Empirical Coordination in a Triangular Multiterminal Network

In this paper, we investigate the problem of the empirical coordination in a triangular multiterminal network. A triangular multiterminal network consists of three terminals where two terminals observe two external i.i.d correlated sequences. The third terminal wishes to generate a sequence with desired empirical joint distribution. For this problem, we derive inner and outer bounds on the empirical coordination capacity region. It is shown that the capacity region of the degraded source network and the inner and outer bounds on the capacity region of the cascade multiterminal network can be directly obtained from our inner and outer bounds. For a cipher system, we establish key distribution over a network with a reliable terminal, using the results of the empirical coordination. As another example, the problem of rate distortion in the triangular multiterminal network is investigated in which a distributed doubly symmetric binary source is available.Comment: Accepted in ISIT 201

On the Shannon Cipher System With a Wiretapper Guessing Subject to Distortion and Reliability Requirements

In this paper we discuss the processes in the Shannon cipher system with discrete memoryless source and a guessing wiretapper. The wiretapper observes a cryptogram of $N$-vector of ciphered messages in the public channel and tries to guess successively the vector of messages within given distortion level $\Delta$ and small probability of error less than $\exp \{-NE\}$ with positive reliability index $E$. The security of the system is measured by the expected number of guesses which wiretapper needs for the approximate reconstruction of the vector of source messages. The distortion, the reliability criteria and the possibility of upper limiting the number of guesses extend the approach studied by Merhav and Arikan. A single-letter characterization is given for the region of pairs $(R_L,R)$ (of the rate $R_L$ of the maximum number of guesses $L(N)$ and the rate $R$ of the average number of guesses) in dependence on key rate $R_K$, distortion level $\Delta$ and reliability $E$.Comment: 14 pages, 3 figures, Submitted to IEEE Transactions on Information Theor

Quantum Noise Randomized Ciphers

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as AlphaEta and show that it is equivalent to a random cipher in which the required randomization is effected by coherent-state quantum noise. We describe the currently known security features of AlphaEta and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how AlphaEta used in conjunction with any standard stream cipher such as AES (Advanced Encryption Standard) provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that AlphaEta is equivalent to a non-random stream cipher.Comment: Accepted for publication in Phys. Rev. A; Discussion augmented and re-organized; Section 5 contains a detailed response to 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 327 (2004) 28-32 /quant-ph/0310168' & 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 346 (2005) 7

Perfectly Secure Index Coding

In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set. We study the minimum key lengths for zero-error and perfectly secure index coding problem. On one hand, this problem is a generalization of the index coding problem (and thus a difficult one). On the other hand, it is a generalization of the Shannon's cipher system. We show that a generalization of Shannon's one-time pad strategy is optimal up to a multiplicative constant, meaning that it obtains the entire boundary of the cone formed by looking at the secure rate region from the origin. Finally, we consider relaxation of the perfect secrecy and zero-error constraints to weak secrecy and asymptotically vanishing probability of error, and provide a secure version of the result, obtained by Langberg and Effros, on the equivalence of zero-error and $\epsilon$-error regions in the conventional index coding problem.Comment: 25 pages, 5 figures, submitted to the IEEE Transactions on Information Theor