We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is error-tolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A secure sketch produces public information about its input w that does not reveal w, and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce error-prone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of “closeness” of input data, such as Hamming distance, edit distance, and set difference.

Abstract. In 1977 Dalenius articulated a desideratum for statistical databases: nothing about an individual should be learnable from the database that cannot be learned without access to the database. We give a general impossibility result showing that a formalization of Dalenius’ goal along the lines of semantic security cannot be achieved. Contrary to intuition, a variant of the result threatens the privacy even of someone not in the database. This state of affairs suggests a new measure, differential privacy, which, intuitively, captures the increased risk to one’s privacy incurred by participating in a database. The techniques developed in a sequence of papers [8, 13, 3], culminating in those described in [12], can achieve any desired level of privacy under this measure. In many cases, extremely accurate information about the database can be provided while simultaneously ensuring very high levels of privacy. 1

Consider two parties holding samples from correlated distributions W and W ′, respectively, where these samples are within distance t of each other in some metric space. The parties wish to agree on a close-to-uniformly distributed secret key R by sending a single message over an insecure channel controlled by an all-powerful adversary who may read and modify anything sent over the channel. We consider both the keyless case, where the parties share no additional secret information, and the keyed case, where the parties share a long-term secret SKBSM that they can use to generate a sequence of session keys {Rj} using multiple pairs {(Wj, W ′ j)}. The former has applications to, e.g., biometric authentication, while the latter arises in, e.g., the bounded-storage model with errors. We show solutions that improve upon previous work in several respects: • The best prior solution for the keyless case with no errors (i.e., t = 0) requires the minentropy of W to exceed 2n/3, where n is the bit-length of W. Our solution applies whenever the min-entropy of W exceeds the minimal threshold n/2, and yields a longer key. • Previous solutions for the keyless case in the presence of errors (i.e., t> 0) required random oracles. We give the first constructions (for certain metrics) in the standard model. • Previous solutions for the keyed case were stateful. We give the first stateless solution. 1

The inability of humans to generate and remember strong secrets makes it difficult for people to manage cryptographic keys. To address this problem, numerous proposals have been suggested to enable a human to repeatably generate a cryptographic key from her biometrics, where the strength of the key rests on the assumption that the measured biometrics have high entropy across the population. In this paper we show that, despite the fact that several researchers have examined the security of BKGs, the common techniques used to argue the security of practical systems are lacking. To address this issue we reexamine two well known, yet sometimes misunderstood, security requirements. We also present another that we believe has not received adequate attention in the literature, but is essential for practical biometric key generators. To demonstrate that each requirement has significant importance, we analyze three published schemes, and point out deficiencies in each. For example, in one case we show that failing to meet a requirement results in a construction where an attacker has a 22 % chance of finding ostensibly 43-bit keys on her first guess. In another we show how an attacker who compromises a user’s cryptographic key can then infer that user’s biometric, thus revealing any other key generated using that biometric. We hope that by examining the pitfalls that occur continuously in the literature, we enable researchers and practitioners to more accurately analyze proposed constructions. 1

Abstract We consider the question of constructing cryptographic pseudorandomgenerators (PRGs) in NC 0, namely ones in which each bit of the output depends on just a constant number of input bits. Previous constructions of suchPRGs were limited to stretching a seed of n bits to n + o(n) bits. This leavesopen the existence of a PRG with a linear (let alone superlinear) stretch in NC0. In this work we study this question and obtain the following mainresults: 1. We show that the existence of a linear-stretch PRG in NC0 impliesnon-trivial hardness of approximation results without relying on PCP machinery. In particular, it implies that Max3SAT is hard to approxi-mate to within some multiplicative constant. 2. We construct a linear-stretch PRG in NC0 under a specific intractabil-ity assumption related to the hardness of decoding "sparsely generated " linear codes. Such an assumption was previously conjectured byAlekhnovich (FOCS 2003).

