We analyze the exact exponential decay rate of the expected amount of information leaked to the wiretapper in Wyner’s wiretap channel setting using wiretap channel codes constructed from both i.i.d. and constant-composition random codes. Our analysis for those sampled from i.i.d. random coding ensemble shows that the previously known achievable secrecy exponent using this ensemble is indeed the exact exponent for an average code in the ensemble. Furthermore, our analysis on wiretap channel codes constructed from the ensemble of constant-composition random codes leads to an exponent which, in addition to being the exact exponent for an average code, is larger than the achievable secrecy exponent that has been established so far in the literature for this ensemble (which in turn was known to be smaller than that achievable by wiretap channel codes sampled from i.i.d. random coding ensemble). We show examples where the exact secrecy exponent for the wiretap channel codes constructed from random constant-composition codes is larger than that of those constructed from i.i.d. random codes and examples where the exact secrecy exponent for the wiretap channel codes constructed from i.i.d. random codes is larger than that of those constructed from constant-composition random codes. We, hence, conclude that, unlike the error correction problem, there is no general ordering between the two random coding ensembles in terms of their secrecy exponent.
Another important problem, in the realm of information-theoretic secrecy, is @cite_5 @cite_3 . The secrecy exponents related to this model are studied in @cite_27 @cite_12 @cite_7 @cite_9 and, in particular, in @cite_12 @cite_9 shown to be exact.
@cite_7 @cite_9 @cite_3 @cite_27 @cite_5 @cite_12
2026910567 2006333615 2064886960 2154832352
In this paper, we address the problem of characterizing the instances of the multiterminal source model of Csiszar and Narayan in which communication from all terminals is needed for establishing a secret key of maximum rate. We give an information-theoretic sufficient condition for identifying such instances. We believe that our sufficient condition is in fact an exact characterization, but we are only able to prove this in the case of the three-terminal source model. We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the channel state may be influenced by some of the parties involved. We derive single-letter expressions for the secret key capacity through a type of source emulation analysis. We also derive lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage. These exponents allow us to determine a set of strongly-achievable secret key rates. For degraded eavesdroppers the maximum strongly-achievable rate equals the secret key capacity; our exponents can also be specialized to previously known results. In deriving our strong achievability results we introduce a coding scheme that combines wiretap coding (to excite the channel) and key extraction (to distill keys from residual randomness). The secret key capacity is naturally seen to be a combination of both source- and channel-type randomness. Through examples we illustrate a fundamental interplay between the portion of the secret key rate due to each type of randomness. We also illustrate inherent tradeoffs between the achievable reliability and secrecy exponents. Our new scheme also naturally accommodates rate limits on the public discussion. We show that under rate constraints we are able to achieve larger rates than those that can be attained through a pure source emulation strategy. In the field of computer security, a problem that received little attention so far is the enforcement of confidentiality properties by supervisory control. Given a critical system G that may leak confidential information, the problem consists in designing a controller C, possibly disabling occurrences of a fixed subset of events of G, so that the closed-loop system G C does not leak confidential information. We consider this problem in the case where G is a finite transition system with set of events ? and an inquisitive user, called the adversary, observes a subset ?a of ?. The confidential information is the fact (when it is true) that the trace of the execution of G on ?* belongs to a regular set S ? ?*, called the secret. The secret S is said to be opaque w.r.t. G (respectively, G C) and ?a if the adversary cannot safely infer this fact from the trace of the execution of G (respectively, G C) on ?a*. In the converse case, the secret can be disclosed. We present an effective algorithm for computing the most permissive controller C such that S is opaque w.r.t. G C and ?a . This algorithm subsumes two earlier algorithms working under the strong assumption that the alphabet ?a of the adversary and the set of events that the controller can disable are comparable. We derive single-letter characterizations of (strong) secrecy capacities for models with an arbitrary number of terminals, each of which observes a distinct component of a discrete memoryless multiple source, with unrestricted and interactive public communication permitted between the terminals. A subset of these terminals can serve as helpers for the remaining terminals in generating secrecy. According to the extent of an eavesdropper's knowledge, three kinds of secrecy capacity are considered: secret key (SK), private key (PK), and wiretap secret key (WSK) capacity. The characterizations of the SK and PK capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements. A general upper bound for WSK capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source, provided randomization is permitted at the terminals. These secrecy capacities are seen to be achievable with noninteractive communication between the terminals. The achievability results are also shown to be universal.