The two-party key agreement problem with public discussion, known as the source model problem, is considered for an erasure model for Eve's side information. By relating the key agreement problem to hypothesis testing, a new coding scheme is developed that yields an upper bound on the maximum erasure probability for which the secret-key (SK) capacity is zero. The bound is shown to be tight when Alice's or Bob's source is binary, and this shows that the new code achieves larger SK rates than the best known coding scheme. A full version of this paper with extensions to general models for Eve's side information is available in [1].
The two-party key agreement problem with public discussion, known as the source model problem, is considered for an erasure model for Eve's side information. By relating the key agreement problem to hypothesis testing, a new coding scheme is developed that yields an upper bound on the maximum erasure probability for which the secret-key (SK) capacity is zero. The bound is shown to be tight when Alice's or Bob's source is binary, and this shows that the new code achieves larger SK rates than the best known coding scheme. A full version of this paper with extensions to general models for Eve's side information is available in [1].
A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of Rényi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables which is of independent interest.
This paper is concerned with secret-key agreement by public discussion. Assume that two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X, Y, and Z, respectively, with joint distribution P/sub XYZ/. The secret-key rate S(X;Y/spl par/Z) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between S and Y when given Z, denoted by I(X;Y/spl darr/Z), which is an upper bound on S(X;Y/spl par/Z). The special scenarios are analyzed where X, Y, and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or two scenarios in which Z is generated by sending X and Y over erasure channels. In the first two scenarios it can be shown that the secret-key rate is strictly positive if and only if I(X;Y/spl darr/Z) is strictly positive. For the third scenario, a new protocol is presented which allows secret-key agreement even when all the previously known protocols fail.
We consider the source model key agreement problem involving two legitimate parties and an eavesdropper who observe n i.i.d. samples of X, Y, and Z, respectively. In this paper, we focus on one of the simplest instances where the key capacity remains open, specifically when X and Y are binary random variables and Z is a function of the pair (X, Y). The best-known upper bound on the key capacity is characterized by an inf-max optimization problem that generally lacks a closed-form solution. We provide general conditions under which the upper bound reduces to I(X;Y). As an example, we consider the XOR setting in which X and Y are binary, and Z is the XOR of X and Y. The upper bound reduces to I(X;Y) for this source. Next, we conjecture that the rate I(X;Y) is not achievable for the XOR source and provide some ideas that might be useful for developing a new upper bound on the source model problem.
We consider the source model key agreement problem involving two legitimate parties and an eavesdropper who observe n i.i.d. samples of X and Y and Z respectively. In this paper, we focus on one of the simplest instances where the key capacity remains open, specifically when X and Y are binary random variables and Z is a function of the pair (X,Y). The best-known upper bound on the key capacity is characterized by an inf-max optimization problem that generally lacks a closedform solution. In this paper, we solve the optimization for some class of sources, thereby providing simple expressions for the upper bound. We provide general conditions under which the upper bound reduces toI(X;Y). As an example, we consider the XOR setting in which X and Y are binary, and Z is the XOR of X and Y. The upper bound reduces toI(X;Y)for this source. Next, we conjecture that the rateI(X;Y)is not achievable for the XOR source, and provide some ideas that might be useful for developing a new upper bound.1
This paper is concerned with secret-key agreement by public discussion: two parties Alice and Bob and an adversary Eve have access to independent realizations of random variables X , Y , and Z, respectively, with joint distribution PXY Z . The secret key rate S(X ; Y jjZ) has been defined as the maximal rate at which Alice and Bob can generate a secret key by communication over an insecure, but authenticated channel such that Eve's information about this key is arbitrarily small. We define a new conditional mutual information measure, the intrinsic conditional mutual information between X and Y when given Z, denoted by I(X ; Y#Z), which is an upper bound on S(X ; Y jjZ). The special scenarios where X , Y , and Z are generated by sending a binary random variable R, for example a signal broadcast by a satellite, over independent channels, or where Z is generated by sending X and Y over erasure channels, are analyzed. In the first scenario it can be shown that the secret key rate is str...
Information-theoretic secret key agreement (SKA) protocols are a fundamental cryptographic primitive that are used to establish a shared secret key between two or more parties. In a two-party SKA in source model, Alice and Bob have samples of two correlated variables that are partially leaked to Eve, and their goal is to establish a shared secret key by communicating over a reliable public channel. Eve must have no information about the established key. In this paper, we study the problem of one-way secret key agreement where the key is established by Alice sending a public message to Bob. We propose a one-way SKA (OW-SKA) protocol, prove that it achieves the one-way secret key capacity, and use it to derive a finite blocklength bound on the achievable secret key length. We compare our results with existing OW-SKAs and show the protocol achieves a longer key, and has a combination of desirable properties.