From 08172f4a3c9ac0ef036c2859a3b6329dfda5c601 Mon Sep 17 00:00:00 2001 From: James Ray Date: Sat, 16 Sep 2017 11:39:11 +1000 Subject: [PATCH] Footnote clarifying meaning of low-order 11 bits --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..ee46bfe6 100644 --- a/Paper.tex +++ b/Paper.tex @@ -353,7 +353,7 @@ \subsubsection{Transaction Receipt} M(O) \equiv \bigvee_{t \in \{O_a\} \cup O_\mathbf{t}} \big( M_{3:2048}(t) \big) \end{equation} -where $M_{3:2048}$ is a specialised Bloom filter that sets three bits out of 2048, given an arbitrary byte sequence. It does this through taking the low-order 11 bits of each of the first three pairs of bytes in a Keccak-256 hash of the byte sequence. Formally: +where $M_{3:2048}$ is a specialised Bloom filter that sets three bits out of 2048, given an arbitrary byte sequence. It does this through taking the low-order 11 bits of each of the first three pairs of bytes in a Keccak-256 hash of the byte sequence./footnote{11 bits $= 2^2048$, and the low-order 11 bits is the modulo 2048 of the operand, which is in this case is "each of the first three pairs of bytes in a Keccak-256 hash of the byte sequence."} Formally: \begin{eqnarray} M_{3:2048}(\mathbf{x}: \mathbf{x} \in \mathbb{B}) & \equiv & \mathbf{y}: \mathbf{y} \in \mathbb{B}_{256} \quad \text{where:}\\ \mathbf{y} & = & (0, 0, ..., 0) \quad \text{except:}\\