This paper presents an enhanced post-quantum key agreement protocol based on Rényi entropy, addressing vulnerabilities in the original construction while preserving information-theoretic security properties. We develop a theoretical framework leveraging entropy-preserving operations and secret-shared verification to achieve provable security against quantum adversaries. Through entropy amplification techniques and quantum-resistant commitments, the protocol establishes $2^{128}$ quantum security guarantees under the quantum random oracle model. Key innovations include a confidentiality-preserving verification mechanism using distributed polynomial commitments, tightened min-entropy bounds with guaranteed non-negativity, and composable security proofs in the quantum universal composability framework. Unlike computational approaches, our method provides information-theoretic security without hardness assumptions while maintaining polynomial complexity. Theoretical analysis demonstrates resilience against known quantum attack vectors, including Grover-accelerated brute force and quantum memory attacks. The protocol achieves parameterization for 128-bit quantum security with efficient $\mathcal{O}(n^{2})$ communication complexity. Extensions to secure multiparty computation and quantum network applications are established, providing a foundation for long-term cryptographic security.
This paper presents an enhanced post-quantum key agreement protocol based on Rényi entropy, addressing vulnerabilities in the original construction while preserving information-theoretic security properties. We develop a theoretical framework leveraging entropy-preserving operations and secret-shared verification to achieve provable security against quantum adversaries. Through entropy amplification techniques and quantum-resistant commitments, the protocol establishes 2128 quantum security guarantees under the quantum random oracle model. Key innovations include a confidentiality-preserving verification mechanism using distributed polynomial commitments, tightened min-entropy bounds with guaranteed non-negativity, and composable security proofs in the quantum universal composability framework. Unlike computational approaches, our method provides information-theoretic security without hardness assumptions while maintaining polynomial complexity. Theoretical analysis demonstrates resilience against known quantum attack vectors, including Grover-accelerated brute force and quantum memory attacks. The protocol achieves parameterization for 128-bit quantum security with efficient O(n2) communication complexity. Extensions to secure multiparty computation and quantum network applications are established, providing a foundation for long-term cryptographic security.
The looming threat of large-scale quantum computers necessitates a paradigm shift in cryptographic design, giving rise to the field of Post-Quantum Cryptography (PQC). While the computational hardness assumptions underpinning PQC schemes are well-studied, their fundamental security limits from an information-theoretic perspective remain an area requiring deeper exploration. This paper introduces and systematically investigates the concept of "entropic resilience," defined as the inherent ability of a cryptographic system to maintain its security guarantees even under an adversary possessing unbounded computational power, provided only limited information about the secret components is revealed. We present a comprehensive framework for analyzing the information-theoretic security of prominent PQC families, including lattice-based, code-based, and hash-based schemes. Our methodology leverages various entropy measures, such as min-entropy and conditional entropy, to quantify the information leakage and the irreducible uncertainty preserved in cryptographic secrets. We derive theoretical bounds on the information-theoretic security for representative PQC constructions and discuss the implications of these bounds for parameter selection, key generation, and resistance against information-theoretic attacks and side channels. The findings highlight critical trade-offs between entropy requirements, efficiency, and the achievable level of provable security in a post-quantum world. Ultimately, this work provides a foundational understanding of the ultimate security boundaries for PQC, guiding the design of more robust and provably secure schemes against both classical and quantum adversaries.
The advent of quantum computing poses a significant threat to the security of current cryptographic systems, including those underpinning secure multi-party computation (MPC). While considerable research has focused on developing post-quantum cryptographic (PQC) primitives, their integration into MPC protocols often inherits the computational security assumptions characteristic of classical cryptography. This paper explores the information-theoretic foundations for designing and analyzing post-quantum secure MPC protocols, aiming to achieve security guarantees that are independent of computational hardness assumptions and resilient against adversaries with unbounded computational power, including quantum adversaries. We delve into how information-theoretic primitives, such as secret sharing and oblivious transfer, can be adapted or combined with post-quantum techniques to construct MPC protocols with enhanced security. The work reviews existing paradigms, identifies challenges in achieving robust post-quantum information-theoretic security, and proposes conceptual frameworks for constructing such protocols. We examine the trade-offs between information-theoretic security, efficiency, and the practical implementation of post-quantum MPC, offering a theoretical perspective on how to achieve strong, long-term security in a quantum era. Our findings suggest that a hybrid approach, leveraging the strengths of both information theory and carefully selected post-quantum primitives, is crucial for building resilient MPC solutions.
