diff --git a/pdf/grandpa.bib b/pdf/grandpa.bib index 469d73a..d8039d3 100644 --- a/pdf/grandpa.bib +++ b/pdf/grandpa.bib @@ -29,7 +29,35 @@ @article{CasperCBC, title={Casper the Friendly Ghost: A “Correct-by-Construction” Blockchain Consensus Protocol}, author={Zamfir,Vlad}, - journal={}, year={2017}, url={https://github.com/ethereum/research/blob/master/papers/CasperTFG/CasperTFG.pdf} -} \ No newline at end of file +} + + +@article{BitcoinBA, + title={Anonymous byzantine consensus from moderately-hard puzzles: A model for bitcoin}, + author={Miller, Andrew and LaViola Jr, Joseph J}, + url={https://nakamotoinstitute.org/research/anonymous-byzantine-consensus/} + year={2014} +} + +@inproceedings{Discoin, + title={Bitcoin meets strong consistency}, + author={Decker, Christian and Seidel, Jochen and Wattenhofer, Roger}, + booktitle={Proceedings of the 17th International Conference on Distributed Computing and Networking}, + pages={13}, + year={2016}, + organization={ACM}, + url={https://arxiv.org/abs/1412.7935} +} + +@article{SCP, + title={SCP: A Computationally-Scalable Byzantine Consensus Protocol For Blockchains.}, + author={Luu, Loi and Narayanan, Viswesh and Baweja, Kunal and Zheng, Chaodong and Gilbert, Seth and Saxena, Prateek}, + journal={IACR Cryptology ePrint Archive}, + volume={2015}, + pages={1168}, + year={2015}, + url={https://www.weusecoins.com/assets/pdf/library/SCP%20-%20%20A%20Computationally-Scalable%20Byzantine.pdf} +} + diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex index 13f9b64..ecac951 100644 --- a/pdf/grandpa.tex +++ b/pdf/grandpa.tex @@ -522,12 +522,8 @@ Now let $C$ be a $1$-bivalent configuration. We can follow the FLP proof to show \subsection{1/5 BFT finality gadget using a common coin} - - - In this section, we will assume the asynchronous gossip network model. By the previous impossibility result, we will need to use randomness to get a finality gadget in this model. We assume that we have access to a common coin protocol. - - + For every vote, We have $n$ voters , at most $f$ of which are Byzantine and $n = 5f+1$. For a voter $v$, Let $V_{r,v}$, $C_{r,v}$ be the set of prevotes and precommits from round $r$ that $v$ has seen. \begin{enumerate}