# 2009 Research Summary

## Information-Theoretic Security in Cryptography

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Amin Aminzadeh Gohari and Venkat Anantharam

National Science Foundation CCF-0424422, TRUST: Cisco, ESCHER, HP, IBM, Intel, Microsoft, National Science Foundation CCF-050023, National Science Foundation CCF-0635372 and National Science Foundation CNS-0627161

In many environments requiring secret key generation, it is possible to provide external randomness to the agents. For example, sensor networks are often deployed in places where it is possible to beam randomness, e.g., from a satellite.

We use information-theoretic tools to study the fundamental problem in cryptography in which Alice, Bob, and Eve have access to possibly correlated random sources. We study the secret key rate of Alice and Bob (secret from Eve). We define a new Slepian-Wolf type problem and prove that the secret key rate reduces to a problem of this type. This parallels known results when there is no external randomness. Furthermore, using the new Slepian-Wolf type problem, we develop techniques to improve the best known bounds on the secret key generation capacity of Alice and Bob hidden from Eve.

- [1]
- A. A. Gohari and V. Anantharam, "New Bounds on the Information-Theoretic Key Agreement of Multiple Terminals,"
*IEEE International Symposium on Information Theory,*July 2008, pp. 742-746. - [2]
- A. A. Gohari and V. Anantharam, "Communication For Omniscience by a Neutral Observer and Information-Theoretic Key Agreement of Multiple Terminals,"
*IEEE International Symposium on Information Theory,*June 2007, pp. 2056-2060.