Combining Shamir & Additive Secret Sharing to Improve Efficiency of SMC Primitives Against Malicious Adversaries

Abstract: Secure multi-party computation provides a wide array of protocols for mutually distrustful parties be able to securely evaluate functions of private inputs. Within recent years, many such protocols have been proposed representing a plethora of strategies to securely and efficiently handle such computation. These protocols have become increasingly efficient, but their performance still is impractical in many settings. We propose new approaches to some of these problems which are either more efficient than previous works within the same security models or offer better security guarantees with comparable efficiency. The goals of this research are to improve efficiency and security of secure multi-party protocols and explore the application of such approaches to novel threat scenarios. Some of the novel optimizations employed are dynamically switching domains of shared secrets, asymmetric computations, and advantageous functional transformations, among others. Specifically, this work presents a novel combination of Shamir and Additive secret sharing to be used in parallel which allows for the transformation of efficient protocols secure against passive adversaries to be secure against active adversaries. From this set of primitives we propose the construction of a comparison protocol which can be implemented under that approach with a complexity which is more efficient than other recent works for common domains of interest. Finally, we present a system which addresses a critical security threat for the protection and obfuscation of information which may be of high consequence.