## Towards Characterizing when Information-Theoretic Key Agreement Is Possible

### Ueli Maurer and Stefan Wolf

This paper is concerned with information-theoretically secure secret key agreement in the general scenario where three parties, Alice, Bob, and Eve, know random variables X, Y, and Z, respectively, with joint distribution P_XYZ, for instance resulting from receiving a sequence of random bits broadcast by a satellite. We consider the problem of determining for a given distribution P_{XYZ} whether Alice and Bob can in principle, by communicating over an insecure channel accessible to Eve, generate a secret key about which Eve's information is arbitrarily small. When X, Y, and Z are random variables that result from a binary random variable being sent through three arbitrary independent channels, it is shown that secret key agreement is possible if and only if I(X;Y|Z)>0, i.e., under the sole condition that X and Y have some (arbitrarily weak) statistical dependence when given Z.

## BibTeX Citation

@inproceedings{MauWol96a, author = {Ueli Maurer and Stefan Wolf}, title = {Towards Characterizing when Information-Theoretic Key Agreement Is Possible}, booktitle = {Advances in Cryptology --- ASIACRYPT~'96}, pages = {196--209}, series = {Lecture Notes in Computer Science}, volume = {1163}, year = {1996}, month = {11}, publisher = {Springer-Verlag}, }