The rapid advancement of quantum computing necessitates the exploration of alternative mathematical frameworks. This paper introduces a novel hybrid cryptographic protocol that combines tropical semirings with well-established classical primitives. Central to our approach is the Tropical Factorization with Discrete Logarithm Problem (TFDLP), a computationally challenging task that underpins the security of the proposed tropical-based key exchange. The protocol integrates this algebraic method with classical primitives (SHA-256 hashing and AES-GCM encryption) to enhance security, ensuring both quantum resistance and computational efficiency. A detailed security analysis highlights the strengths of our protocol against known cryptanalytic attacks and offers recommendations for secure implementation. Potential use cases for this hybrid scheme include quantum-safe secure messaging, blockchain technologies, and the protection of critical infrastructure systems.
The rapid advancement of quantum computing necessitates the exploration of alternative mathematical frameworks. This paper introduces a novel hybrid cryptographic protocol that combines tropical semirings with well-established classical primitives. Central to our approach is the Tropical Factorization with Discrete Logarithm Problem (TFDLP), a computationally challenging task that underpins the security of the proposed tropical-based key exchange. The protocol integrates this algebraic method with classical primitives (SHA-256 hashing and AES-GCM encryption) to enhance security, ensuring both quantum resistance and computational efficiency. A detailed security analysis highlights the strengths of our protocol against known cryptanalytic attacks and offers recommendations for secure implementation. Potential use cases for this hybrid scheme include quantum-safe secure messaging, blockchain technologies, and the protection of critical infrastructure systems.
The rapid development of quantum computing presents a substantial threat to traditional cryptographic algorithms, particularly those relying on mathematical problems such as integer factorization and elliptic curve operations. As a response, the cryptographic community has accelerated the design of post-quantum cryptographic schemes that can withstand attacks from both classical and quantum computers. However, many of these new schemes exhibit inherent trade-offs between performance, key sizes, and implementation complexity. To address this, we propose a novel hybrid cryptographic framework tailored for secure and efficient data transmission in future quantum-aware environments. The proposed system combines three algorithmic paradigms: a lattice-based encryption method for fast and lightweight data protection, a hash-based signature mechanism for authenticity, and a code-based key exchange method to ensure session confidentiality. This layered integration is designed to capitalize on each algorithm’s strengths while mitigating individual limitations. The system is implemented using modular components in a testbed simulating real-world deployments, and its performance is benchmarked across multiple metrics including encryption latency, signature generation time, key sizes, and throughput. Comparative results indicate that the hybrid approach outperforms monolithic schemes in critical areas such as execution time and cryptographic strength under quantum adversary models. The findings support the practicality of using multiple post-quantum primitives in tandem to build robust communication systems. This research contributes a realistic implementation and evaluation of post-quantum security models and highlights key directions for future research and standardization efforts as the global transition to quantum-safe infrastructure begins.
Shor’s quantum algorithm establishes a polynomial time attack on the discrete logarithm problem in any group. Recent announcements of progress in building quantum computers highlight the need for new concepts to create cryptosystems that are resistant to quantum attacks. In this paper, we present а new message encryption scheme. To enhance the security of the scheme, we suggest double key-exchange protocol (KEP). The first stage of the key exchange uses a matrix power function (MPF) in a tropical semiring. These functions are based on the action of a matrix semiring acting on some matrix set. MPFs can be considered as one-way functions because they are based on some generalized satisfiability problems that are potentially NP-complete. The obtained shared secret key at the first stage of the key exchange serves as an input for the second stage. The security of the second phase relies on the difficulty of the semiring action problem. In our protocol, we suggest using left or right action of the tropical semiring (which can be both min-plus and max-plus) on the group of commutative matrices (circulant matrices, in our case). The fact that the key-exchange protocol works in two phases contributes to its security, since an attacker needs to solve two difficult problems in order to break it. The main advantages of the presented protocol are: the increased efficiency and improved security.
Quantum computing advancements create threat to encryption systems which protect modern digital communication networks. The integer factorization and discrete logarithm problems which RSA and ECC algorithms depend on become vulnerable to Shor's algorithm when large-scale quantum computers achieve operational status. Billions of small IoT devices operating in resource-constrained environments face a major security risk because their lightweight encryption methods lack protection against quantum-level attacks. The research investigates Post-Quantum Cryptography(PQC) as a new cryptographic framework which protects against both quantum and classical attacks. The proposed system integrates three advanced elements that work together to provide lattice-based encryption for mathematical security and hash-based signature schemes for authentication and an intelligent threat detection system. The hybrid framework provides complete security protection while maintaining high performance and low processing requirements which makes it suitable for protecting IoT networks.
