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 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 current public-key cryptographic systems, necessitating a transition to post-quantum cryptography (PQC). While the computational and communication overheads of PQC schemes are actively studied, the fundamental entropic costs associated with achieving and maintaining secrecy in this new paradigm remain underexplored. This paper delves into the concept of entropic cost within post-quantum secrecy, defining it as the quantity and quality of randomness required for secure key generation, cryptographic operations, and resistance against information leakage. We review the theoretical underpinnings of information-theoretic security and apply these principles to analyze the entropic demands of leading PQC candidates, including lattice-based, code-based, and hash-based schemes. Our methodology establishes metrics for quantifying entropy consumption and evaluates how different PQC design choices impact these costs. The results indicate that PQC generally imposes higher entropic demands than classical cryptography, particularly in terms of volume and specific statistical distributions of random numbers needed. This elevated requirement has substantial implications for the design and implementation of true random number generators (TRNGs), resource-constrained environments, and side-channel attack resilience. We discuss the trade-offs between security, performance, and entropic efficiency, highlighting the critical need for robust entropy sources to ensure the long-term quantum-resilient security of PQC systems. Future research directions are proposed, emphasizing optimized entropy generation and management strategies.
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 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 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 fundamental security of cryptographic protocols hinges on two intertwined pillars: secrecy and randomness. In classical cryptography, the relationship between these concepts is well-understood, often formalized through information theory and computational complexity. However, the advent of quantum computing poses a significant threat to many classical cryptographic primitives, necessitating a transition to post-quantum cryptography (PQC). This paper explores the critical notion of the secrecy-randomness equivalence within the context of post-quantum protocols. We delve into how the definitions and relationships between perfect secrecy, computational secrecy, true randomness, and pseudorandomness are impacted by quantum adversaries and quantum information theory. Specifically, we investigate whether the classical equivalence – where sufficient randomness can guarantee secrecy and robust secrecy often relies on high-quality randomness – holds or requires re-evaluation in a post-quantum landscape. We analyze the implications for the design and security proofs of various PQC families, including lattice-based, code-based, and hash-based schemes, considering the role of quantum random number generators (QRNGs) and the potential for quantum-enhanced attacks on randomness. Our findings suggest that while the core principles remain, the practical realization and theoretical guarantees of this equivalence become more nuanced, demanding careful consideration of quantum-resistant randomness sources and revised security models to ensure the long-term integrity of post-quantum cryptographic systems.