From 185781a83fae8091e29d15f31244825a34618e04 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Mon, 20 Feb 2017 18:01:32 +0100 Subject: [PATCH 01/35] Make sure that message call consumes all gas when exceptional halting happens --- Paper.tex | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1948eb98..87ba3880 100644 --- a/Paper.tex +++ b/Paper.tex @@ -774,7 +774,11 @@ \section{Message Call} \label{ch:call} \boldsymbol{\sigma} & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ \boldsymbol{\sigma}^{**} & \text{otherwise} \end{cases} \\ -(\boldsymbol{\sigma}^{**}, g', \mathbf{s}, \mathbf{o}) & \equiv & \begin{cases} +g' & \equiv & \begin{cases} +0 & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ +g^{**} & \text{otherwise} +\end{cases} \\ +(\boldsymbol{\sigma}^{**}, g^{**}, \mathbf{s}, \mathbf{o}) & \equiv & \begin{cases} \Xi_{\mathtt{ECREC}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 1 \\ \Xi_{\mathtt{SHA256}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 2 \\ \Xi_{\mathtt{RIP160}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 3 \\ From 824b7b3066509dd511ac6b5b0ee8b06eb7e8137a Mon Sep 17 00:00:00 2001 From: Gav Wood Date: Thu, 2 Mar 2017 18:22:28 +0100 Subject: [PATCH 02/35] Add alt link --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index f3e4b58f..8a1b7805 100644 --- a/README.md +++ b/README.md @@ -2,6 +2,6 @@ [![Gitter](https://badges.gitter.im/ethereum/yellowpaper.svg)](https://gitter.im/ethereum/yellowpaper?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge) -The paper comes as a single ``latex`` file ``Paper.tex``. The latest version is generally available as a PDF at https://ethereum.github.io/yellowpaper/paper.pdf . +The paper comes as a single ``latex`` file ``Paper.tex``. The latest version is generally available as a PDF at https://ethereum.github.io/yellowpaper/paper.pdf or just yellowpaper.io . In order to build, use the supplied build script (``build.sh``). Following the first time, you can use the standard `pdflatex` tools like http://latex.informatik.uni-halle.de/latex-online/latex.php for compiling/preview. It can be viewed in ``PDF`` format after building. From e5eff48a21690e7be9ab953d8258d4f80f01d6d3 Mon Sep 17 00:00:00 2001 From: Gav Wood Date: Thu, 2 Mar 2017 18:23:01 +0100 Subject: [PATCH 03/35] Provide anchor for alt link. --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 8a1b7805..fabebcb8 100644 --- a/README.md +++ b/README.md @@ -2,6 +2,6 @@ [![Gitter](https://badges.gitter.im/ethereum/yellowpaper.svg)](https://gitter.im/ethereum/yellowpaper?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge) -The paper comes as a single ``latex`` file ``Paper.tex``. The latest version is generally available as a PDF at https://ethereum.github.io/yellowpaper/paper.pdf or just yellowpaper.io . +The paper comes as a single ``latex`` file ``Paper.tex``. The latest version is generally available as a PDF at https://ethereum.github.io/yellowpaper/paper.pdf or just [yellowpaper.io](http://yellowpaper.io/) . In order to build, use the supplied build script (``build.sh``). Following the first time, you can use the standard `pdflatex` tools like http://latex.informatik.uni-halle.de/latex-online/latex.php for compiling/preview. It can be viewed in ``PDF`` format after building. From 047999c4c2348550f01bd4758bf6d9e384763e33 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Tue, 21 Mar 2017 16:24:47 +0100 Subject: [PATCH 04/35] In evaluation of \Xi, drop the fourth element and extract the remaining gas from the machine state --- Paper.tex | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Paper.tex b/Paper.tex index 11eca5e7..a7193097 100644 --- a/Paper.tex +++ b/Paper.tex @@ -850,7 +850,8 @@ \subsection{Execution Overview} The empty sequence, denoted $()$, is not equal to the empty set, denoted $\varnothing$; this is important when interpreting the