Sign Modules in Secure Arithmetic Circuits

In this paper, we study the complexity of secure multiparty computation using only the secure arithmetic black-box of a finite field, counting the cost by the number of secure multiplications. We observe that a specific type of quadratic patterns exists in all finite fields, and the existence of these patterns can be utilized to improve the efficiency of secure computation to a remarkable extent. We define sign modules as partial functions that simulate integer signs in an effective range using a polynomial number of arithmetic operations on a finite field. Let denote the bitlength of a finite field size. We show the existence of /5 -“effective” sign modules in any finite field that has a sufficiently large characteristic. When is decided first, we further show the existence of prime fields that contain an Ω( log )-“effective” sign module and we propose an efficient probabilistic algorithm that finds concrete instances of sign modules. Let Zp be any odd pri...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Ching-Hua Yu
• Keywords: Arithmetic Operations, IACR 2011, Polynomial Number, Probabilistic Algorithm