privacy and security are dominant concerns. The novel paradigm of certificateless anonymous proxy signcryption introduced in this work allows the original signer to expose the proxy signer’s identity if it is misused, while simultaneously granting anonymity to the proxy signer. We design a CL-APSC mechanism and it’s security is proven by using the Diffie-Hellman and discrete logarithm problem in the elliptic curve. Additionally, we provide a security model and a formal definition of the certificateless anonymous proxy signcryption (CL-APSC) technique. Since the proposed approach operates in a certificateless environment, it eliminates the overhead of maintaining certificates and avoids the key escrow problem. Our aim in this article is to reduce the computational cost with the existing schemes and also provides anonymity to the proxy identity.

The fast growth of quantum computing puts widely used public-key cryptosystems like RSA and Elliptic Curve Cryptography (ECC) at risk because Shor's algorithm can quickly factor integers and find discrete logarithms. Grover’s algorithm similarly weakens symmetric ciphers like AES, necessitating larger key sizes. This work proposes the Hyperring RSA–AES Hybrid Encryption Scheme (HRA-HES), a hybrid cryptosystem that achieves post-quantum security for simple ciphers while preserving practical usability. HRA-HES derives session keys via Hyperring Learning with Noise within a Key Encapsulation Mechanism, and AES-256-GCM uses these keys to encrypt large data blocks. The multi-valued hyperaddition in the underlying hyperring structure disrupts the periodicity exploited by quantum period-finding algorithms. Implementation results show an encryption throughput of 850 Mbps and an average key generation time of about 2.1 ms, yielding improvements of up to 44% over prior baselines while maintaining low resource consumption, thus offering a scalable, quantum-aware transition framework.

We give a new approach to the fundamental question of whether proof complexity lower bounds for concrete propositional proof systems imply super-polynomial Boolean circuit lower bounds. We observe that any general implication from proof complexity lower bounds for a propositional proof system to super-polynomial Boolean circuit lower bounds implies unconditionally that \({\sf NEXP} \) does not have Boolean circuits of polynomial size. We explore connections that are possible to establish without settling this long-standing and famously hard open question. For any poly-time computable function f , we define the witnessing formulas \(w_n^k(f) \) , which are propositional formulas stating that for any circuit C of size n k on n variables and for any formula ϕ of size n , either C computes a satisfying assignment to ϕ or f verifiably refutes that C computes \({\sf SAT} \) on instances of length n . We show that if the witnessing formulas are tautologies, then any super-polynomial lower bound for Extended Frege augmented with \(w_n^k(f) \) axioms implies that \({\sf SAT} \) requires super-polynomial size Boolean circuits. We also give an unconditional equivalence between circuit lower bounds for the Discrete Logarithm problem and proof complexity lower bounds (for propositional formulas efficiently encoding the statement that the Discrete Logarithm problem is computable by small circuits) for a concretely defined strong (non-uniform) propositional proof system. We give consequences of our connections for the meta-mathematics of several major questions in computational complexity, including whether one-way functions can be based on the worst-case hardness of NP, whether there is a dichotomy between one-way functions and worst-case learning with membership queries over the uniform distribution, and whether there are feasibly constructible anti-checkers for Satisfiability. We show that for each of these questions, provability of a positive answer in essentially any standard mathematical theory would imply new connections between propositional proof complexity and circuit complexity. Our results rely on a new notion of “self-provability” of upper bounds, which might be independently interesting, and involve a novel application of random self-reducibility to proof complexity.

Data security has become one of the primary concerns, particularly for images, as conventional encryption methods such as the Vigenere cipher or ring [Formula: see text] -based methods are no longer robust against modern types of attacks. To resolve the issue, this paper introduces a novel hybrid image encryption technique that combines elliptic curve cryptography (ECC), finite field extensions integrating the AJ chaotic map for dynamic parameters generation and image-dependent key adaptation. First, the method depends on the pseudorandom selection of an elliptic curve over the field [Formula: see text] designed based on an irreducible polynomial of degree 8. Second, two substitution tables are designed based on discrete logarithm and exponentiation operations to improve the impact of the confusion and diffusion. Numerous in-depth security experiments, including entropy, NPCR, UACI, correlation coefficients, and the NIST statistical test, have been performed, indicating high cryptographic robustness against known attacks. The findings affirm the performance of the proposed method in achieving an average entropy of 7.9998 bits per pixel, a correlation coefficient of adjacent pixels less than 0.001, NPCR of 99.79%, and UACI of 33.59% for the Peppers color image. In addition, our technique achieves a competitive execution time, confirming both its security and efficiency. Therefore, it is evident that the employment of ECC over a finite body along with a dynamically designed SBox is an ideal high-performance method for privacy protection, secure data storage, and trustworthy transmission of sensitive data.

