Asymptotically Optimal Two-Round Perfectly Secure Message Transmission

Abstract. The problem of perfectly secure message transmission concerns two synchronized non-faulty processors sender (S) and receiver (R) that are connected by a synchronous network of n 2t + 1 noiseless 2way communication channels. Their goal is to communicate privately and reliably, despite the presence of an adversary that may actively corrupt at most t of those channels. These properties should hold information theoretically and without error. We propose an asymptotically optimal solution for this problem. The proposed protocol consists of two communication rounds, and a total of O( n) bits are exchanged in order to transmit a message of bits. Earlier, at CRYPTO 2004, an equally optimal solution has been claimed. However, we give a counter-example showing that their result is not perfectly reliable. The flaw seems to be fundamental and non-trivial to repair. Our approach is overall entirely different, yet it also makes essential use of their neat communication efficient technique...

• Type: Conference
• Year: 2006
• Where: CRYPTO
• Authors: Saurabh Agarwal, Ronald Cramer, Robbert de Haan
• Keywords: CRYPTO 2006, Cryptology, Noiseless 2way Communication, Non-faulty Processors Sender, Optimal Solution