A Full Characterization of Completeness for Two-Party Randomized Function Evaluation

  • Daniel Kraschewski
  • Hemanta K. Maji
  • Manoj Prabhakaran
  • Amit Sahai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8441)


We settle a long standing open problem which has pursued a full characterization of completeness of (potentially randomized) finite functions for 2-party computation that is secure against active adversaries. Since the first such complete function was discovered [Kilian, FOCS 1988], the question of which finite 2-party functions are complete has been studied extensively, leading to characterization in many special cases. In this work, we completely settle this problem.

We provide a polynomial time algorithm to test whether a 2-party finite secure function evaluation (SFE) functionality (possibly randomized) is complete or not. The main tools in our solution include:

We show that any function f, if complete, can implement any (randomized) circuit C using only O(|C| + κ) calls to f, where κ is the statistical security parameter. In particular, for any two-party functionality g, this establishes a universal notion of its quantitative “cryptographic complexity” independent of the setup and has close connections to circuit complexity.


Active Adversary Full Characterization Noisy Channel Circuit Complexity Oblivious Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Daniel Kraschewski
    • 1
  • Hemanta K. Maji
    • 2
  • Manoj Prabhakaran
    • 3
  • Amit Sahai
    • 4
  1. 1.TechnionHaifaIsrael
  2. 2.Los AngelesUSA
  3. 3.Univ. of IllinoisUrbana-ChampaignUSA
  4. 4.Univ. of CaliforniaLos AngelesUSA

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