Noisy channels are a valuable resource from a cryptographic point of view. They can be used for exchanging secret-keys as well as realizing other cryptographic primitives such as commitment and oblivious transfer. To be really useful, noisy channels have to be considered in the scenario where a cheating party has some degree of control over the channel characteristics. Damgård et al. (EUROCRYPT 1999) proposed a more realistic model where such level of control is permitted to an adversary, the so called unfair noisy channels, and proved that they can be used to obtain commitment and oblivious transfer protocols. Given that noisy channels are a precious resource for cryptographic purposes, one important question is determining the optimal rate in which they can be used. The commitment capacity has already been determined for the cases of discrete memoryless channels and Gaussian channels. In this work we address the problem of determining the commitment capacity of unfair noisy channels. We compute a single-letter characterization of the commitment capacity of unfair noisy channels. In the case where an adversary has no control over the channel (the fair case) our capacity reduces to the well-known capacity of a discrete memoryless binary symmetric channel.

Interactive hashing has featured as an essential ingredient in protocols realizing a large variety of cryptographic tasks, notably oblivious transfer in the bounded storage model. In interactive hashing, a sender transfers a bit string to a receiver such that two strings are received, the original string and a second string that appear to be chosen at random. This paper presents a self-contained, information theoretic study of interactive hashing. We start by formalizing the notion of interactive hashing as a cryptographic primitive, disentangling it from the specifics of its various implementations. To this end, we present an application-independent set of information theoretic conditions that all interactive hashing protocols must ideally satisfy. We then provide a detailed analysis of a standard implementation of interactive hashing which is shown to satisfy all the conditions of our definition. Our analysis represents a significant improvement over previous attempts in more restricted contexts. Despite its generality, it offers a considerably simpler proof of security. Moreover, it establishes a tighter upper bound on the cheating probability of a dishonest sender, who wishes to manipulate the protocol so that both output strings have some rare desirable property. In particular, we prove that if the set of desirable strings for the dishonest sender represents a fraction f of all strings, then the probability that both outputs will be from this set is no larger than 15.6805 · f. This upper bound is valid for any f and is tight up to a small constant, since a sender acting honestly would get two outputs from this set with probability very close to f. We illustrate the power of interactive hashing as a cryptographic tool by surveying protocols achieving oblivious transfer in the bounded storage model, which typically rely heavily on interactive hashing.

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any \left[ {\frac{{n - 1}} {2}} \right] cheaters among n players. Previous protocols for these tasks tolerated \left[ {\frac{{n - 1}} {4}} \right] and \left[ {\frac{{n - 1}} {6}} \right] cheaters, respectively. The threshold we achieve is tight -- even in the classical case, "fair" multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum errorcorrecting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in faulttolerant quantum circuits.

Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states. We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s. The scheme requires a secret key of size 2m+O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically. This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.

Multi-party computing, also called secure function evaluation, has been extensively studied in classical cryptography. We consider the extension of this task to computation with quantum inputs and circuits. Our protocols are information-theoretically secure, i.e. no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to show how to perform any multi-party quantum computation as long as the number of dishonest players is less than n/6.

We propose a protocol for oblivious transfer that is unconditionally secure under the sole assumption that the memory size of the receiver is bounded. The model assumes that a random bit string slightly larger than the receiver's memory is broadcast (either by the sender or by a third party). In our construction, both parties need memory of size in /spl theta/(n/sup 2-2/spl alpha//) for some /spl alpha//spl beta/>0, whereas a malicious receiver can have up to /spl gamma/N bits of memory for any /spl gamma/<1. In the course of our analysis, we provide a direct study of an interactive hashing protocol closely related to that of M. Naor et al. (1998).

