Computational Security Models

Takeshi Nakai

Abstract Secure computation with penalties aims to achieve fairness in secure computation protocols by imposing monetary penalties on adversarial parties. A fundamental problem in constructing protocols that involves monetary entities is how to formalize them in a computational model. Bentov and Kumaresan (CRYPTO 2014) introduced a new computational model with special atomic entities called coins that capture currency and showed a protocol for secure computation with penalties in the model. Their model, secure computation with coins, assumes coins have several properties that are natural in the sense of expressing currency. However, on the other hand, it also requires the unnatural assumption “all coins are indistinguishable from each other" for a technical reason to accomplish the security proof. The motivation of this work is to remove this assumption to make the model a more general. We propose a new model, secure computation with color coins, such that coins have identifiable colors and do not hold the indistinguishability property. Furthermore, our model allows us to set different prices for each color. We show that secure computation with penalties can be realized in our model. To do this, we make some modifications to the ideal functionality of secure computation with penalties to adapt it to our model without losing the essence, i.e., fairness with penalties.

Silvio M. Micali, Phillip Rogaway

Ye Wang, Prakash Ishwar, Shantanu D. Rane

The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated through the BGW protocol for computing quadratic and Hamming distances; this protocol is secure under the passive model, but is shown to be not secure under the active model.

Ran Canetti, Ling Cheung A, Dilsun Kaynar +2 more

Eun Jee Lee, Emmanuel A. Abbe

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.

Geoffroy Couteau