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

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 . 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 (potentially many gigabytes of information), only by increasing the size of the secret key and without any other loss of efficiency in communication or computation. Concretely, given any leakage parameter , security parameter λ, and any desired fraction 0 < δ ≤ 1, our schemes have the following properties:Secret key size is (1 + δ) + O(λ). In particular, the attacker can learn an approximately (1 − δ) fraction of the secret key.Public key size is O(λ), and independent of . Communication complexity is O(λ/δ), and independent of . All computation reads at most O(λ/δ2 ) locations of the secret key, independently of .Lastly, we show that our schemes allow for repeated "invisible updates" of the secret key, allowing us to tolerate up to bits of leakage in between any two updates, and an unlimited amount of leakage overall. These updates require that the parties can securely store a short "master update key" (e.g. on a separate secure device protected against leakage), which is only used for updates and not during protocol execution. The updates are invisible in the sense that a party can update its secret key at any point in time, without modifying the public key or notifying the other users.

Public-Key Encryption in the Bounded-Retrieval Model

“…The name serves as an analogy to the Bounded Storage Model (BSM) of [Mau92], which restricts the amount of data that an adversary can store after observing a huge public random string, rather than the amount of data an adversary can retrieve from a huge secret key. With the exception of [ADW09], all of the work on the BRM is in the symmetric-key setting, where two parties share a huge secret key. The recent work of Alwen et al [ADW09] gave the first public-key results in the BRM, by constructing identification schemes, (variants of) signatures, and authenticated-key-agreement protocols.…”

“…With the exception of [ADW09], all of the work on the BRM is in the symmetric-key setting, where two parties share a huge secret key. The recent work of Alwen et al [ADW09] gave the first public-key results in the BRM, by constructing identification schemes, (variants of) signatures, and authenticated-key-agreement protocols. However, these primitives cannot be used to encrypt a message non-interactively, as is done in the current work.…”

“…However, these primitives cannot be used to encrypt a message non-interactively, as is done in the current work. Moreover, the authenticated-key agreement protocols of [ADW09] required the use of Random Oracles, while we offer (some) constructions in the standard model. We note that many of the prior schemes in the BRM and BSM employ ideas similar to the "parallel repetition" and "random-subset selection" that we described in the introduction.…”

“…This assumption is very reasonable for some attacks, such as the cold-boot attack, where all memory contents decay uniformly over time. [Dzi06,CLW06,ADW09] is a generalization of the relative-leakage model. In this model, the leakage-parameter is an arbitrary and independent parameter of the system, which is based on practical considerations about how much leakage the system needs to tolerate on an absolute scale.…”

Efficient Leakage-Resilient Signature Schemes in the Generic Bilinear Group Model

“…Which means that designing algorithms such that their description already provides security against those attacks. Leakage-resilient cryptography is an increasingly active area in recent years and many leakage models have been proposed, such as only computation leaks information (OCLI) [19,21,27, 24], memory leakage [1,17], bounded retrieval [2,3,14], and auxiliary input models [15,21,20,34], etc. In this work, we design leakage-resilient signature schemes based on the following two leakage models:…”