Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Fix typo: T_t should be T_\mathbf{t} #285

Merged
merged 1 commit into from
Apr 12, 2017
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions Paper.tex
Original file line number Diff line number Diff line change
Expand Up @@ -161,7 +161,7 @@ \section{Conventions}\label{ch:conventions}

Scalars and fixed-size byte sequences (or, synonymously, arrays) are denoted with a normal lower-case letter, \eg $n$ is used in the document to denote a transaction nonce. Those with a particularly special meaning may be greek, \eg $\delta$, the number of items required on the stack for a given operation.

Arbitrary-length sequences are typically denoted as a bold lower-case letter, \eg $\mathbf{o}$ is used to denote the byte-sequence given as the output data of a message call. For particularly important values, a bold uppercase letter may be used.
Arbitrary-length sequences are typically denoted as a bold lower-case letter, \eg $\mathbf{o}$ is used to denote the byte sequence given as the output data of a message call. For particularly important values, a bold uppercase letter may be used.

Throughout, we assume scalars are positive integers and thus belong to the set $\mathbb{P}$. The set of all byte sequences is $\mathbb{B}$, formally defined in Appendix \ref{app:rlp}. If such a set of sequences is restricted to those of a particular length, it is denoted with a subscript, thus the set of all byte sequences of length $32$ is named $\mathbb{B}_{32}$ and the set of all positive integers smaller than $2^{256}$ is named $\mathbb{P}_{256}$. This is formally defined in section \ref{ch:block}.

Expand Down Expand Up @@ -282,9 +282,9 @@ \subsection{The Transaction} \label{ch:transaction}
\mathbb{P}_n = \{ P: P \in \mathbb{P} \wedge P < 2^n \}
\end{equation}

The address hash $T_\mathbf{t}$ is slightly different: it is either a 20-byte address hash or, in the case of being a contract-creation transaction (and thus formally equal to $\varnothing$), it is the RLP empty byte-series and thus the member of $\mathbb{B}_0$:
The address hash $T_\mathbf{t}$ is slightly different: it is either a 20-byte address hash or, in the case of being a contract-creation transaction (and thus formally equal to $\varnothing$), it is the RLP empty byte sequence and thus the member of $\mathbb{B}_0$:
\begin{equation}
T_t \in \begin{cases} \mathbb{B}_{20} & \text{if} \quad T_t \neq \varnothing \\
T_\mathbf{t} \in \begin{cases} \mathbb{B}_{20} & \text{if} \quad T_t \neq \varnothing \\
\mathbb{B}_{0} & \text{otherwise}\end{cases}
\end{equation}

Expand Down Expand Up @@ -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 series. 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 series. 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. 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:}\\
Expand Down