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 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 advent of quantum computing presents a paradigm shift in modern cybersecurity, threatening the foundations of classical cryptographic systems such as RSA, ECC, and Diffie–Hellman key exchange. Quantum algorithms like Shor’s and Grover’s can efficiently break these schemes, rendering existing encryption mechanisms vulnerable and obsolete. This growing risk necessitates the development of quantum-resilient or post-quantum cryptographic (PQC) solutions that can safeguard data and computation in the era of quantum networks. Secure Multi-Party Computation (SMPC), a cornerstone of privacy-preserving computation, enables multiple entities to jointly compute a function over their private inputs without revealing them. However, its traditional security assumptions are also undermined by quantum threats. This research aims to explore and evaluate quantum-safe cryptographic protocols for integrating PQC into SMPC frameworks, thereby ensuring both confidentiality and correctness even in the presence of quantum-capable adversaries. The study focuses on lattice-based, hash-based, and code-based cryptographic primitives, analyzing their resilience, efficiency, and scalability when applied to distributed systems. A comparative framework is proposed to assess the performance and security trade-offs of different post-quantum SMPC implementations under realistic network conditions. The findings are expected to contribute to the design of a new class of cryptographic protocols capable of resisting quantum attacks, supporting the secure functioning of next-generation networks, and guiding policymakers and technologists toward practical post-quantum standardization. Ultimately, this research strengthens the bridge between theoretical cryptography and real-world cybersecurity readiness in the post-quantum era.
The advent of quantum computing poses a significant threat to conventional cryptographic schemes, which rely on computational hardness assumptions vulnerable to quantum algorithms. While post-quantum cryptography (PQC) focuses on developing new computationally secure primitives, the ultimate goal of perfect secrecy, rooted in Shannon's information theory, demands a re-evaluation. This paper explores the landscape of information-theoretic security (ITS) in post-quantum regimes, moving beyond the classical Shannon limit. We review foundational concepts of ITS, including the one-time pad and its implications for perfect secrecy, and examine how quantum adversaries challenge these notions. The work delves into various approaches to achieve ITS against quantum attacks, including quantum key distribution (QKD) as a primary example, and investigates the potential for information-theoretic security from classical physical layer properties enhanced by quantum mechanics. We discuss the limitations and practical challenges of implementing such schemes, as well as the theoretical implications. This paper proposes a textit{Hybrid Information-Theoretic and Computationally Secure Architecture (HITCSA)} as a novel framework for integrating robust PQC with information-theoretically secure primitives, providing a comprehensive overview of the theoretical underpinnings and practical considerations for achieving truly secure communication in a quantum-threatened world.
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 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.
The advent of quantum computing poses a fundamental threat to classical public-key cryptographic systems grounded in integer factorization and discrete logarithm problems. This paradigm shift has catalyzed the development of post-quantum cryptographic protocols rooted in advanced number-theoretic constructs such as lattices, error-correcting codes, multivariate polynomials, and isogeny-based systems. This paper presents a systematic review of number-theoretic foundations underpinning post-quantum cryptography, emphasizing their algorithmic structures, architectural implementations, and integration into modern software engineering ecosystems. The methodology involves a structured analysis of recent literature spanning 2018 to 2025, focusing on cryptographic primitives, security assumptions, performance trade-offs, and practical deployment considerations. The findings reveal a dominant shift toward lattice-based constructions due to their efficiency and strong worst-case hardness guarantees, alongside emerging hybrid models incorporating artificial intelligence for parameter tuning and security evaluation. The paper contributes a comprehensive synthesis of existing approaches, identifies critical research gaps in scalability and standardization, and outlines future directions for integrating post-quantum protocols into secure software pipelines.