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
A minimal model for secure computation (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Privacy preserving auctions and mechanism design
Proceedings of the 1st ACM conference on Electronic commerce
Communications of the ACM
A Cost-Effective Pay-Per-Multiplication Comparison Method for Millionaires
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Multiparty Computation from Threshold Homomorphic Encryption
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Client/Server Tradeoffs for Online Elections
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Privacy-preserving distributed k-means clustering over arbitrarily partitioned data
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A New Protocol for Conditional Disclosure of Secrets and Its Applications
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Solving Linear Programs Using Multiparty Computation
Financial Cryptography and Data Security
Secure Multiparty Computation Goes Live
Financial Cryptography and Data Security
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient proofs that a committed number lies in an interval
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Practical and secure solutions for integer comparison
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
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
Efficient and secure comparison for on-line auctions
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Conditional encrypted mapping and comparing encrypted numbers
FC'06 Proceedings of the 10th 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
Secure equality and greater-than tests with sublinear online complexity
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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The classic problem in the field of secure computation is Yao's millionaires' problem; we consider two new protocols solving a variation of this: a number of parties, P1,...,Pn, securely hold two l- bit values, x and y - e.g. x and y could be encrypted or secret shared. They wish to obtain a bit stating whether x is greater than y using only secure arithmetic; this should be done without revealing any information, even the output should remain secret. The present setting is special in the sense that it is assumed that two specific parties, referred to as Alice and Bob, are non-colluding. Though this assumption is not satisfied in general, it clearly is for the main example of this work: two-party computation based on Paillier encryption. The first solution requires O(log(l)(κ + loglog(l))) secure arithmetic operations in O(log(l)) rounds, where κ is a correctness parameter. The second solution requires only a constant number of rounds, but increases complexity to O(√l(κ + log(l))) arithmetic operations. For the motivating setting, each arithmetic operation requires a constant number of Paillier encryptions to be exchanged between Alice and Bob. This implies that both solutions require only a sub-linear number of invocations (in the bit-length, l) of the cryptographic primitives. This does not imply sub-linear communication, though, as the size of each encryption transmitted is more than l bits.