Secure equality and greater-than tests with sublinear online complexity

Secure multiparty computation (MPC) allows multiple parties to evaluate functions without disclosing the private inputs. Secure comparisons (testing equality and greater-than) are important primitives required by many MPC applications. We propose two equality tests for ℓ-bit values with O(1) online communication that require O(ℓ) respectively O(κ) total work, where κ is a correctness parameter.Combining these with ideas of Toft [16], we obtain (i) a greater-than protocol with sublinear online complexity in the arithmetic black-box model (O(c) rounds and O(c·ℓ1/c ) work online, with c = logℓ resulting in logarithmic online work). In difference to Toft, we do not assume two mutually incorruptible parties, but O(ℓ) offline work is required, and (ii) two greater-than protocols with the same online complexity as the above, but with overall complexity reduced to O(logℓ(κ + loglogℓ)) and O(c·ℓ1/c (κ + logℓ)); these require two mutually incorruptible parties, but are highly competitive with respect to online complexity when compared to existing protocols.