We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, -symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for -symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.
The setting considered in this paper is related to the wiretap channel II in that a fraction of the source symbols is hidden from a possible adversary. Oliveira al investigated in @cite_6 a related setting in the context of data storage over untrusted networks that do not collude, introducing a solution based on Vandermonde matrices. The MDS coding scheme introduced in this paper is similar to @cite_6 , albeit the framework developed here is more general.
@cite_6
2006333615 2164586990 2162970283 2123658733
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. We consider distributed storage over two untrusted networks, whereby coding is used as a means to achieve a prescribed level of confidentiality. The key idea is to exploit the algebraic structure of the Vandermonde matrix to mix the input blocks, before they are stored in different locations. The proposed scheme ensures that eavesdroppers with access to only one of the networks are unable to decode any symbol even if they are capable of guessing some of the missing blocks. Information-theoretic techniques allow us to quantify the achievable level of confidentiality. Moreover, the proposed approach is shown to offer low complexity and optimal rate. In this paper we consider tandem error control coding and cryptography in the setting of the wiretap channel due to Wyner. In a typical communications system a cryptographic application is run at a layer above the physical layer and assumes the channel is error free. However, in any real application the channels for friendly users and passive eavesdroppers are not error free and Wyner's wiretap model addresses this scenario. Using this model, we show the security of a common cryptographic primitive, i.e. a keystream generator based on linear feedback shift registers (LFSR), can be strengthened by exploiting properties of the physical layer. A passive eavesdropper can be made to experience greater difficulty in cracking an LFSR-based cryptographic system insomuch that the computational complexity of discovering the secret key increases by orders of magnitude, or is altogether infeasible. This result is shown for two fast correlation attacks originally presented by Meier and Staffelbach, in the context of channel errors due to the wiretap channel model. In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.