Constant-Rounds, Almost-Linear Bit-Decomposition of Secret Shared Values

  • Tomas Toft
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5473)


Bit-decomposition of secret shared values – securely computing sharings of the binary representation – is an important primitive in multi-party computation. The problem of performing this task in a constant number of rounds has only recently been solved.

This work presents a novel approach at constant-rounds bit-decomposition. The basic idea provides a solution matching the big-\(\mathcal{O}\)-bound of the original while decreasing the hidden constants. More importantly, further solutions improve asymptotic complexity with only a small increase in constants, reducing it from \(\mathcal O(\ell{\rm log}(\ell))\) to \(\mathcal O({\ell}{\rm log}^*(\ell))\) and even lower. Like previous solutions, the present one is unconditionally secure against both active and adaptive adversaries.


Secret Sharing Constant-rounds Multi-party Computation Bit-decomposition 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tomas Toft
    • 1
    • 2
  1. 1.CWI AmsterdamThe Netherlands
  2. 2.TU EindhovenThe Netherlands

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