How to attain the ordinary channel capacity securely in wiretap channels

On the secrecy capacity of arbitrary wiretap channels

“…Hayashi [11] recently analyzed the connection between coding for the wiretap channel and resolvability using the informationspectrum approach [12], and derived the secrecy capacity of arbitrary wiretap channels for the case in which the output alphabet at the eavesdropper is finite. With the notable exception of [13], [14] Motivated by the perspective of a general result encompassing many wiretap channel models, we also investigate the information-spectrum approach to arbitrary wiretap channels. Section I-B reviews classic definitions of information spectra and sets the notation used throughout the paper.…”

Degraded Gaussian Diamond–Wiretap Channel

“…By applying the above lower bound to (6), we obtain nR ≤ nC 1 + nC 2 − I(X n 1 , X n 2 ; U n |M ) + I(X n 1 ; U n |X n 2 ) + I(X n 2 ; U n |X n 1 ) + nǫ n .…”

Multiplex Coding of Bit Commitment Based on a Discrete Memoryless Channel

“…We now define the achievable rate region of the bit commitment protocol as follows. The achievable rate region R is defined as (6) (7) (8) (9) R _ {(Rs, Ru): (Rs, Ru) is achievable}. (10) The achievable region defined in Definition 1 is determined by the following theorem.…”

“…Furthermore, by using the similar analytical techniques to [5], Kobayashi-Yamamoto-Ogawa (KYO) [7] [8] proved, by devising a multiplex coding of plural mutually independent secrets, that even if the total coding rate of secrets exceed the so-called secrecy capacity, we can attain the perfect secrecy of each secret individually. In this paper, we show that the multiplex coding can also be applied to the bit commitment, and the several mutually independent secrets can be committed at the same time attaining the perfect secrecy of each secret individually with the total coding rate of log IX , where IX is the cardinality of X and, hence, log IXI is usually larger than the bit commitment capacity CbIn section 2, we prove a new coding theorem for the case of one secret, which was treated by WNI [3].…”

“…MULTIPLEX CODING FOR BIT COMMITMENT From Theorem 1, we can attain the bit commitment with rate H(X Y) via a DMC V. Since rate I(X; Y) is required to attain the concealing condition, the transmission rate in the bit commitment is reduced from H(X) to H(X Y). But, as shown in KYO[7][8], other secrets than S can be substituted into the random number U securely in the multiplex coding for wiretap channels. In this section, we show that the multiplex coding can be applied to the coding of bit commitment and the total rate of committed secrets can be increased to H(X).…”