2006 | OriginalPaper | Buchkapitel
Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation
verfasst von : Ivan Damgård, Matthias Fitzi, Eike Kiltz, Jesper Buus Nielsen, Tomas Toft
Erschienen in: Theory of Cryptography
Verlag: Springer Berlin Heidelberg
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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 = ⌈ log
2
p
⌉,
a
0
,...,
a
l
− 1
∈ {0,1} and
a
= ∑
i
= 0
ℓ− − 1
a
i
2
i
. 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.