From 2b8b183f42e36671e21c52a13d1fcec7575788e3 Mon Sep 17 00:00:00 2001 From: James Ray Date: Sat, 16 Sep 2017 11:58:49 +1000 Subject: [PATCH] to proof [sic] that a correct DAG has been used --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..891ab544 100644 --- a/Paper.tex +++ b/Paper.tex @@ -479,7 +479,7 @@ \subsubsection{Block Header Validity} \end{equation} with $(n, m) = \mathtt{PoW}(H_{\hcancel{n}}, H_n, \mathbf{d})$. -Where $H_{\hcancel{n}}$ is the new block's header $H$, but \textit{without} the nonce and mix-hash components, $\mathbf{d}$ being the current DAG, a large data set needed to compute the mix-hash, and $\mathtt{PoW}$ is the proof-of-work function (see section \ref{ch:pow}): this evaluates to an array with the first item being the mix-hash, to proof that a correct DAG has been used, and the second item being a pseudo-random number cryptographically dependent on $H$ and $\mathbf{d}$. Given an approximately uniform distribution in the range $[0, 2^{64})$, the expected time to find a solution is proportional to the difficulty, $H_d$. +Where $H_{\hcancel{n}}$ is the new block's header $H$, but \textit{without} the nonce and mix-hash components, $\mathbf{d}$ being the current DAG, a large data set needed to compute the mix-hash, and $\mathtt{PoW}$ is the proof-of-work function (see section \ref{ch:pow}): this evaluates to an array with the first item being the mix-hash, to prove that a correct DAG has been used, and the second item being a pseudo-random number cryptographically dependent on $H$ and $\mathbf{d}$. Given an approximately uniform distribution in the range $[0, 2^{64})$, the expected time to find a solution is proportional to the difficulty, $H_d$. This is the foundation of the security of the blockchain and is the fundamental reason why a malicious node cannot propagate newly created blocks that would otherwise overwrite (``rewrite'') history. Because the nonce must satisfy this requirement, and because its satisfaction depends on the contents of the block and in turn its composed transactions, creating new, valid, blocks is difficult and, over time, requires approximately the total compute power of the trustworthy portion of the mining peers.