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.

Abstract. Proofs of Retrievability (PoR), introduced by Juels and Kaliski [JK07], allow the client to store a file F on an untrusted server, and later run an efficient audit protocol in which the server proves that it (still) possesses the client's data. Constructions of PoR schemes attempt to minimize the client and server storage, the communication complexity of an audit, and even the number of file-blocks accessed by the server during the audit. In this work, we identify several different variants of the problem (such as bounded-use vs. unbounded-use, knowledgesoundness vs. information-soundness), and giving nearly optimal PoR schemes for each of these variants. Our constructions either improve (and generalize) the prior PoR constructions, or give the first known PoR schemes with the required properties. In particular, we The main insight of our work comes from a simple connection between PoR schemes and the notion of hardness amplification, extensively studied in complexity theory. In particular, our improvements come from first abstracting a purely information-theoretic notion of PoR codes, and then building nearly optimal PoR codes using state-of-the-art tools from coding and complexity theory.

Abstract.Consider an abstract storage device Σ(G) that can hold a single element x from a fixed, publicly known finite group G. Storage is private in the sense that an adversary does not have read access to Σ(G) at all. However, Σ(G) is non-robust in the sense that the adversary can modify its contents by adding some offset ∆ ∈ G. Due to the privacy of the storage device, the value ∆ can only depend on an adversary's a priori knowledge of x. We introduce a new primitive called an algebraic manipulation detection (AMD) code, which encodes a source s into a value x stored on Σ(G) so that any tampering by an adversary will be detected, except with a small error probability δ. We give a nearly optimal construction of AMD codes, which can flexibly accommodate arbitrary choices for the length of the source s and security level δ. We use this construction in two applications:-We show how to efficiently convert any linear secret sharing scheme into a robust secret sharing scheme, which ensures that no unqualified subset of players can modify their shares and cause the reconstruction of some value s ′ = s. -We show how how to build nearly optimal robust fuzzy extractors for several natural metrics. Robust fuzzy extractors enable one to reliably extract and later recover random keys from noisy and non-uniform secrets, such as biometrics, by relying only on non-robust public storage. In the past, such constructions were known only in the random oracle model, or required the entropy rate of the secret to be greater than half. Our construction relies on a randomly chosen common reference string (CRS) available to all parties.

We study the question of basing symmetric key cryptography on weak secrets. In this setting, Alice and Bob share an n-bit secret W , which might not be uniformly random, but the adversary has at least k bits of uncertainty about it (formalized using conditional min-entropy). Since standard symmetrickey primitives require uniformly random secret keys, we would like to construct an authenticated key agreement protocol in which Alice and Bob use W to agree on a nearly uniform key R, by communicating over a public channel controlled by an active adversary Eve. We study this question in the information theoretic setting where the attacker is computationally unbounded. We show that single-round (i.e. one message) protocols do not work when k ≤ n 2 , and require poor parameters even when n 2 < k n. On the other hand, for arbitrary values of k, we design a communication efficient two-round (challenge-response) protocol extracting nearly k random bits. This dramatically improves the previous construction of Renner and Wolf [RW03], which requires Θ(λ + log(n)) rounds where λ is the security parameter. Our solution takes a new approach by studying and constructing "non-malleable" seeded randomness extractors -if an attacker sees a random seed X and comes up with an arbitrarily related seed X , then we bound the relationship between R = Ext(W ; X) and R = Ext(W ; X ).We also extend our two-round key agreement protocol to the "fuzzy" setting, where Alice and Bob share "close" (but not equal) secrets W A and W B , and to the Bounded Retrieval Model (BRM) where the size of the secret W is huge.

Abstract.We construct the first public-key encryption scheme in the Bounded-Retrieval Model (BRM), providing security against various forms of adversarial "key leakage" attacks. In this model, the adversary is allowed to learn arbitrary information about the decryption key, subject only to the constraint that the overall amount of "leakage" is bounded by at most bits. The goal of the BRM is to design cryptographic schemes that can flexibly tolerate arbitrarily leakage bounds (few bits or many Gigabytes), by only increasing the size of secret key proportionally, but keeping all the other parameters -including the size of the public key, ciphertext, encryption/decryption time, and the number of secret-key bits accessed during decryption -small and independent of . As our main technical tool, we introduce the concept of an IdentityBased Hash Proof System (IB-HPS), which generalizes the notion of hash proof systems of Cramer and Shoup [CS02] to the identity-based setting. We give three different constructions of this primitive based on: (1) bilinear groups, (2) lattices, and (3) quadratic residuosity. As a result of independent interest, we show that an IB-HPS almost immediately yields an Identity-Based Encryption (IBE) scheme which is secure against (small) partial leakage of the target identity's decryption key. As our main result, we use IB-HPS to construct public-key encryption (and IBE) schemes in the Bounded-Retrieval Model.