**On A Measure of Private Common Information**

**Amin Aminzadeh**

Sharif University of Technology, Iran

Suppose we have three random variables X, Y and Z distributed according to some given joint distribution p(x,y,z). We are looking for a measure of the common part of X and Y which is private against Z (Private Common Information (PCI)). We want the measure to have some natural properties: (i) when Z is independent of (X,Y), PCI equals to mutual information I(X;Y), (ii) when X is independent of Y, PCI equals zero regardless of what Z is. We show the so-called "source model key agreement capacity" has all the desired properties. Introduced by Ahlswede and Csiszar, the key agreement capacity is a fundamental open problem in information theoretic security. We will review the history of this problem and the sequence of ideas that led to better and better lower and upper bounds on this problem. Finally, new results on the problem will be given as well.

This is joint work with Onur Gunlu and Prof. Gerhard Kramer.

Amin Gohari received his B.Sc. degree from Sharif University, Iran, in 2004 and his Ph.D. degree in electrical engineering from the University of California, Berkeley in 2010. He was a postdoc at the Chinese University of Hong Kong, Institute of Network Coding. He is currently an Associate professor at Sharif University of Technology.

Dr. Gohari received the 2010 Eli Jury Award from UC Berkeley, Department of Electrical Engineering and Computer Sciences and the 2009-2010 Bernard Friedman Memorial Prize in Applied Mathematics from UC Berkeley, Department of Mathematics. He also received the Gold Medal from the 41st International Mathematical Olympiad (IMO 2000) and the First Prize from the 9th International Mathematical Competition for University Students (IMC 2002). He was a finalist for the best student paper award at IEEE International Symposium on Information Theory (ISIT) in three consecutive years, 2008, 2009 and 2010. He was also a co-author of a paper that won the ISIT 2013 Jack Wolf student paper award, and two that were finalists in 2012 and 2014. He was selected as an exemplary reviewer for IEEE Transactions on Communications in 2016 and 2017.