output of $H$, which evaluates to $\varnothing$ when execution is to continue but a series (potentially empty) when execution should halt. \begin{eqnarray} -\Xi(\boldsymbol{\sigma}, g, I) & \equiv & X_{0,1,2,4}\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0, I)\big) \\ +\Xi(\boldsymbol{\sigma}, g, I) & \equiv & (\boldsymbol{\sigma}'\!, \boldsymbol{\mu}'_g, A, \mathbf{o}) \\ +(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, I'\!, \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ \boldsymbol{\mu}_g & \equiv & g \\ \boldsymbol{\mu}_{pc} & \equiv & 0 \\ \boldsymbol{\mu}_\mathbf{m} & \equiv & (0, 0, ...) \\ @@ -871,7 +872,7 @@ \subsection{Execution Overview} (a, b, c) \cdot d & \equiv & (a, b, c, d) \end{eqnarray} -Note that we must drop the fourth value in the tuple returned by $X$ to correctly evaluate $\Xi$, hence the subscript $X_{0,1,2,4}$. +Note that, when we evaluate $\Xi$, we drop the fourth element $I'$ and extract the remaining gas $\boldsymbol{\mu}'_g$ from the resultant machine state $\boldsymbol{\mu}'$. $X$ is thus cycled (recursively here, but implementations are generally expected to use a simple iterative loop) until either $Z$ becomes true indicating that the present state is exceptional and that the machine must be halted and any changes discarded or until $H$ becomes a series (rather than the empty set) indicating that the machine has reached a controlled halt. From 1862248a784edb44ca5ab1cce60b3797c2154cbc Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Tue, 21 Mar 2017 16:25:26 +0100 Subject: [PATCH 05/35] Instead of concatenating a triple with an element, now we need to concatenate a quadruple with an element --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index a7193097..07d327ef 100644 --- a/Paper.tex +++ b/Paper.tex @@ -869,7 +869,7 @@ \subsection{Execution Overview} where \begin{eqnarray} \mathbf{o} & \equiv & H(\boldsymbol{\mu}, I) \\ -(a, b, c) \cdot d & \equiv & (a, b, c, d) +(a, b, c, d) \cdot e & \equiv & (a, b, c, d, e) \end{eqnarray} Note that, when we evaluate $\Xi$, we drop the fourth element $I'$ and extract the remaining gas $\boldsymbol{\mu}'_g$ from the resultant machine state $\boldsymbol{\mu}'$. From 8ba2906dab43f3911b7496b749ab4af345a2ba8a Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Thu, 23 Mar 2017 10:27:49 +0100 Subject: [PATCH 06/35] Make sure only one version of the protocol is described --- Paper.tex | 35 +++++++---------------------------- 1 file changed, 7 insertions(+), 28 deletions(-) diff --git a/Paper.tex b/Paper.tex index 11eca5e7..4dceed5d 100644 --- a/Paper.tex +++ b/Paper.tex @@ -33,8 +33,6 @@ \definecolor{lightyellow}{rgb}{1,0.98,0.9} \definecolor{lightpink}{rgb}{1,0.94,0.95} -\newcommand{\firsthomesteadblock}{\ensuremath{N_H}} - \DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} \newcommand*\eg{e.g.\@\xspace} \newcommand*\Eg{e.g.\@\xspace} @@ -147,6 +145,8 @@ \subsection{Which History?} The scheme we use in order to generate consensus is a simplified version of the GHOST protocol introduced by \cite{cryptoeprint:2013:881}. This process is described in detail in section \ref{ch:ghost}. +Sometimes, a path follows a new protocol from a particular height. This document describes one version of the protocol. In order to follow back the history of a path, one might need to reference multiple versions of this document. + \section{Conventions}\label{ch:conventions} I use a number of typographical conventions for the formal notation, some of which are quite particular to the present work: @@ -233,14 +233,6 @@ \subsection{World State} \label{ch:state} \quad v(x) \equiv x_n \in \mathbb{P}_{256} \wedge x_b \in \mathbb{P}_{256} \wedge x_s \in \mathbb{B}_{32} \wedge x_c \in \mathbb{B}_{32} \end{equation} -\subsection{Homestead} \label{ch:homestead} - -A significant block number for compatibility with the public network is the block marking the transition between the {\it Frontier} and {\it Homestead} phases of the platform, which we denote with the symbol \firsthomesteadblock, defined thus -\begin{equation} -\firsthomesteadblock \equiv 1,\! 