## Cryptology ePrint Archive: Report 2013/738

On the Resilience and Uniqueness of CPA for Secure Broadcast

Chris Litsas and Aris Pagourtzis and Giorgos Panagiotakos and Dimitris Sakavalas

Abstract: We consider the Secure Broadcast problem in incomplete networks. We study the resilience of the Certified Propagation Algorithm (CPA), which is particularly suitable for ad hoc networks. We address the issue of determining the maximum number of corrupted players $t^{\mathrm{CPA}}_{\max}$ that CPA can tolerate under the $t$-locally bounded adversary model, in which the adversary may corrupt at most $t$ players in each player's neighborhood. For any graph $G$ and dealer-node $D$ we provide upper and lower bounds on $t^{\mathrm{CPA}}_{\max}$ that can be efficiently computed in terms of a graph theoretic parameter that we introduce in this work. Along the way we obtain an efficient 2-approximation algorithm for $t^{\mathrm{CPA}}_{\max}$. We further introduce two more graph parameters, one of which matches $t^{\mathrm{CPA}}_{\max}$exactly. Our approach allows to provide an affirmative answer to the open problem of CPA Uniqueness posed by Pelc and Peleg in 2005.

Category / Keywords: cryptographic protocols / distributed cryptography ; ad hoc networks; secure broadcast; byzantine generals; t-locally bounded adversary model

Original Publication (with major differences): Proceedings of ADHOC-NOW 2013, 12th International Conference, LNCS 7960, pp. 269-280, Springer.
DOI:
10.1007/978-3-642-39247-4_23