Atomic secure multi-party multiplication with low communication

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Abstract

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, Crépeau, 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 = ⊖(n) and t

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Cramer, R., Damgård, I., & De Haan, R. (2007). Atomic secure multi-party multiplication with low communication. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4515 LNCS, pp. 329–346). Springer Verlag. https://doi.org/10.1007/978-3-540-72540-4_19

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