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

Joël Alwen, Yevgeniy Dodis, Daniel Wichs

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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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•Jan 1, 2017•0 citations
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
Based on users’ permanent private keys and ephemeral secret keys (randomness secret values), authenticated key agreement (AKA) protocols are used to construct a common session key between two session parties while authenticating each other. Recently, the design of leakage-resilient AKA (LR-AKA) resisting side-channel attacks has received significant attention from researchers. By side-channel attacks, an adversary is allowed to obtain fractional leakage information of private (secret) keys during the computation rounds of LR-AKA protocols. However, most LR-AKA protocols have a restriction, namely, the overall fractional leakage information must be bounded. In this paper, we propose an efficient LR-AKA protocol with overall unbounded leakage property in the continual leakage extended Canetti-Krawczyk model. Security analysis is given to demonstrate that our LR-AKA protocol is provably secure in the generic bilinear group model. By comparisons, our protocol is better than the previously proposed LR-AKA protocols in terms of computation cost, security model, and leakage properties.
In this paper we address the problem of large space consumption for protocols in the Bounded Retrieval Model (BRM), which require users to store large secret keys subject to adversarial leakage. We propose a method to derive keys for such protocols on-the-fly from weakly random private data (like text documents or photos, users keep on their disks anyway for non-cryptographic purposes) in such a way that no extra storage is needed. We prove that any leakage-resilient protocol (belonging to a certain, arguably quite broad class) when run with a key obtained this way retains a similar level of security as the original protocol had. Additionally, we guarantee privacy of the data the actual keys are derived from. That is, an adversary can hardly gain any knowledge about the private data except that he could otherwise obtain via leakage. Our reduction works in the Random Oracle model.
Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.
Security models for two-party authenticated key exchange (AKE) protocols have developed over time to provide security even when the adversary learns certain secret keys. In this work, we advance the modelling of AKE protocols by considering more granular, continuous leakage of long-term secrets of protocol participants: the adversary can adaptively request arbitrary leakage of long-term secrets even after the test session is activated, with limits on the amount of leakage per query but no bounds on the total leakage. We present a security model supporting continuous leakage even when the adversary learns certain ephemeral secrets or session keys, and give a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the model; our protocol achieves continuous, after-the-fact leakage resilience with not much more cost than a previous protocol with only bounded, non-after-the-fact leakage.
Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.
Leakage attacks, including various kinds of side-channel attacks, allow an attacker to learn partial information about the internal secrets such as the secret key and the randomness of a cryptographic system. Designing a strong, meaningful, yet achievable security notion to capture practical leakage attacks is one of the primary goals of leakage-resilient cryptography. In this work, we revisit the modelling and design of authenticated key exchange (AKE) protocols with leakage resilience. We show that the prior works on this topic are inadequate in capturing realistic leakage attacks. To close this research gap, we propose a new security notion named leakage-resilient eCK model w.r.t. auxiliary inputs (AI-LR-eCK) for AKE protocols, which addresses the limitations of the previous models. Our model allows computationally hard-to-invert leakage of both the long-term secret key and the randomness, and also addresses a limitation existing in most of the previous models where the adversary is disallowed to make leakage queries during the challenge session. As another major contribution of this work, we present a generic framework for the construction of AKE protocols that are secure under the proposed AI-LR-eCK model. An instantiation based on the decision Diffie–Hellman (DDH) assumption in the standard model is also given to demonstrate the feasibility of our proposed framework.