A Shannon Approach to Secure Multi-party Computations

• Published in: arXiv.org
• Main Authors: Eun Jee Lee, Abbe, Emmanuel
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 26.03.2014
• Subjects: Computer Science - Cryptography and Security; Computer Science - Information Theory; Computing costs; Dependence; Mathematics - Information Theory; Probabilistic models; Randomness
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1401.7360

In secure multi-party computations (SMC), parties wish to compute a function on their private data without revealing more information about their data than what the function reveals. In this paper, we investigate two Shannon-type questions on this problem. We first consider the traditional one-shot model for SMC which does not assume a probabilistic prior on the data. In this model, private communication and randomness are the key enablers to secure computing, and we investigate a notion of randomness cost and capacity. We then move to a probabilistic model for the data, and propose a Shannon model for discrete memoryless SMC. In this model, correlations among data are the key enablers for secure computing, and we investigate a notion of dependency which permits the secure computation of a function. While the models and questions are general, this paper focuses on summation functions, and relies on polar code constructions.