### Cryptography with One-Way Communication

Sanjam Garg, Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, and Amit Sahai

##### Abstract

There is a large body of work on using noisy communication channels for realizing different cryptographic tasks. In particular, it is known that secure message transmission can be achieved unconditionally using only {\em one-way} communication from the sender to the receiver. In contrast, known solutions for more general secure computation tasks inherently require interaction, even when the entire input originates from the sender. We initiate a general study of cryptographic protocols over noisy channels in a setting where only one party speaks. In this setting, we show that the landscape of what a channel is useful for is much richer. Concretely, we obtain the following results. [-] Relationships between channels. The binary erasure channel (BEC) and the binary symmetric channel (BSC), which are known to be securely reducible to each other in the interactive setting, turn out to be qualitatively different in the setting of one-way communication. In particular, a BEC cannot be implemented from a BSC, and while the erasure probability of a BEC can be manipulated in both directions, the crossover probability of a BSC can only be manipulated in one direction. [-] Zero-knowledge proofs and secure computation of deterministic functions. One-way communication over BEC or BSC is sufficient for securely realizing any deterministic (possibly reactive) functionality which takes its inputs from a sender and delivers its outputs to a receiver. This provides the first truly non-interactive solutions to the problem of zero-knowledge proofs. [-] Secure computation of randomized functions. One-way communication over BEC or BSC {\em cannot} be used for realizing general randomized functionalities which take input from a sender and deliver output to a receiver. On the other hand, one-way communication over other natural channels, such as bursty erasure channels, can be used to realize such functionalities. This type of protocols can be used for distributing certified cryptographic keys without revealing the keys to the certification authority.

Available format(s)
Category
Foundations
Publication info
A minor revision of an IACR publication in Crypto 2015
Keywords
secure computationnoisy channels
Contact author(s)
sanjamg @ berkeley edu
History
2015-07-15: revised
See all versions
Short URL
https://ia.cr/2014/914

CC BY

BibTeX

@misc{cryptoeprint:2014/914,
author = {Sanjam Garg and Yuval Ishai and Eyal Kushilevitz and Rafail Ostrovsky and Amit Sahai},
title = {Cryptography with One-Way Communication},
howpublished = {Cryptology ePrint Archive, Paper 2014/914},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/914}},
url = {https://eprint.iacr.org/2014/914}
}

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