Secure Computation, I/O-Efficient Algorithms and Distributed Signatures

  • Ivan Damgård
  • Jonas Kölker
  • Tomas Toft
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7178)


We consider a setting where a set of n players use a set of m servers to store a large, private data set. Later the players decide on functions they want to compute on the data without the servers needing to know which computation is done, while the computation should be secure against a malicious adversary corrupting a constant fraction of the players and servers. Using packed secret sharing, the data can be stored in a compact way but will only be accessible in a block-wise fashion. We explore the possibility of using I/O-efficient algorithms to nevertheless compute on the data as efficiently as if random access was possible. We show that for sorting, priority queues and data mining, this can indeed be done. We show actively secure protocols of complexity within a constant factor of the passively secure solution. As a technical contribution towards this goal, we develop techniques for generating values of form r, g r for random secret-shared r ∈ ℤ q and g r in a group of order q. This costs a constant number of exponentiation per player per value generated, even if less than n/3 players are malicious. This can be used for efficient distributed computing of Schnorr signatures. We further develop the technique so we can sign secret data in a distributed fashion at essentially the same cost.


Signature Scheme Secret Sharing Secure Protocol Secure Computation Byzantine Agreement 
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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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Jonas Kölker
    • 1
  • Tomas Toft
    • 1
  1. 1.Dept. of Computer ScienceAarhus UniversityDenmark

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