A-6-9 An Information Theoretically Secure Cryptographic Primitive from Continuous Noisy Channels

Motohiko Isaka

In this paper, we consider an information theoretically secure cryptographic primitive known as oblivious transfer based on noisy channels. We present a protocol and two approaches to base the primitive on much wider class of signal sets and continuous channels than the existing results on the Gaussian channel. We also evaluate the associated information theoretic efficiency of the protocol for some cases of interest.

Claude Crépeau

Claude Crépeau

Vinícius de Morais Alves, Rafael Dowsley, Rafael T. de Sousa +1 more

Realizing fundamental cryptographic primitives with unconditional security is a central topic in information-theoretic cryptography. These primitives can be realized based on physical assumptions, such as the existence of noisy channels, an upper bound on the storage capacity, or the laws of quantum mechanics. Palmieri and Pereira [1] demonstrated that delays in communication channels can be used as a reasonable and effective assumption to obtain an unconditionally secure oblivious transfer protocol against honest-but-curious adversaries. While any oblivious transfer protocol secure against malicious adversaries can be used to implement commitment, the reduction does not work if the oblivious transfer protocol is only secure against honest-but-curious adversaries. Thus, the question of obtaining a secure commitment protocol based on channel delays is still open. In this paper, we provide a concrete protocol for implementing string commitments based on packet reordering – a consequence of channel delays in packet networks.

Anuj Kumar Yadav, Manideep Mamindlapally, Pranav Joshi +1 more

As computation and communication become increasingly ubiquitous, data security remains a key consideration. Hence, cryptographic primitives lie at the heart of several modern digital technologies. In this work, we study one such important cryptographic primitive called commitment. Here two parties, say Alice and Bob, aim to realize a protocol with the following functionality: Alice seeks to share or commit to a bit string securely with Bob with the requirement that the string is hidden from Bob until she chooses to reveal it to him. Bob wants to ensure that the protocol binds Alice to her original choice of bit string by allowing him to successfully detect when she cheats at the time of revealing her string. This seemingly elementary cryptographic functionality is extremely powerful and finds wide use in technologies like blockchains, digital contracts, cryptocurrencies, etc.. More generally, commitment has also been widely studied for applications like sealed-bid auctions, distributed coin tossing, etc.. Building on Wyner's classic work on wiretap channels, unconditionally-secure or information-theoretically secure protocols have been realized for a wide variety of problems, including commitment, using noisy channels as a resource. Crucially, however, the security guarantees are intimately tied to the knowledge of the noise statistics; these could be compromised when noise statistics are imprecisely known. In this work, we seek to study information-theoretically secure commitment over a class of unreliable noisy channels called compound channels. In particular, we study commitment over compound discrete memoryless channels (compound-DMCs) where the instantiated channel is known to be a DMC but its realization or channel state is not known exactly and can only be localized to a potential set of possible states. We precisely characterize the optimal throughput or commitment capacity over general compound DMCs. We also study the effect of state-awareness at the two parties, when the parties are honest and when they are malicious, on the commitment capacity of such compound DMCs. Interestingly, we show that committer-side state-awareness can non-trivially increase the commitment throughput over the compound DMC which is not the case when one has only receiver-side state awareness. In particular, we completely characterize the commitment capacity for all state-aware configurations for compound DMCs.

Hideichi Sasaoka