The notion of non-malleable cryptography, an extension of semantically secure cryptography, is defined. Informally, in the context of encryption the additional requirement is that given the ciphertext it is impossible to generate a different ciphertext so that the respective plaintexts are related. The same concept makes sense in the contexts of string commitment and zero-knowledge proofs of possession of knowledge. Non-malleable schemes for each of these three problems are presented. The schemes do not assume a trusted center; a user need not know anything about the number or identity of other system users. Our cryptosystem is the first proven to be secure against a strong type of chosen ciphertext attack proposed by Rackoff and Simon, in which the attacker knows the ciphertext she wishes to break and can query the decryption oracle on any ciphertext other than the target.

“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]

Entity authentication and key distribution are central cryptographic problems in distributed computing -- but up until now, they have lacked even a meaningful definition. One consequence is that incorrect and inefficient protocols have proliferated. This paper provides the first treatment of these problems in the complexity-theoretic framework of modern cryptography. Addressed in detail are two problems of the symmetric, two-party setting: mutual authentication and authenticated key exchange. For each we present a definition, protocol, and proof that the protocol meets its goal, assuming the (minimal) assumption of pseudorandom function. When this assumption is appropriately instantiated, the protocols given are practical and efficient.

Publicly accessible databases are an indispensable resource for retrieving up to date information. But they also pose a significant risk to the privacy of the user, since a curious database operator can follow the user's queries and infer what the user is after. Indeed, in cases where the users ' intentions are to be kept secret, users are often cautious about accessing the database. It can be shown that when accessing a single database, to completely guarantee the privacy of the user, the whole database should be downloaded, namely n bits should be communicated (where n is the number of bits in the database). In this work, we investigate whether by replicating the database, more efficient solutions to the private retrieval problem can be obtained. We describe schemes that enable a user to access k replicated copies of a database (k * 2) and privately retrieve information stored in the database. This means that each individual database gets no information on the identity of the item retrieved by the user. Our schemes use the replication to gain substantial saving. In particular, we have ffl A two database scheme with communication complexity of O(n1=3). ffl A scheme for a constant number, k, of databases with communication complexity O(n1=k). ffl A scheme for 13 log2 n databases with polylogarithmic (in n) communication complexity.

We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function that is hard for C. This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences. The most direct one is that efficient deterministic simulation of randomized algorithms is possible under much weaker assumptions than previously known. The efficiency ofthe simulations depends on the strength of the assumptions, and may achieve P =BPP. Webelieve that our results are very strong evidence that the gap between randomized and deterministic complexity is not large. Using the known lower bounds for constant depth circuits, our construction yields an unconditionally proven pseudorandom generator for constant depth circuits. As an application of this generator we characterize the power of NP with a random oracle. 1.

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We show how a pseudo-random generator can provide a bit commitment protocol. We also analyze the number of bits communicated when parties commit to many bits simultaneously, and show that the assumption of the existence of pseudo-random generators suffices to assure amortized O(1) bits of communication per bit commitment.

We show that any randomized algorithm that runs in space S and time T and uses poly(S) random bits can be simulated using only O(S) random bits in space S and time T poly(S). A deterministic simulation in space S follows. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits. 1

The prospect of a world in which all text, audio, picture, and video documents are in digital form on easily modifiable media raises the issue of how to certify when a document was created or last changed. The problem is to time-stamp the data, not the medium. We propose computationally practical procedures for digital time-stamping of such documents so that it is infeasible for a user either to back-date or to forward-date his document, even with the collusion of a time-stamping service. Our procedures maintain complete privacy of the documents themselves, and require no record-keeping by the time-stamping service. Appeared, with minor editorial changes, in Journal of Cryptology, Vol. 3, No. 2, pp. 99--111, 1991. 0 Time's glory is to calm contending kings, To unmask falsehood, and bring truth to light, To stamp the seal of time in aged things, To wake the morn, and sentinel the night, To wrong the wronger till he render right. The Rape of Lucrece, l. 941 1 Introduction ...

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.