The rapid advancement of quantum computing presents a fundamental challenge to modern cryptographic security, particularly in the domain of hash functions that ensure data integrity, authentication, and blockchain security. Traditional crypto graphic hash functions such as SHA-256, SHA-3, and BLAKE2 rely on computational hardness assumptions that become obsolete in the presence of large-scale quantum computers. Shor’s algorithm can efficiently break RSA and ECC-based cryptosys tems, while Grover’s algorithm reduces the security of traditional hash functions by square root complexity, significantly weakening their preimage and collision resistance. This quantum threat necessitates the development of post-quantum secure hashing techniques that remain resilient against both classical and quantum adversaries. This paper proposes Quantum Hashing, a novel cryptographic framework that integrates quantum entanglement, lattice-based cryptography, and hybrid quantum classical hashing to construct post-quantum secure hash functions. We introduce a formal model for Quantum Collision Resistance (QCR) and provide entropy-based ran domness enhancement to ensure unpredictable hash outputs. Unlike classical hashing approaches, our framework leverages the hardness of lattice problems (e.g., Shortest Vector Problem, Learning with Errors) to withstand quantum attacks while incorpo rating Quantum Key Distribution (QKD) mechanisms to enhance entropy and key management. Furthermore, we evaluate the security of Quantum Hashing under various attack models, comparing its resistance against Grover’s search and collision attacks. We benchmark its performance against NIST Post-Quantum Cryptography (PQC) final ists, including CRYSTALS-DILITHIUM, SPHINCS+, and Falcon, demonstrating that our approach offers superior resilience while maintaining computational feasibility. Additionally, we present an implementation of Quantum Hashing using Qiskit, show casing its practical applicability in quantum circuits and quantum-secure blockchain architectures. Our findings highlight that Quantum Hashing provides a scalable, entropy-efficient, and post-quantum resilient cryptographic primitive suitable for next-generation cryptographic applications. This work paves the way for secure post-quantum digital signatures, blockchain consensus mechanisms, and zero-knowledge proof systems that require tamper-resistant hashing in a quantum computing era.
The advent of quantum computing poses a significant threat to the security of currently deployed public-key cryptosystems. In response, the field of post-quantum cryptography (PQC) has emerged, proposing new algorithms based on mathematical problems believed to be hard for both classical and quantum computers. While the security of these systems is typically analyzed using computational complexity theory, this paper explores an alternative and complementary approach rooted in information theory. We investigate the security of PQC schemes by establishing entropic bounds on the information available to a quantum adversary. By leveraging concepts such as conditional min-entropy and Rényi divergence, we formulate a framework to quantify the uncertainty of secret keys and plaintexts from an adversary's perspective. This paper derives explicit entropic security bounds for several major families of post-quantum cryptosystems, including lattice-based, code-based, and hash-based schemes. We demonstrate that the security of these systems can be directly related to the entropy of the underlying hard problems' solutions. The results provide a new lens through which to assess and compare the security of PQC candidates, offering insights that are independent of specific computational models and algorithmic assumptions. This information-theoretic perspective not only strengthens the security foundations of PQC but also offers practical guidance for parameter selection to ensure long-term resilience against future cryptanalytic advances.
The advent of quantum computing poses a significant threat to the security of currently deployed public-key cryptosystems. In response, the field of post-quantum cryptography (PQC) has emerged, proposing new algorithms based on mathematical problems believed to be hard for both classical and quantum computers. While the security of these systems is typically analyzed using computational complexity theory, this paper explores an alternative and complementary approach rooted in information theory. We investigate the security of PQC schemes by establishing entropic bounds on the information available to a quantum adversary. By leveraging concepts such as conditional min-entropy and Rényi divergence, we formulate a framework to quantify the uncertainty of secret keys and plaintexts from an adversary's perspective. This paper derives explicit entropic security bounds for several major families of post-quantum cryptosystems, including lattice-based, code-based, and hash-based schemes. We demonstrate that the security of these systems can be directly related to the entropy of the underlying hard problems' solutions. The results provide a new lens through which to assess and compare the security of PQC candidates, offering insights that are independent of specific computational models and algorithmic assumptions. This information-theoretic perspective not only strengthens the security foundations of PQC but also offers practical guidance for parameter selection to ensure long-term resilience against future cryptanalytic advances.
Quantum computing poses a growing challenge to conventional public-key cryptographic systems, particularly those relying on integer factorization and discrete logarithm problems. Widely deployed schemes such as RSA and elliptic curve cryptography are expected to become vulnerable as large-scale quantum computing capabilities emerge. This concern has intensified the demand for communication frameworks capable of maintaining long-term confidentiality in the presence of both classical and quantum-enabled adversaries. This paper presents a Hybrid Quantum-Resilient Key Exchange Algorithm (HKEA) that combines classical cryptographic mechanisms with lattice-based post-quantum cryptographic techniques to establish secure session keys. The proposed framework employs a dual-layer key establishment process in which classical and post-quantum shared secrets are integrated to generate a strengthened hybrid session key. The design aims to preserve compatibility with existing communication infrastructures while improving resistance to future quantum attacks and mitigating risks associated with Harvest-Now-Decrypt-Later (HNDL) threats. A prototype implementation was developed using Python-based cryptographic and post-quantum security libraries. The framework was evaluated using key generation time, latency, throughput, computational overhead, and security strength as performance indicators. Comparative analysis against conventional cryptographic approaches indicates that the proposed HKEA provides enhanced quantum resilience with only a modest increase in computational cost. The proposed approach offers a practical pathway toward secure and scalable communication systems for next-generation quantum-era network environments.