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Paper: Multiparty Computation from Threshold Homomorphic Encryption

Authors:
Ronald Cramer
Ivan Damgård
Jesper Buus Nielsen
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URL: http://eprint.iacr.org/2000/055
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Abstract: We introduce a new approach to multiparty computation (MPC) basing it on homomorphic threshold crypto-systems. We show that given keys for any sufficiently efficient system of this type, general MPC protocols for $n$ players can be devised which are secure against an active adversary that corrupts any minority of the players. The total number of bits sent is $O(nk|C|)$, where $k$ is the security parameter and $|C|$ is the size of a (Boolean) circuit computing the function to be securely evaluated. An earlier proposal by Franklin and Haber with the same complexity was only secure for passive adversaries, while all earlier protocols with active security had complexity at least quadratic in $n$. We give two examples of threshold cryptosystems that can support our construction and lead to the claimed complexities.
BibTeX
@misc{eprint-2000-11399,
  title={Multiparty Computation from Threshold Homomorphic Encryption},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / threshold cryptography},
  url={http://eprint.iacr.org/2000/055},
  note={ buus@brics.dk 11257 received 27 Oct 2000},
  author={Ronald Cramer and Ivan Damgård and Jesper Buus Nielsen},
  year=2000
}