Atomic Secure Multi-party Multiplication with Low Communication

We consider the standard secure multi-party multiplication protocol due to M. Rabin. This protocol is based on Shamir’s secret sharing scheme and it can be viewed as a practical variation on one of the central techniques in the foundational results of Ben-Or, Goldwasser, and Wigderson and Chaum, Cr´epeau, and Damgaard on secure multi-party computation. Rabin’s idea is a key ingredient to virtually all practical protocols in threshold cryptography. Given a passive t-adversary in the secure channels model with synchronous communication, for example, secure multiplication of two secretshared elements from a finite field K based on this idea uses one communication round and has the network exchange O(n2 ) field elements, if t = Θ(n) and t < n/2 and if n is the number of players. This is because each of O(n) players must perform Shamir secret sharing as part of the protocol. This paper demonstrates that under a few restrictions much more efficient protocols are possible; even at...

• Type: Conference
• Year: 2007
• Where: EUROCRYPT
• Authors: Ronald Cramer, Ivan Damgård, Robbert de Haan
• Keywords: Cryptography, EUROCRYPT 2007, Rabin’s Idea, Secure Multi-party Multiplication, Secure Multiplication