150,\! 000 -\end{equation} -The protocol was upgraded at this block, so this symbol appears in some equations to account for the changes. - \subsection{The Transaction} \label{ch:transaction} A transaction (formally, $T$) is a single cryptographically-signed instruction constructed by an actor externally to the scope of Ethereum. While it is assumed that the ultimate external actor will be human in nature, software tools will be used in its construction and dissemination\footnote{Notably, such `tools' could ultimately become so causally removed from their human-based initiation---or humans may become so causally-neutral---that there could be a point at which they rightly be considered autonomous agents. \eg contracts may offer bounties to humans for being sent transactions to initiate their execution.}. There are two types of transactions: those which result in message calls and those which result in the creation of new accounts with associated code (known informally as `contract creation'). Both types specify a number of common fields: @@ -442,7 +434,6 @@ \subsubsection{Block Header Validity} \end{equation} \newcommand{\mindifficulty}{D_0} -\newcommand{\frontiermod}{\ensuremath{\varsigma_1}} \newcommand{\homesteadmod}{\ensuremath{\varsigma_2}} \newcommand{\expdiffsymb}{\ensuremath{\epsilon}} \newcommand{\diffadjustment}{x} @@ -451,7 +442,6 @@ \subsubsection{Block Header Validity} \begin{equation} D(H) \equiv \begin{dcases} \mindifficulty & \text{if} \quad H_i = 0\\ -\text{max}\!\left(\mindifficulty, {P(H)_H}_d + \diffadjustment\times\frontiermod + \expdiffsymb \right) & \text{if} \quad H_i<\firsthomesteadblock\\ \text{max}\!\left(\mindifficulty, {P(H)_H}_d + \diffadjustment\times\homesteadmod + \expdiffsymb \right) & \text{otherwise}\\ \end{dcases} \end{equation} @@ -463,12 +453,6 @@ \subsubsection{Block Header Validity} \diffadjustment \equiv \left\lfloor\frac{{P(H)_H}_d}{2048}\right\rfloor \end{equation} \begin{equation} -\frontiermod \equiv \begin{cases} -1 & \text{if} \quad H_s < {P(H)_H}_s + 13 \\ --1 & \text{otherwise} \\ -\end{cases} -\end{equation} -\begin{equation} \homesteadmod \equiv \text{max}\left( 1 - \left\lfloor\frac{H_s - {P(H)_H}_s}{10}\right\rfloor, -99 \right) \end{equation} \begin{equation} @@ -561,11 +545,11 @@ \subsection{Execution} We define intrinsic gas $g_0$, the amount of gas this transaction requires to be paid prior to execution, as follows: \begin{align} g_0 \equiv {} & \sum_{i \in T_\mathbf{i}, T_\mathbf{d}} \begin{cases} G_{txdatazero} & \text{if} \quad i = 0 \\ G_{txdatanonzero} & \text{otherwise} \end{cases} \\ -{} & + \begin{cases} G_\text{txcreate} & \text{if} \quad T_t = \varnothing \wedge H_i \geq \firsthomesteadblock \\ 0 & \text{otherwise} \end{cases} \\ +{} & + \begin{cases} G_\text{txcreate} & \text{if} \quad T_t = \varnothing \\ 0 & \text{otherwise} \end{cases} \\ {} & + G_{transaction} \end{align} -where $T_\mathbf{i},T_\mathbf{d}$ means the series of bytes of the transaction's associated data and initialisation EVM-code, depending on whether the transaction is for contract-creation or message-call. $G_\text{txcreate}$ is added if the transaction is contract-creating, but not if a result of EVM-code or before the {\it Homestead transition}. $G$ is fully defined in Appendix \ref{app:fees}. +where $T_\mathbf{i},T_\mathbf{d}$ means the series of bytes of the transaction's associated data and initialisation EVM-code, depending on whether the transaction is for contract-creation or message-call. $G_\text{txcreate}$ is added if the transaction is contract-creating, but not if a result of EVM-code. $G$ is fully defined in Appendix \ref{app:fees}. %todo Explain g_d reason? @@ -712,12 +696,10 @@ \section{Contract Creation} \label{ch:create} \begin{align} \quad g' &\equiv \begin{cases} 0 & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ -g^{**} & \text{if} \quad g^{**} Date: Thu, 23 Mar 2017 13:24:58 +0100 Subject: [PATCH 07/35] Use bold font for \mu_s as in other occurrences. --- Paper.