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
2006333615 1652585999 2108777864 2148587342 2106833918 2027642452
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 this paper, we evaluate the asymptotics of equivocations and their exponents. Specifically, we consider the effect of applying a hash function on a source and we quantify the level of non-uniformity and dependence of the compressed source from another correlated source. Unlike previous works that use the Shannon information measures to quantify randomness or information, in this paper, we consider a more general class of information measures, i.e., the Renyi information measures and their Gallager forms. We prove tight asymptotic results for the equivocation and its exponential decay rates by establishing new non-asymptotic bounds on the equivocation and evaluating these bounds asymptotically. As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered. The concept of key-capacity is defined. Single-letter formulas of key-capacity are obtained for several models, and bounds to key-capacity are derived for other models. > We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett 's bound based on the Renyi entropy of order 2 because the bound obtained here uses the Renyi entropy of order 1+s for s ∈ [0,1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi 's exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion. The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution P sub XYZ , can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of P sub XYZ are presented. Lower bounds on the rate H(S) N (as N to infinity ) are derived for the case in which X=(X sub 1 , . . ., X sub N ), Y=(Y sub 1 , . . ., Y sub N ) and Z=(Z sub 1 , . . ., Z sub N ) result from N independent executions of a random experiment generating X sub i , Y sub i and Z sub i for i=1, . . ., N. It is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels, even when the enemy's channel is superior to the other two channels. > Motivated by the desirability of universal composability, we analyze in terms of L1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s ∈ [0,1], we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wiretap channel model and to secret key generation (distillation) by public discussion.