The emergence of quantum computing poses a fundamental threat to current public key cryptographic systems. This threat is necessitating a transition to quantum resistant cryptographic alternatives in all the applications. In this work, we present the implementation of a practical hybrid end-to-end encryption system that combines classical and post-quantum cryptographic primitives to achieve both security and efficiency. Our system employs CRYSTALS-Kyber, a NIST-standardized lattice-based key encapsulation mechanism, for quantum-safe key exchange, coupled with AES-256-GCM for efficient authenticated symmetric encryption and SHA-256 for deterministic key derivation. The architecture follows a zero-trust model where a relay server facilitates communication without accessing plaintext messages or cryptographic keys. All encryption and decryption operations occur exclusively at client endpoints. The system demonstrates that NIST standardized post-quantum cryptography can be effectively integrated into practical messaging systems with acceptable performance characteristics, offering protection against both classical and quantum adversaries. As our focus is on implementation rather than on novelty, we also provide an open-source implementation to facilitate reproducibility and further research in post quantum secure communication systems.
Cryptography, the practice of concealing messages for private exchange, has evolved significantly to address the challenges posed by new communication methods. In today`s digital world, cryptography has become the cornerstone of cybersecurity, using advanced mathematics like number theory and computational complexity to protect digital information through algorithms. The upcoming arrival of quantum computers poses a serious threat to traditional cryptographic methods, especially those based on asymmetric key cryptography. Quantum Safe Cryptography (QSC) represents the next step in information security, designed to develop cryptographic systems that can withstand attacks from both quantum and classical computers. As quantum computing moves from theory to reality, it`s becoming clear that current cryptographic methods based on integer factorization and discrete logarithm problems are vulnerable to quantum algorithms like Shor`s algorithm. This study highlights the security risks that quantum computing poses to existing encryption methods and proposes a comprehensive approach to quantum-safe cryptography. The transition to quantum-resistant algorithms involves replacing vulnerable cryptographic systems with alternatives that can resist quantum computational attacks. Current analysis shows that while asymmetric key cryptography faces immediate vulnerability, symmetric key algorithms and hash functions remain relatively secure in the near term with appropriate adjustments. Quantum cryptography, which directly uses quantum mechanical principles, offers highly secure encryption mechanisms, notably Quantum Key Distribution (QKD). This research aims to enhance the security of digital infrastructure against quantum threats by evaluating hybrid cryptographic implementations that combine classical and quantum-resistant approaches for optimal security.
The advent of quantum computing poses an existential threat to contemporary cryptographic standards, particularly those securing decentralized blockchain networks and cloud infrastructures.Classical public-key cryptosystems such as RSA, ECC, and DH, which rely on factorization and discrete logarithm problems, are rendered obsolete by Shor's algorithm, necessitating the transition toward post-quantum cryptographic (PQC) solutions.This study explores the integration of PQC algorithms, including lattice-based, hash-based, code-based, multivariate, and isogeny-based cryptographic mechanisms, within blockchain-ledger technologies and cloud architectures to ensure long-term security against quantum adversaries.A comparative analysis is conducted to evaluate computational efficiency, key size implications, communication overhead, and security resilience under quantum attack models.The research highlights the adaptation of PQC within blockchain consensus mechanisms, smart contract execution, and cryptographic primitives such as digital signatures, zero-knowledge proofs, and secure multi-party computation (MPC).Additionally, it examines the impact of PQC on cloud security, addressing challenges in quantum-safe key exchange protocols, homomorphic encryption for secure computations, and cross-platform interoperability within hybrid quantum-classical cloud ecosystems.Real-world implementations and benchmarking data provide insights into the feasibility of large-scale adoption, shedding light on standardization efforts by NIST and industry consortia.The study concludes with future directions, emphasizing the need for efficient PQC algorithm optimization, lightweight cryptographic frameworks for IoT-driven blockchain applications, and scalable post-quantum identity management systems.By establishing quantum-resistant security frameworks, this research underscores the imperative need for early adoption to mitigate cryptographic vulnerabilities in the impending post-quantum era.