Truly efficient 2-round perfectly secure message transmission scheme

Authors:
Kaoru Kurosawa;Kazuhiro Suzuki
Affiliations:
Department of Computer and Information Sciences, Ibaraki University, Ibaraki, Japan;Department of Electronics and Informatics Frontier, Kanagawa University, Yokohama, Kanagawa, Japan
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 11
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Abstract

In the model of perfectly secure message transmission (PSMT) schemes, there are n channels between a sender and a receiver. An infinitely powerful adversary A may corrupt (observe and forge) the messages sent through t out of n channels. The sender wishes to send a secret s to the receiver perfectly privately and perfectly reliably without sharing any key with the receiver. In this paper, we show the first 2-round PSMT for n =2t+1 such that not only the transmission rate is O(n) but also the computational costs of the sender and the receiver are both polynomial in n. This means that we solve the open problem raised by Agarwal, Cramer, and de Haan at CRYPTO 2006. The main novelty of our approach is to introduce a notion of pseudobasis to the coding theory. It will be an independent interest for coding theory, too.