Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multi party computations: past and present
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
Robustness for Free in Unconditional Multi-party Computation
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
How to Solve any Protocol Problem - An Efficiency Improvement
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Efficient Secure Multi-party Computation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application 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
Robust multiparty computation with linear communication complexity
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Scalable secure multiparty computation
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Hi-index | 0.00 |
In the Crypto'07 paper [5], Desmedt et al. studied the problem of achieving secure n -party computation over non-Abelian groups. The function to be computed is f G (x 1 ,...,x n ) : = x 1 ·...·x n where each participant P i holds an input x i from the non-commutative group G . The settings of their study are the passive adversary model, information-theoretic security and black-box group operations over G . They presented three results. The first one is that honest majority is needed to ensure security when computing f G . Second, when the number of adversary $t\leq\lceil\frac{n}{2}\rceil-1$, they reduced building such a secure protocol to a graph coloring problem and they showed that there exists a deterministic secure protocol computing f G using exponential communication complexity. Finally, Desmedt et al. turned to analyze random coloring of a graph to show the existence of a probabilistic protocol with polynomial complexity when t n /μ , in which μ is a constant less than 2.948. We call their analysis method of random coloring the counting method as it is based on the counting of the number of a specific type of random walks. This method is inspiring because, as far as we know, it is the first instance in which the theory of self-avoiding walk appears in multiparty computation. In this paper, we first give an altered exposition of their proof. This modification will allow us to adapt this method to a different lattice and reduce the communication complexity by 1/3, which is an important saving for practical implementations of the protocols. We also show the limitation of the counting method by presenting a lower bound for this technique. In particular, we will deduce that this approach would not achieve the optimal collusion resistance $\lceil \frac{n}{2} \rceil - 1$.