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STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
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Multiparty computation for interval, equality, and comparison without bit-decomposition protocol
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Efficient binary conversion for paillier encrypted values
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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Linear, constant-rounds bit-decomposition
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Accelerating multiparty computation by efficient random number bitwise-sharing protocols
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Batching multiple protocols to improve efficiency of multi-party computation
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An efficient and probabilistic secure bit-decomposition
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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.