Linear, Constant-Rounds Bit-Decomposition

When performing secure multiparty computation, tasks may often be simple or difficult depending on the representation chosen. Hence, being able to switch representation efficiently may allow more efficient protocols. We present a new protocol for bit-decomposition: converting a ring element x ∈ ZM to its binary representation, x(logM)-1, ..., x0. The protocol can be based on arbitrary secure arithmetic in ZM; this is achievable for Shamir shared values as well as (threshold) Paillier encrypted ones, implying solutions for both these popular MPC primitives. For additively homomorphic primitives (which is typical, and the case for both examples) the solution is constant-rounds and requires only O(log M) secure ring multiplications. The solution is secure against active adversaries assuming the existence of additional primitives. These exist for both the Shamir sharing based approach as well as the Paillier based one.

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