Assume A owns t secret k-bit strings. She is willing to disclose one of them to B, at his choosing, provided he does not learn anything about the other strings. Conversely, B does not want A to learn which secret he chose to learn. A protocol for the above task is said to implement one-out-of-t string oblivious transfer, denoted (/sup t//sub 1/)-OT/sup k//sub 2/. This primitive is particularly useful in a variety of cryptographic settings. An apparently simpler task corresponds to the case k=1 and t=2 of two 1-bit secrets: this is known as one-out-of-two bit oblivious transfer, denoted (/sup 2//sub 1/)-OT/sub 2/. We address the question of implementing (/sup t//sub 1/)-OT/sup k//sub 2/ assuming the existence of a (/sup 2//sub 1/)-OT/sub 2/. In particular, we prove that unconditionally secure (/sup 2//sub 1/)-OT/sup k//sub 2/ can be implemented from /spl Theta/(k) calls to (/sup 2//sub 1/)-OT/sub 2/. This is optimal up to a small multiplicative constant. Our solution is based on the notion of self-intersecting codes. Of independent interest, we give several efficient new constructions for such codes. Another contribution of this paper is a set of information-theoretic definitions for correctness and privacy of unconditionally secure oblivious transfer.

This paper, provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard, and Robert for a special scenario. Privacy amplification is a process that allows two parties to distil a secret key from a common random variable about which an eavesdropper has partial information. The two parties generally know nothing about the eavesdropper's information except that it satisfies a certain constraint. The results have applications to unconditionally secure secret-key agreement protocols and quantum cryptography, and they yield results on wiretap and broadcast channels for a considerably strengthened definition of secrecy capacity.

We describe a complete protocol for bit commitment based on the transmission of polarized photons. We show that under the laws of quantum physics, this protocol cannot be cheated by either party except with exponentially small probability (exponential in the running time needed to implement the honest protocol). A more thorough analysis is required to adjust all the constants used in this paper to get the best performance from our construction. Better performances may probably be achieved by using a third conjugate transmission-reception basis of circular polarization.>

The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophisticated cryptographic device. They also present an application to quantum cryptography.>

Under the assumption that each pair of participants em communieatc secretly, we show that any reasonable multiparty protwol can be achieved if at least Q of the Participants am honest. The secrecy achieved is unconditional, It does not rely on any assumption about computational intractability. 1.

A zero-knowledge interactive proof is a protocol by which Alice can convince a polynomially-bounded Bob of the truth of some theorem without giving him any hint as to how the proof might proceed. Under cryptographic assumptions, we give a general technique for achieving this goal for every problem in NP. This extends to a presumably larger class, which combines the powers of non-determinism and randomness. Our protocol is powerful enough to allow Alice to convince Bob of theorems for which she does not even have a proof: it is enough for Alice to convince herself probabilistically of a theorem, perhaps thanks to her knowledge of some trap-door information, in order for her to be able to convince Bob as well, without compromising the trap-door in any way. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A perfect zero-knowledge interactive proof is a protocol by which Alice can convince Bob of the truth of some theorem in a way that yields no information as to how the proof might proceed (in the sense of Shannon's information theory). We give a general technique for achieving this goal for any problem in NP (and beyond). The fact that our protocol is perfect zero-knowledge does not depend on unproved cryptographic assumptions. Furthermore, our protocol is powerful enough to allow Alice to convince Bob of theorems for which she does not even have a proof. Whenever Alice can convince herself probabilistically of a theorem, perhaps thanks to her knowledge of some trap-door information, she can convince Bob as well without compromising the trap-door in any way. This results in a non-transitive transfer of confidence from Alice to Bob, because Bob will not be able to subsequently convince someone else that the theorem is true. Our protocol is dual to those of [GMW1, BC].

Alice disposes of some number of secrets. She is willing to disclose one of them to Bob. Although she agrees to let him choose which secret he wants, she is not willing to allow him to gain any information on more than one secret. On the other hand, Bob does not want Alice to know which secret he wishes. An all-or-nothing disclosure is one by which, as soon as Bob has gained any information whatsoever on one of Alice's secrets, he has wasted his chances to learn anything about the other secrets. We assume that Alice is honest when she claims to be willing to disclose one secret to Bob (i.e. she is not about to send junk). The only cheating Alice is susceptible of trying is to figure out which secret is of interest to Bob. We address the following question from an information theoretic point of view: what is the most elementary disclosure problem? The main result is that the general all-or-nothing disclosure of secrets is equivalent to a much simpler problem, which we call the two-bit problem.