Abstract
We devise a novel method of interactive set reconciliation for efficient block distribution. Our approach, called Graphene, couples a Bloom filter with an IBLT. We evaluate performance analytically and show that Graphene blocks are always smaller. For example, while a 17.5 KB Xtreme Thinblock can be encoded in 10 KB with Compact Blocks, the same information can be encoded in 2.6 KB with Graphene. We show in simulation that Graphene reduces traffic overhead by reducing block overhead.
Supported in part by an equipment grant from the Collaborative R&D Fund managed by the Massachusetts Technology Collaborative.
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Notes
- 1.
Actual implementations of Bloom filters and IBLTs involve several (non-continuous) ceiling functions such that we can re-write:
$$\begin{aligned} T(a) =&\left( \lceil \ln (\frac{m-n}{a})\rceil \left\lceil \frac{n\ln (\frac{m-n}{a})}{\lceil \ln (\frac{m-n}{a})\rceil \ln ^2(2)} \right\rceil \right) \frac{1}{8} + \lceil a\rceil \tau . \end{aligned}$$(2)The optimal value of Eq. 2 can be found with a simple brute force loop. We compared the value of a picked by using \(a=n/(c\tau )\) to the cost for that a from Eq. 2, for valid combinations of \(50\le n \le 2000\) and \(50\le m \le 10000\). We found that it is always within 37% of the cost of the optimal value from Eq. 2, with a median difference of 16%. In practice, a for-loop brute-force search for the lowest value of a is almost no cost to perform, and we do so in our simulations.
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Pinar Ozisik, A., Andresen, G., Bissias, G., Houmansadr, A., Levine, B. (2017). Graphene: A New Protocol for Block Propagation Using Set Reconciliation. In: Garcia-Alfaro, J., Navarro-Arribas, G., Hartenstein, H., Herrera-Joancomartí, J. (eds) Data Privacy Management, Cryptocurrencies and Blockchain Technology. DPM CBT 2017 2017. Lecture Notes in Computer Science(), vol 10436. Springer, Cham. https://doi.org/10.1007/978-3-319-67816-0_24
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