An Efficient Secure Division Protocol Using Approximate Multi-Bit Product and New Constant-Round Building Blocks

Abstract

Integer division is one of the most fundamental arithmetic operators and is ubiquitously used. However, the existing division protocols in secure multi-party computation (MPC) are inefficient and very complex, and this has been a barrier to applications of MPC such as secure machine learning. We already have some secure division protocols working in Z 2 . However, these existing results have drawbacks that those protocols needed many communication rounds and needed to use bigger integers than in/output. In this paper, we improve a secure division protocol in two ways. First, we construct a new protocol using only the same size integers as in/output. Second, we build efficient constant-round building blocks used as subprotocols in the division protocol. With these two improvements, communication rounds of our division protocol are reduced to about 36% (87 rounds → 31 rounds) for 64-bit integers in comparison with the most efficient previous one.

Memory and Round-Efficient MPC Primitives in the Pre-Processing Model from Unit Vectorization

“…In particular, for the input lengths which we consider here (ℓ = 16, 32, 64, 128), the exact numbers of rounds in our protocol are 2x to 5.6x lower and the communication cost is improved by 2.8x to 5.4x, when compared to [28]. Comparing to [19], ours has lower numbers of rounds while the communication cost is improved up to 25x.…”

“…Their scheme requires 3 rounds for secure comparison and 2 rounds for other functionalities, but the storage cost increases exponentially in the input length. Hiwatashi et al modified these protocols to obtain a constant round complexity [19]. Their protocols use field arithmetic instead of multi-input multiplication, reducing round complexity but increasing communication and storage complexities.…”

“…Secure Division and Square Root Protocols. Previous secure division protocols and square root protocols often employ the Goldschmidt method [9,19,24,28]. The Goldschmidt method typically offers division protocols with 𝑂 (log ℓ) online rounds.…”

“…The Goldschmidt method typically offers division protocols with 𝑂 (log ℓ) online rounds. To the best of our knowledge, the state-of-the art for secure division is the twoparty secret-shared protocol of Hiwatashi et al [19], who improved upon the work of [28]. The round complexity in [19] is 𝑂 (⌈log 4 ℓ⌉).…”

“…Given two secretshared values as input, the protocol returns a sharing of the integer part of the quotient. The online round complexity is 𝑂 (ℓ), which is asymptotically less efficient than existing protocols such as [19,28] but more efficient when the input is of reasonable length. In particular, for the input lengths which we consider here (ℓ = 16, 32, 64, 128), the exact numbers of rounds in our protocol are 2x to 5.6x lower and the communication cost is improved by 2.8x to 5.4x, when compared to [28].…”