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Paper.tex b/Paper.tex index 11eca5e7..722845c1 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1762,12 +1762,12 @@ \subsection{Instruction Set} &&&& This is gas price specified by the originating transaction.\\ \midrule 0x3b & {\small EXTCODESIZE} & 1 & 1 & Get size of an account's code. \\ -&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \lVert \boldsymbol{\sigma}[\boldsymbol{\mu}_s[0] \mod 2^{160}]_c \rVert$ \\ +&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \lVert \boldsymbol{\sigma}[\boldsymbol{\mu}_\mathbf{s}[0] \mod 2^{160}]_c \rVert$ \\ \midrule 0x3c & {\small EXTCODECOPY} & 4 & 0 & Copy an account's code to memory. \\ &&&& $\forall_{i \in \{ 0 \dots \boldsymbol{\mu}_\mathbf{s}[3] - 1\} } \boldsymbol{\mu}'_\mathbf{m}[\boldsymbol{\mu}_\mathbf{s}[1] + i ] \equiv \begin{cases} \mathbf{c}[\boldsymbol{\mu}_\mathbf{s}[2] + i] & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] + i < \lVert \mathbf{c} \rVert \\ \text{\small STOP} & \text{otherwise} \end{cases}$\\ -&&&& where $\mathbf{c} \equiv \boldsymbol{\sigma}[\boldsymbol{\mu}_s[0] \mod 2^{160}]_c$ \\ +&&&& where $\mathbf{c} \equiv \boldsymbol{\sigma}[\boldsymbol{\mu}_\mathbf{s}[0] \mod 2^{160}]_c$ \\ &&&& $\boldsymbol{\mu}'_i \equiv M(\boldsymbol{\mu}_i, \boldsymbol{\mu}_\mathbf{s}[1], \boldsymbol{\mu}_\mathbf{s}[3])$ \\ &&&& The additions in $\boldsymbol{\mu}_\mathbf{s}[2] + i$ are not subject to the $2^{256}$ modulo. \\ \bottomrule From b454e16cc2d3ec1f673b8b11c3793a48dac1a6c8 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Thu, 23 Mar 2017 14:44:44 +0100 Subject: [PATCH 08/35] Zero-th power of zero Fixes #257 --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 11eca5e7..c522d6a6 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1615,7 +1615,7 @@ \subsection{Instruction Set} \begin{tabular*}{\columnwidth}[h]{rlrrl} \toprule \multicolumn{5}{c}{\textbf{0s: Stop and Arithmetic Operations}} \\ -\multicolumn{5}{l}{All arithmetic is modulo $2^{256}$ unless otherwise noted.} \vspace{5pt} \\ +\multicolumn{5}{l}{All arithmetic is modulo $2^{256}$ unless otherwise noted. The zero-th power of zero $0^0$ is defined to be one.} \vspace{5pt} \\ \textbf{Value} & \textbf{Mnemonic} & $\delta$ & $\alpha$ & \textbf{Description} \vspace{5pt} \\ 0x00 & {\small STOP} & 0 & 0 & Halts execution. \\ \midrule From a4e17758383f30c456091254404eeb63f7d33351 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Fri, 24 Mar 2017 19:43:16 +0100 Subject: [PATCH 09/35] Replace a broken link Fixes #247 --- Biblio.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Biblio.bib b/Biblio.bib index 4314259f..f3c0ee9c 100644 --- a/Biblio.bib +++ b/Biblio.bib @@ -102,7 +102,7 @@ @InProceedings{miller1997future } @article{buterin2013ethereum, - url = {{http://ethereum.org/ethereum.html}}, + url = {{https://github.com/ethereum/wiki/wiki/White-Paper}}, author = {Vitalik Buterin}, title = {{Ethereum: A Next-Generation Smart Contract and Decentralized Application Platform}}, year = {{2013}}, From bb1114e263483c7f3e6e1be46acd5a7f4ce34a20 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Thorkil=20V=C3=A6rge?