Efficient Secure Linear Algebra in the Presence of Covert or Computationally Unbounded Adversaries

In this work we study the design of secure protocols for linear algebra problems. All current solutions to the problem are either inefficient in terms of communication complexity or assume that the adversary is honest but curious. We design protocols for two different adversarial settings: First, we achieve security in the presence of a covert adversary, a notion recently introduced by [Aumann and Lindell, TCC 2007]. Roughly speaking, this guarantees that if the adversary deviates from the protocol in a way that allows him to cheat, then he will be caught with good probability. Second, we achieve security against arbitrary malicious behaviour in the presence of a computationally unbounded adversary that controls less than a third of the parties. Our main result is a new upper bound of O(n2+1/t ) communication for testing singularity of a shared n

• Type: Conference
• Year: 2008
• Where: CRYPTO
• Authors: Payman Mohassel, Enav Weinreb
• Keywords: Adversarial Settings, CRYPTO 2008, Cryptology, Homomorphic Encryption Scheme, Secure Protocols