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Unprovability of Leakage-Resilient Cryptography Beyond the Information-Theoretic Limit.

Rafael Pass

Published Jan 1, 2021• 0 citations
OpenAlex

Abstract

In recent years, leakage-resilient cryptography—the design of cryptographic protocols resilient to bounded leakage of honest players’ secrets—has received significant attention. A major limitation of known provably-secure constructions (based on polynomial hardness assumptions) is that they require the secrets to have sufficient actual (i.e., information-theoretic), as opposed to comptutational, min-entropy even after the leakage.

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Entropic Resilience: Information-Theoretic Limits of Post-Quantum Cryptography

PAULO SÉRGIO DE ANDRADE

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.

•Nov 23, 2025•0 citations

Unprovability of Leakage-Resilient Cryptography Beyond the Information-Theoretic Limit

Rafael Pass

Lecture notes in computer science•Jan 1, 2020•0 citations

Leakage-Resilient Public-Key Cryptography in the Bounded-Retrieval Model.

Joël Alwen, Yevgeniy Dodis, Daniel Wichs

We study the design of cryptographic primitives resilient to key-leakage attacks, where an attacker can repeatedly and adaptively learn information about the secret key, subject only to the constraint that the overall amount of such information is bounded by some parameter ℓ. We construct a variety of leakage-resilient public-key systems including the first known identification schemes (ID), signature schemes and authenticated key agreement protocols (AKA). Our main result is an efficient three-round leakage-resilient AKA in the Random-Oracle model. This protocol ensures that session keys are private and authentic even if (1) the adversary leaks a large fraction of the long-term secret keys of both users prior to the protocol execution and (2) the adversary completely learns the long-term secret keys after the protocol execution. In particular, our AKA protocol provides qualitatively stronger privacy guarantees than leakage-resilient public-encryption schemes (constructed in prior and concurrent works), since such schemes necessarily become insecure if the adversary can perform leakage attacks after seing a ciphertext. Moreover, our schemes can be flexibly extended to the Bounded-Retrieval Model, allowing us to tolerate very large absolute amount of adversarial leakage ℓ (potentially many gigabytes of

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Barriers in Cryptography with Weak, Correlated and Leaky Sources.

Daniel Wichs

There has been much recent progress in constructing cryptosystems that maintain their security without requiring uniform randomness and perfect secrecy. These schemes are motivated by a diverse set of problems such as providing resilience to side-channel leakage, using weak physical sources of randomness as secret keys, and allowing deterministic encryption for high-entropy messages. The study of these problems has significantly deepened our understanding of how randomness is used in cryptographic constructions and proofs. Nevertheless, despite this progress, some basic and seemingly achievable security properties have eluded our reach. For example, we are unable to prove the security of basic tools for manipulating weak/leaky random sources, such as as pseudo-entropy generators and seed-dependent computational condensers. We also do not know how to prove leakage-resilient security of any cryptosystem with a uniquely determined secret key. In the context of deterministic encryption we do not have a standardmodel constructions achieving the strongest notion of security proposed by Bellare, Boldyreva and O’Neill (CRYPTO ’07), that would allow us to encrypt arbitrarily correlated messages of sufficiently large individual entropy. In this work, we provide broad black-box separation results, showing that the security of such primitives cannot be proven under virtually any standard cryptographic hardness assumption via a reduction that treats the adversary as a black box. We do so by formalizing the intuition that “the only way that a reduction can simulate the correctly distributed view for an attacker is to know all the secrets, in which case it does not learn anything useful from the attack”. Such claims are often misleading and clever way of getting around them allow us to achieve a wealth of positive results with imperfect/leaky randomness. However, in this work we show that this intuition can be formalized and that it indeed presents a real barrier for the examples given above. ∗IBM Research. wichs@cs.nyu.edu

