Publications: Abstract

# Unconditionally Secure Key Agreement and the Intrinsic Conditional Information

## Ueli Maurer and Stefan Wolf

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_{XYZ}\$. The secret key rate \$S(X;Y||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 \$X\$ and \$Y\$ when given \$Z\$, denoted by \$\ida\$, which is an upper bound on \$S(X;Y||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 \$\ida\$ 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.