We present a positive obfuscation result for a traditional cryptographic functionality. This positive result stands in contrast to well-known impossibility results [3] for general obfuscation and recent impossibility and improbability [13] results for obfuscation of many cryptographic functionalities. Whereas other positive obfuscation results in the standard model apply to very simple point functions, our obfuscation result applies to the significantly more complex and widely-used re-encryption functionality. This functionality takes a ciphertext for message m encrypted under Alice’s public key and transforms it into a ciphertext for the same message m under Bob’s public key. To overcome impossibility results and to make our results meaningful for cryptographic functionalities, our scheme satisfies a definition of obfuscation which incorporates more security-aware provisions.

Data sharing with multiple parties over a third-party distribution framework requires that both data integrity and confidentiality be assured. One of the most widely used data organization structures is the tree structure. When such structures encode sensitive information (such as in XML documents), it is crucial that integrity and confidentiality be assured not only for the content, but also for the structure. Digital signature schemes are commonly used to authenticate the integrity of the data. The most widely used such technique for tree structures is the Merkle hash technique, which however is known to be “not hiding”, thus leading to unauthorized leakage of information. Most techniques in the literature are based on the Merkle hash technique and thus suffer from the problem of unauthorized information leakages. Assurance of integrity and confidentiality (no leakages) of tree-structured data is an important problem in the context of secure data publishing and content distribution systems. In this paper, we propose a signature scheme for tree structures, which assures both confidentiality and integrity and is also efficient, especially in third-party distribution environments. Our integrity assurance technique, which we refer to as the “Structural signature scheme”, is based on the structure of the tree as defined by tree traversals (pre-order, post-order, in-order) and is defined using a randomized notion of such traversal numbers. In addition to formally defining the technique, we prove that it protects against violations of content and structural integrity and information leakages. We also show through complexity and performance analysis that the structural signature scheme is efficient; with respect to the Merkle hash technique, it incurs comparable cost for signing the trees and incurs lower cost for user-side integrity verification.

Although biometrics have garnered significant interest as a source of entropy for cryptographic key generation, recent studies indicate that many biometric modalities may not actually offer enough uncertainty for this purpose. In this paper, we exploit a novel source of entropy that can be used with any biometric modality but that has yet to be utilized for key generation, namely associating uncertainty with the way in which the biometric input is measured. Our construction poses only a modest requirement on a user: the ability to remember a low-entropy password. We identify the technical challenges of this approach, and develop novel techniques to overcome these difficulties. Our analysis of this approach indicates that it may offer the potential to generate stronger keys: In our experiments, 40 % of the users are able to generate keys that are at least 2 30 times stronger than passwords alone. Categories and Subject Descriptors E.3 [Data Encryption]; H.1 [Models and Principles]: User/Machine

In 1977 Tore Dalenius articulated a desideratum for statistical databases: nothing about an individual should be learnable from the database that cannot be learned without access to the database. We give a general impossibility result showing that a natural formalization of Dalenius’ goal cannot be achieved if the database is useful. The key obstacle is the side information that may be available to an adversary. Our results hold under very general conditions regarding the database, the notion of privacy violation, and the notion of utility. Contrary to intuition, a variant of the result threatens the privacy even of someone not in the database. This state of affairs motivated the notion of differential privacy [15, 16], a strong ad omnia privacy which, intuitively, captures the increased risk to one’s privacy incurred by participating in a database. 1

Abstract. We consider the problem of secure identification: user U proves to server S that he knows an agreed (possibly low-entropy) password w, while giving away as little information on w as possible, namely the adversary can exclude at most one possible password for each execution of the scheme. We propose a solution in the bounded-quantum-storage model, where U and S may exchange qubits, and a dishonest party is assumed to have limited quantum memory. No other restriction is posed upon the adversary. An improved version of the proposed identification scheme is also secure against a man-in-the-middle attack, but requires U and S to additionally share a high-entropy key k. However, security is still guaranteed if one party loses k to the attacker but notices the loss. In both versions of the scheme, the honest participants need no quantum memory, and noise and imperfect quantum sources can be tolerated. The schemes compose sequentially, and w and k can securely be re-used. A small modification to the identification scheme results in a quantum-key-distribution (QKD) scheme, secure in the bounded-quantum-storage model, with the same re-usability properties of the keys, and without assuming authenticated channels. This is in sharp contrast to known QKD schemes (with unbounded adversary) without authenticated channels, where authentication keys must be updated, and unsuccessful executions can cause the parties to run out of keys. 1