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.

We combine well-known techniques from the areas of errorcorrecting codes and cryptography to achieve a new type of cryptographic primitive that we refer to as a fuzzy commitment scheme. Like a conventional cryptographic commitment scheme, our fuzzy commitment scheme is both concealing and binding: it is infeasible for an attacker to learn the committed value, and also for the committer to decommit a value in more than one way. In a conventional scheme, a commitment must be opened using a unique witness, which acts, essentially, as a decryption key. By contrast, our scheme is fuzzy in the sense that it accepts a witness that is close to the original encrypting witness in a suitable metric, but not necessarily identical. This characteristic of our fuzzy commitment scheme makes it useful for applications such as biometric authentication systems, in which data is subject to random noise. Because the scheme is tolerant of error, it is capable of protecting biometric data just as conventional cryptographic techniques, like hash functions, are used to protect alphanumeric passwords. This addresses a major outstanding problem in the theory of biometric authentication. We prove the security characteristics of our fuzzy commitment scheme relative to the properties of an underlying cryptographic hash function.

We show that a number of recent definitions and constructions of fuzzy extractors are not adequate for multiple uses of the same fuzzy secret—a major shortcoming in the case of biometric applications. We propose two particularly stringent security models that specifically address the case of fuzzy secret reuse, respectively from an outsider and an insider perspective, in what we call a chosen perturbation attack. We characterize the conditions that fuzzy extractors need to satisfy to be secure, and present generic constructions from ordinary building blocks. As an illustration, we demonstrate how to use a biometric secret in a remote error tolerant authentication protocol that does not require any storage on the client’s side. 1

This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X , Y , and Z, respectively, with joint distribution PXY Z . The secret key rate S(X ; Y jjZ) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between X and Y when given Z, denoted by I(X ; Y # Z), which is an upper bound on S(X ; Y jjZ). The special scenarios are analyzed where X , Y , and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or two scenarios in which Z is generated by sending X and Y over erasure channels. In the first two scenarios it can be sho...

We propose a private-key cryptosystem and a protocol for key agreement by public discussion that are unconditionally secure based on the sole assumption that an adversary's memory capacity is limited. No assumption about her computing power is made. The scenario assumes that a random bit string of length slightly larger than the adversary's memory capacity can be received by all parties. The random bit string can for instance be broadcast by a satellite or over an optical network, or transmitted over an insecure channel between the communicating parties. The proposed schemes require very high bandwidth but can nevertheless be practical. 1 Introduction One of the most important properties of a cryptographic system is a proof of its security under reasonable and general assumptions. However, every design involves a trade-off between the strength of the security and further important qualities of a cryptosystem, such as efficiency and practicality. The security of all currently used cryp...

We present a new and very simple commitment scheme that does not depend on any assumptions about computational complexity; the Sender and Receiver may both be computationally unbounded. Instead, the scheme utilizes a "trusted initializer " who participates only in an initial setup phase. The scheme also utilizes private channels between each pair of parties. The Sender is able to easily commit to a large value; the scheme is not just a "bit-commitment " scheme. We also observe that 1-out-of-n oblivious transfer is easily handled in the same model, using a simple OT protocol due to Bennett et al.[2].

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

In our opinion, the Foundations of Cryptography are the paradigms, approaches and techniques used to conceptualize, define and provide solutions to natural cryptographic problems. In this essay, we survey some of these paradigms, approaches and techniques as well as some of the fundamental results obtained using them. Special effort is made in attempt to dissolve common misconceptions regarding these paradigms and results. c flCopyright 1998 by Oded Goldreich. Permission to make copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that new copies bear this notice and the full citation on the first page. Abstracting with credit is permitted. A preliminary version of this essay has appeared in the proceedings of Crypto97 (Springer's Lecture Notes in Computer Science, Vol. 1294). 0 Contents 1 Introduction 2 I Basic Tools 6 2 Central Paradigms 6 2.1 Computati...

cachinlacm.org Abstract. We show that oblivious transfer can be based on a very general notion of asymmetric information difference. We investigate a Universal Oblivious Ransfer, denoted UOT(X, Y), that gives Bob the free-dom to access Alice’s input X in an arbitrary way as long as he does not obtain full information about X. Alice does not learn which information Bob has chosen. We show that oblivious transfer can be reduced to a sin-gle execution of UOT(X, Y) with Bob’s knowledge Y restricted in terms of RCnyi entropy of order a> 1. For independently repeated UOT the reduction works even if only Bob’s Shannon information is restricted, i.e. if H(XIY)> 0 in every UOT(X, Y). Our protocol requires that honest Bob obtains at least half of Alice’s information X without error.

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