Secure Equality and Greater-Than Tests with Sublinear Online Complexity

  • Helger Lipmaa
  • Tomas Toft
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


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.


Additively homomorphic encryption arithmetic black box secure comparison secure equality test 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Helger Lipmaa
    • 1
  • Tomas Toft
    • 2
  1. 1.Institute of CSUniversity of TartuEstonia
  2. 2.Dept. of CSAarhus UniversityDenmark

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