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
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Communications of the ACM
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Efficient multi-party computation over rings
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
On secure multi-party computation in black-box groups
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Counting Method for Multi-party Computation over Non-abelian Groups
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Graph Design for Secure Multiparty Computation over Non-Abelian Groups
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On secure multi-party computation in black-box groups
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Collusion-resistant privacy-preserving data mining
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Active security in multiparty computation over black-box groups
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
| Hi-index | 0.00 |
We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function fG(x1, . . . , xn) = x1 ċ x2 . . . xn in an arbitrary finite group (G, ċ), where the input of party Pi is xi ∈ G for i = 1, . . . , n. For flexibility, we are interested in protocols for fG which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G, ċ) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing fG exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for fG based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t n/2, but has exponential communication complexity O(n(2t+1/t)2) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t n/µ for a graph-related constant µ ≤ 2.948, and has efficient communication complexity O(nt2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.