Paper 2008/421

Truly Efficient 2-Round Perfectly Secure Message Transmission Scheme

Kaoru Kurosawa and Kazuhiro Suzuki

Abstract

In the model of perfectly secure message transmission schemes (PSMTs), 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.

Note: Sec.2.2 and Sec.2.3 are revised.