Biblio

To discuss secure key generation from imperfect random numbers, we address the secure key generation length. There are several studies for its asymptotic expansion up to the order √n or log n. However, these expansions have errors of the order o(√n) or o(log n), which does not go to zero asymptotically. To resolve this problem, we derive the asymptotic expansion up to the constant order for upper and lower bounds of these optimal values. While the expansions of upper and lower bonds do not match, they clarify the ranges of these optimal values, whose errors go to zero asymptotically.

Secure network coding realizes the secrecy of the message when the message is transmitted via noiseless network and a part of edges or a part of intermediate nodes are eavesdropped. In this framework, if the channels of the network has noise, we apply the error correction to noisy channel before applying the secure network coding. In contrast, secure physical layer network coding is a method to securely transmit a message by a combination of coding operation on nodes when the network is given as a set of noisy channels. In this paper, we give several examples of network, in which, secure physical layer network coding realizes a performance that cannot be realized by secure network coding.