STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Communications of the ACM
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Multiparty Computation from Threshold Homomorphic Encryption
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Unbounded fan-in circuits and associative functions
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Constant-Rounds, Almost-Linear Bit-Decomposition of Secret Shared Values
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
Multiparty computation for interval, equality, and comparison without bit-decomposition protocol
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Linear, constant-rounds bit-decomposition
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
Modulo reduction for paillier encryptions and application to secure statistical analysis
FC'10 Proceedings of the 14th international conference on Financial Cryptography and Data Security
Efficient binary conversion for paillier encrypted values
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
TCC'06 Proceedings of the Third conference on Theory of Cryptography
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
An efficient and probabilistic secure bit-decomposition
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
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Bit-decomposition is an important primitive in multi-party computation (MPC). With the help of bit-decomposition, we will be able to construct constant-rounds protocols for various MPC problems, such as equality test, comparison, public modulo reduction and private exponentiation, which are four main applications of bit-decomposition. However, when considering perfect security, bit-decomposition does not have a linear communication complexity; thus any protocols involving bit-decomposition inherit this inefficiency. Constructing protocols for MPC problems without relying on bit-decomposition is a meaningful work because this may provide us with perfectly secure protocols with linear communication complexity. It is already proved that equality test, comparison and public modulo reduction can be solved without involving bit-decomposition and the communication complexity can be reduced to linear. However, it remains an open problem whether private exponentiation could be done without relying on bit-decomposition. In this paper, maybe somewhat surprisingly, we show that it can. That is to say, we construct a constant-rounds, linear, perfectly secure protocol for private exponentiation without relying on bit-decomposition though it seems essential to this problem. In a recent work, Ning and Xu proposed a generalization of bit-decomposi-tion and, as a simplification of their generalization, they also proposed a linear protocol for public modulo reduction. In this paper, we show that their generalization can be further generalized; more importantly, as a simplification of our further generalization, we propose a public modulo reduction protocol which is more efficient than theirs.