•Jan 1, 2012•1 citation

Improved Bound on the Local Leakage-resilience of Shamir’s Secret Sharing

Hemanta K. Maji, Hai H. Nguyen, Anat Paskin-Cherniavsky +1 more

Side-channel attacks have repeatedly falsified the assumption that cryptosystems are black boxes. Leakage-resilient cryptography studies the robustness of cryptographic constructions when an unforeseen revelation of information occurs. In this context, recently, Benhamouda, Degwekar, Ishai, and Rabin (CRYPTO–2018) motivated the study of the local leakage resilience of secret-sharing schemes against an adversary who obtains independent leakage from each secret share.Motivated by applications in secure computation, Benhamouda et al. (CRYPTO–2018) initiated the study of the local leakage resilience of Shamir’s secret-sharing scheme, an essential primitive for nearly all threshold cryptography. The objective is to achieve local leakage resilience with as small a fractional reconstruction threshold as possible. Previously, Benhamouda et al. showed that the reconstruction threshold k being at least 0.907 times the number of parties n is sufficient for Shamir’s secretsharing scheme to be resilient against arbitrary single-bit local leakage from each secret share. After that, Maji et al. (CRYPTO–2021) and Benhamouda et al. (Journal of Cryptology–2021) independently lowered this threshold to k/n ⩾ 0.8675 and k/n ⩾0.85, respectively.This paper contributes to this line of research and proves that k/n ⩾ 0.78 is sufficient. Next, motivated by applications in GMW-style leakage-resilient secure computation, our work extends this bound to a more general adversary who corrupts some parties (obtaining their entire secret shares) and obtains leakage from the remaining honest parties’ secret shares.Our technical analysis proceeds by Fourier analysis and accurately estimates an exponential sum arising in this analysis.

IEEE International Symposium on Information Theory (ISIT)•Jun 26, 2022•18 citations

Review on Leakage Resilient Key Exchange Security Model

Zheng Wei Clement Chan, Chai Wen Chuah, Janaka Alawatugoda

In leakage resilient cryptography, leakage resilient key exchange protocols are constructed to defend against leakage attacks. Then, the key exchange protocol is proved with leakage resilient security model to determine whether its security proof can provide the security properties it claimed or to find out any unexamined flaw during protocol building. It is an interesting work to review the meaningful security properties provided by these security models. This work review how a leakage resilient security model for a key exchange protocol has been evolved over years according to the increasing security requirement which covers a different range of attacks. The relationship on how an adversary capability in the leakage resilient security model can be related to real-world attack scenarios is studied. The analysis work for each leakage resilient security model here enables a better knowledge on how an adversary query addresses different leakage attacks setting, thereby understand the motive of design for a cryptographic primitive in the security model.