Elliptic curve digital signature scheme with enhanced chaotic characteristics using dynamic S-boxes

A provably quasi-polynomial algorithm for the discrete logarithm problem in finite fields of small characteristic

This study aims to propose the improvement of RSA to secure the digital signature. This algorithm, which is called FE-RSA, focuses on two primary challenges: security and computing efficiency. A secret key and a fake public key are selected for the implementation to provide an additional security layer. In fact, FE-RSA attempts to protect against digital signature forgery. Moreover, the other main point of FE-RSA is that although an attacker can factor the modulus, FE-RSA is still secure. In addition, 512-bit, 1024-bit, and 2048-bit key sizes across four cryptography algorithms, including RSA, Multi-Prime RSA, the application of RSA and ElGamal (RSA-ElGamal), and FE-RSA, are selected for the experiment. Performance evaluations focused on processing time for the generation and validation processes. The experimental results demonstrate that FE-RSA regularly outperforms Multi-Prime RSA and RSA-ElGamal in terms of signing and verifying speed. In the signing process, FE-RSA is approximately 92.47%, 64.50%, and 3.82% faster than RSA-ElGamal for key sizes of 512-bit, 1024-bit, and 2048-bit, respectively. However, in the verification process, this method reduces processing time by about 97.12%, 87.53%, and 34.33% for identical key sizes. Then, it implies that FE-RSA provides the most significant performance benefit in the verification process. Although the processing time required in FE-RSA is slower than that of RSA, the security is higher than that of RSA. The reason is that RSA is based on only the Integer Factorization Problem (IFP). On the other hand, FE-RSA is based on both the Discrete Logarithm Problem (DLP) and IFP. However, FE-RSA is effectively applied in situations when a specific and reliable verifier has the secret key. In fact, FE-RSA integrates enhanced computing efficiency with multi-layered security. Therefore, the proposed method is established as a viable and resilient option for digital signature systems.

The article examines a block cryptographic algorithm using a two-component shared secret key obtained according to the Diffie-Hellman key exchange principle on elliptic curve points over the field Z p . The goal is to eliminate shortcom­ings of individual classical algorithms and, through their combination, increase overall system strength. Key generation and exchange between users are carried out using elliptic curve cryptographic systems with public key. Two methods are proposed for generating shared secret keys for interacting users: applying the Diffie-Hellman cryptographic protocol on multiple elliptic curve points or additionally using a recurrence formula. Encryption elements are represented by blocks as square matrices constructed on elliptic curve point coordinates. Encryption proceeds in two stages: the first uses stream cipher with scalar multiplication of elliptic curve points, and the second involves forming matrix blocks and performing Hill matrix transformation with feedback. Each encryption stage utilizes its corresponding component of the users’ shared secret key: a numerical gamma sequence or a square key matrix. The cryptographic strength is based on the computational complexity of solving the discrete logarithm problem on elliptic curves and the security of the sharing service with secure authentication of interacting users. The block implementation of the second encryption stage ensures the system’s resistance to frequency analysis. As an illustration of the presented algorithm’s operation, the article provides a step-by-step example of encrypting/decrypting a text message.

GenElGamal is an extension of the ElGamal public key encryption scheme, which modifies the key generation and encryption steps, proposed by Sow and Sow in [24]. With the rise of quantum computing, the security of public key cryptosystems based on the discrete logarithm problem, particularly GenElGamal, is threatened. In this paper, we propose a post-quantum version of the GenElGamal cryptosystem called PQ-GenElGamal using the difficult modulo 1 factoring problem (M1FP) that is resistant to post-quantum attacks. We describe our scheme and prove its security against both classical and post-quantum attacks.

