"Efficient cryptographic protocols based on noisy channels," Advances in Cryptology-EUROCRYPT'97

Claude Crépeau

Iftach Haitner, Jonathan J. Hoch, Omer Reingold +1 more

We study the round and communication complexities of various cryptographic protocols. We give tight lower bounds on the round and communication complexities of any fully black-box reduction of a statistically hiding commitment scheme from one-way permutations and from trapdoor permutations. As a corollary, we derive similar tight lower bounds for several other cryptographic protocols, such as single-server private information retrieval, interactive hashing, and oblivious transfer that guarantees statistical security for one of the parties. Our techniques extend the collision-finding oracle due to Simon [Advances in Cryptology---EUROCRYPT'98, Lecture Notes in Comput. Sci. 1403, Springer, Berlin, 1998, pp. 334--345] to the setting of interactive protocols and the reconstruction paradigm of Gennaro and Trevisan [Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS), IEEE Press, Piscataway, NJ, 2000, pp. 305--313].

Claude Crépeau, Rafael Dowsley, Anderson C. A. Nascimento

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.

Bartosz Przydatek

Jürg Wullschleger

Abstract. Various results show that oblivious transfer can be implemented using the assumption of noisy channels. Unfortunately, this assumption is not as weak as one might think, because in a cryptographic setting, these noisy channels must satisfy very strong security requirements. Unfair noisy channels, introduced by Damg˚ard, Kilian and Salvail [Eurocrypt ’99], reduce these limitations: They give the adversary an unfair advantage over the honest player, and therefore weaken the security requirements on the noisy channel. However, this model still has many shortcomings: For example, the adversary’s advantage is only allowed to have a very special form, and no error is allowed in the implementation. In this paper we generalize the idea of unfair noisy channels. We introduce two new models of cryptographic noisy channels that we call the weak erasure channel and the weak binary symmetric channel, and show how they can be used to implement oblivious transfer. Our models are more general and use much weaker assumptions than unfair noisy channels, which makes implementation a more realistic prospect. For example, these are the first models that allows the parameters to come from experimental evidence. 1

Salil Vadhan