Abstract
We show that if a set of players hold shares of a value \(a \in \mathbb{F}_p \) for some prime p (where the set of shares is written [a] p ), it is possible to compute, in constant rounds and with unconditional security, sharings of the bits of a, i.e., compute sharings [a 0] p , ..., [a ℓ− − 1] p such that ℓ = ⌈ log2 p ⌉, a 0,...,a l − 1 ∈ {0,1} and a = ∑ i = 0 ℓ− − 1 a i 2i. Our protocol is secure against active adversaries and works for any linear secret sharing scheme with a multiplication protocol. The complexity of our protocol is \(\mathcal{O}(l {\rm log} l)\) invocations of the multiplication protocol for the underlying secret sharing scheme, carried out in \(\mathcal{O}(1)\) rounds.
This result immediately implies solutions to other long-standing open problems such as constant-rounds and unconditionally secure protocols for deciding whether a shared number is zero, comparing shared numbers, raising a shared number to a shared exponent and reducing a shared number modulo a shared modulus.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-540-32732-5_32
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Keywords
- Secure Protocol
- Secret Sharing Scheme
- Multiplication Protocol
- Modulo Reduction
- Symmetric Boolean Function
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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Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T. (2006). Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In: Halevi, S., Rabin, T. (eds) Theory of Cryptography. TCC 2006. Lecture Notes in Computer Science, vol 3876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11681878_15
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