International Journal of Communication Networks and Information Security (IJCNIS)•Apr 17, 2022•5 citations
In recent years, leakage-resilient cryptography—the design of cryptographic protocols resilient to bounded leakage of honest players’ secrets—has received significant attention. A major limitation of known provably-secure constructions (based on polynomial hardness assumptions) is that they require the secrets to have sufficient actual (i.e., information-theoretic), as opposed to comptutational, min-entropy even after the leakage.
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.
We study the design of cryptographic primitives resilient to key-leakage attacks, where an attacker can repeatedly and adaptively learn information about the secret key, subject only to the constraint that the overall amount of such information is bounded by some parameter ℓ. We construct a variety of leakage-resilient public-key systems including the first known identification schemes (ID), signature schemes and authenticated key agreement protocols (AKA). Our main result is an efficient three-round leakage-resilient AKA in the Random-Oracle model. This protocol ensures that session keys are private and authentic even if (1) the adversary leaks a large fraction of the long-term secret keys of both users prior to the protocol execution and (2) the adversary completely learns the long-term secret keys after the protocol execution. In particular, our AKA protocol provides qualitatively stronger privacy guarantees than leakage-resilient public-encryption schemes (constructed in prior and concurrent works), since such schemes necessarily become insecure if the adversary can perform leakage attacks after seing a ciphertext. Moreover, our schemes can be flexibly extended to the Bounded-Retrieval Model, allowing us to tolerate very large absolute amount of adversarial leakage ℓ (potentially many gigabytes of
There has been much recent progress in constructing cryptosystems that maintain their security without requiring uniform randomness and perfect secrecy. These schemes are motivated by a diverse set of problems such as providing resilience to side-channel leakage, using weak physical sources of randomness as secret keys, and allowing deterministic encryption for high-entropy messages. The study of these problems has significantly deepened our understanding of how randomness is used in cryptographic constructions and proofs. Nevertheless, despite this progress, some basic and seemingly achievable security properties have eluded our reach. For example, we are unable to prove the security of basic tools for manipulating weak/leaky random sources, such as as pseudo-entropy generators and seed-dependent computational condensers. We also do not know how to prove leakage-resilient security of any cryptosystem with a uniquely determined secret key. In the context of deterministic encryption we do not have a standardmodel constructions achieving the strongest notion of security proposed by Bellare, Boldyreva and O’Neill (CRYPTO ’07), that would allow us to encrypt arbitrarily correlated messages of sufficiently large individual entropy. In this work, we provide broad black-box separation results, showing that the security of such primitives cannot be proven under virtually any standard cryptographic hardness assumption via a reduction that treats the adversary as a black box. We do so by formalizing the intuition that “the only way that a reduction can simulate the correctly distributed view for an attacker is to know all the secrets, in which case it does not learn anything useful from the attack”. Such claims are often misleading and clever way of getting around them allow us to achieve a wealth of positive results with imperfect/leaky randomness. However, in this work we show that this intuition can be formalized and that it indeed presents a real barrier for the examples given above. ∗IBM Research. wichs@cs.nyu.edu
Side-channel attacks have repeatedly falsified the assumption that cryptosystems are black boxes. Leakage-resilient cryptography studies the robustness of cryptographic constructions when an unforeseen revelation of information occurs. In this context, recently, Benhamouda, Degwekar, Ishai, and Rabin (CRYPTO–2018) motivated the study of the local leakage resilience of secret-sharing schemes against an adversary who obtains independent leakage from each secret share.Motivated by applications in secure computation, Benhamouda et al. (CRYPTO–2018) initiated the study of the local leakage resilience of Shamir’s secret-sharing scheme, an essential primitive for nearly all threshold cryptography. The objective is to achieve local leakage resilience with as small a fractional reconstruction threshold as possible. Previously, Benhamouda et al. showed that the reconstruction threshold k being at least 0.907 times the number of parties n is sufficient for Shamir’s secretsharing scheme to be resilient against arbitrary single-bit local leakage from each secret share. After that, Maji et al. (CRYPTO–2021) and Benhamouda et al. (Journal of Cryptology–2021) independently lowered this threshold to k/n ⩾ 0.8675 and k/n ⩾0.85, respectively.This paper contributes to this line of research and proves that k/n ⩾ 0.78 is sufficient. Next, motivated by applications in GMW-style leakage-resilient secure computation, our work extends this bound to a more general adversary who corrupts some parties (obtaining their entire secret shares) and obtains leakage from the remaining honest parties’ secret shares.Our technical analysis proceeds by Fourier analysis and accurately estimates an exponential sum arising in this analysis.
In leakage resilient cryptography, leakage resilient key exchange protocols are constructed to defend against leakage attacks. Then, the key exchange protocol is proved with leakage resilient security model to determine whether its security proof can provide the security properties it claimed or to find out any unexamined flaw during protocol building. It is an interesting work to review the meaningful security properties provided by these security models. This work review how a leakage resilient security model for a key exchange protocol has been evolved over years according to the increasing security requirement which covers a different range of attacks. The relationship on how an adversary capability in the leakage resilient security model can be related to real-world attack scenarios is studied. The analysis work for each leakage resilient security model here enables a better knowledge on how an adversary query addresses different leakage attacks setting, thereby understand the motive of design for a cryptographic primitive in the security model.