RASSS: A perfidy-aware protocol for designing trustworthy distributed systems
Robust Adaptive Secure Secret Sharing (RASSS) is a protocol for reconstructing secrets and information in distributed computing systems even in the presence of a large number of untrusted participants. Since the original Shamir's Secret Sharing scheme, there have been efforts to secure the technique against dishonest shareholders. Early on, researchers determined that the Reed-Solomon encoding property of the Shamir's share distribution equation and its decoding algorithm could tolerate cheaters up to one third of the total shareholders. However, if the number of cheaters grows beyond the error correcting capability (distance) of the Reed-Solomon codes, the reconstruction of the secret is hindered. Untrusted participants or cheaters could hide in the decoding procedure, or even frame up the honest parties. In this paper, we solve this challenge and propose a secure protocol that is no longer constrained by the limitations of the Reed-Solomon codes. As long as there are a minimum number of honest shareholders, the RASSS protocol is able to identify the cheaters and retrieve the correct secret or information in a distributed system with a probability close to 1 with less than 60% of hardware overhead. Furthermore, the adaptive nature of the protocol enables considerable hardware and timing resource savings more »
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10065460
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2017 IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFT)
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1 to 6
2. Establishing the complexity of {\em Bounded Distance Decoding} for Reed-Solomon codes is a fundamental open problem in coding theory, explicitly asked by Guruswami and Vardy (IEEE Trans. Inf. Theory, 2005). The problem is motivated by the large current gap between the regime when it is NP-hard, and the regime when it is efficiently solvable (i.e., the Johnson radius). We show the first NP-hardness results for asymptotically smaller decoding radii than the maximum likelihood decoding radius of Guruswami and Vardy. Specifically, for Reed-Solomon codes of length $N$ and dimension $K=O(N)$, we show that it is NP-hard to decode more than $N-K- c\frac{\log N}{\log\log N}$ errors (with $c>0$ an absolute constant). Moreover, we show that the problem is NP-hard under quasipolynomial-time reductions for an error amount $> N-K- c\log{N}$ (with $c>0$ an absolute constant). An alternative natural reformulation of the Bounded Distance Decoding problem for Reed-Solomon codes is as a {\em Polynomial Reconstruction} problem. In this view, our results show that it is NP-hard to decide whether there exists a degree $K$ polynomial passing through $K+ c\frac{\log N}{\log\log N}$ points from a given set of points $(a_1, b_1), (a_2, b_2)\ldots, (a_N, b_N)$. Furthermore, it is NP-hard under quasipolynomial-time reductions to decidemore »