Modern security models for public-key cryptography, such as one-way encryption under chosen plaintext attack (OWE-CPA) or indistinguishability under chosen plaintext attack (IND-CPA), rely on reductions between the security of cryptographic schemes and well-studied hard problems, such as integer factorization, discrete logarithm, quadratic residuosity, or learning with errors. The reduction can go from the hard problem to the security property under study, or vice versa, or in both directions (in which case we say there is an equivalence). Equivalences fundamentally tie the security property to the hard problem, thus offering multiple benefits. But obtaining an equivalence between a security property and a computational hard problem can be challenging, as is the case with the equivalence between the OWE-CPA security of the textbook RSA cryptosystem and the integer factorization problem. In this paper, we introduce a new computational problem, namely, distinguishing the Jacobi symbols of the solutions of a quadratic congruence modulo an RSA modulus (JSP(QC)). We show that this problem is at least as hard as the quadratic residuosity problem. Then, we show that the IND-CPA security of two public-key encryption schemes due to Cocks is equivalent to JSP(QC). We then specialize JSP(QC) to roots of quadratic residues and establish several computational indistinguishability results.

Land registration in Bangladesh continues to rely on paper-based processes that are susceptible to forgery, duplication, and inefficiency. These vulnerabilities contribute to widespread disputes over property ownership and create barriers to transparent governance. Recognizing that the root of these issues lies in the absence of a secure mechanism for verification, this study turns to algebraic cryptography as a potential solution. This paper introduces an algebraic cryptographic framework for securing land registration through Elliptic Curve Cryptography (ECC), specifically the Elliptic Curve Digital Signature Algorithm (ECDSA). It is built upon the hardness of the elliptic curve discrete logarithm problem, which ensures signatures that are computationally unforgeable. This study also considers the theoretical advantages of ECC over the Rivest–Shamir–Adleman (RSA) algorithm, particularly its ability to deliver equivalent security with smaller key sizes, faster verification, and lower storage requirements. The mathematical model developed in this paper formalizes these properties and evaluates their implications for a large-scale registry system. It explores how compact signatures, low verification latency, and limited data growth can be aligned with the resource constraints of Bangladeshi land offices. The contribution of this work lies in connecting rigorous mathematical security with a practical national need. By embedding algebraic cryptography into land registration, the framework provides a pathway to prevent fraudulent transfers and enhance institutional trust. This vision points toward a future in which property rights in Bangladesh are secured not by fragile paper, but by the certainty of algebraic cryptography. Dhaka Univ. J. Sci. 74(1): 179-185, 2026 (January)

Abstract Recent years have seen the widespread adoption of zkSNARKs constructed over small fields, including but not limited to, the Goldilocks field, small Mersenne prime fields, and tower of binary fields. Their appeal stems primarily from their efficacy in proving computations with small bit widths, which facilitates efficient proving of general computations and offers significant advantages, notably yielding remarkably fast proving efficiency for tasks such as proof of knowledge of hash preimages. Nevertheless, employing these SNARKs to prove algebraic statements (e.g., RSA, ECDSA signature verification) presents efficiency challenges, particularly in critical applications like zk-bridges and zkVMs that require verifying standard cryptographic primitives. To address this problem, we first define a new circuit model: arithmetic circuits with additional exponentiation gates . These gates serve as fundamental building blocks for establishing more intricate algebraic relations. Then we present a Hash-committed Commit-and-Prove (HCP) framework to construct Non-interactive Zero-knowledge (NIZK) proofs for the satisfiability of these circuits. Specifically, when proving knowledge of group exponentiations in discrete logarithm hard groups and RSA groups, compared to verifying complex group exponentiations within SNARK circuits, our approach requires proving only more lightweight computations within the SNARK, such as zk-friendly hash functions (e.g., Poseidon hash function). The number of these lightweight computations depends solely on the security parameter. This differentiation leads to substantial speedups for the prover relative to direct SNARK methods, while maintaining competitive proof size and verification cost.