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
Multiparty unconditionally secure protocols
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
The round complexity of secure protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of 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
Lower Bounds for Constant Depth Circuits for Prefix Problems
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Unbounded fan-in circuits and associative functions
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Optimizing robustness while generating shared secret safe primes
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
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
Practical PIR for electronic commerce
Proceedings of the 18th ACM conference on Computer and communications security
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We propose constant-round protocols for interval tests, equality tests, and comparisons where shared secret inputs are not given bitwise. In [9]. Damgård et al. presented a novel protocol called the bit-decomposition, which can convert a polynomial sharing of an element in prime field p into sharings of bits. Though, by using the bit-decomposition protocol, those protocols can be constructed with constant round complexities theoretically, it involves expensive computation, leading to relatively high round and communication complexities. In this paper, we construct more efficient protocols for those protocols without relying on the bit-decomposition protocol. In the interval test protocol, checking whether a shared secret exists in the known interval is reduced to checking whether a bitwise-shared random secret exists in the appropriate interval. In the comparison protocol, comparing two shared secrets is reduced to comparing the two secrets via p/2 indirectly where p is an odd prime for an underlying linear secret sharing scheme. In the equality test protocol, checking whether two shared secrets are equal is reduced to checking whether the difference of the two secrets is zero and furthermore checking whether the difference is a zero is reduced to checking quadratice residuosity of a random secret in a probabilistic way.