= Date: Sun, 26 Mar 2017 13:19:28 +0200 Subject: [PATCH 10/35] Fix stack index error in SELFDESTRUCT SELFDESTRUCT sends balance to mu_s[0], not to mu_s[1]. --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 11eca5e7..76f7160e 100644 --- a/Paper.tex +++ b/Paper.tex @@ -2037,7 +2037,7 @@ \subsection{Instruction Set} 0 & \text{otherwise} \end{cases}$ \\ &&&& $C_{\text{\tiny SELFDESTRUCT}}(\boldsymbol{\sigma}, \boldsymbol{\mu}) \equiv G_{selfdestruct} + \begin{cases} -G_{newaccount} & \text{if} \quad \boldsymbol{\sigma}[\boldsymbol{\mu}_\mathbf{s}[1] \mod 2^{160}] = \varnothing \\ +G_{newaccount} & \text{if} \quad \boldsymbol{\sigma}[\boldsymbol{\mu}_\mathbf{s}[0] \mod 2^{160}] = \varnothing \\ 0 & \text{otherwise} \end{cases}$ \\ \bottomrule From 56475f1d303252cd6bfd3e8839efdd85091b64b6 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Thu, 30 Mar 2017 12:52:42 +0200 Subject: [PATCH 11/35] Turn an unused I' into underscore --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 07d327ef..25f85d33 100644 --- a/Paper.tex +++ b/Paper.tex @@ -851,7 +851,7 @@ \subsection{Execution Overview} The empty sequence, denoted $()$, is not equal to the empty set, denoted $\varnothing$; this is important when interpreting the output of $H$, which evaluates to $\varnothing$ when execution is to continue but a series (potentially empty) when execution should halt. \begin{eqnarray} \Xi(\boldsymbol{\sigma}, g, I) & \equiv & (\boldsymbol{\sigma}'\!, \boldsymbol{\mu}'_g, A, \mathbf{o}) \\ -(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, I'\!, \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ +(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, \_, \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ \boldsymbol{\mu}_g & \equiv & g \\ \boldsymbol{\mu}_{pc} & \equiv & 0 \\ \boldsymbol{\mu}_\mathbf{m} & \equiv & (0, 0, ...) \\ From 95b86e524b58bfba2ea09ff1c1456763804fb20e Mon Sep 17 00:00:00 2001 From: Gav Wood Date: Thu, 30 Mar 2017 13:06:17 +0200 Subject: [PATCH 12/35] underscore becomes standard ellision operator --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 25f85d33..cbe8e448 100644 --- a/Paper.tex +++ b/Paper.tex @@ -851,7 +851,7 @@ \subsection{Execution Overview} The empty sequence, denoted $()$, is not equal to the empty set, denoted $\varnothing$; this is important when interpreting the output of $H$, which evaluates to $\varnothing$ when execution is to continue but a series (potentially empty) when execution should halt. \begin{eqnarray} \Xi(\boldsymbol{\sigma}, g, I) & \equiv & (\boldsymbol{\sigma}'\!, \boldsymbol{\mu}'_g, A, \mathbf{o}) \\ -(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, \_, \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ +(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, ..., \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ \boldsymbol{\mu}_g & \equiv & g \\ \boldsymbol{\mu}_{pc} & \equiv & 0 \\ \boldsymbol{\mu}_\mathbf{m} & \equiv & (0, 0, ...) \\ From 1f57dc57c510869e6cffed2d4c6f54daf1a08743 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Fri, 25 Nov 2016 11:37:36 +0100 Subject: [PATCH 13/35] Update the fee schedule following EIP 160 https://github.com/ethereum/EIPs/issues/160 --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 7d3311ad..883d54c1 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1478,7 +1478,7 @@ \section{Fee Schedule}\label{app:fees} $G_{callstipend}$ & 2300 & A stipend for the called contract subtracted from $G_{callvalue}$ for a non-zero value transfer. \\ $G_{newaccount}$ & 25000 & Paid for a {\small CALL} or {\small SELFDESTRUCT} operation which creates an account. \\ $G_{exp}$ & 10 & Partial payment for an {\small EXP} operation. \\ -$G_{expbyte}$ & 10 & Partial payment when multiplied by $\lceil\log_{256}(exponent)\rceil$ for the {\small EXP} operation. \\ +$G_{expbyte}$ & 50 & Partial payment when multiplied by $\lceil\log_{256}(exponent)\rceil$ for the {\small EXP} operation. \\ $G_{memory}$ & 3 & Paid for every additional word when expanding memory. \\ $G_\text{txcreate}$ & 32000 & Paid by all contract-creating transactions after the {\it Homestead transition}.\\ $G_{txdatazero}$ & 4 & Paid for every zero byte of data or code for a transaction. \\ From 722b87df973329d47a7c63f6b799921e794e425a Mon Sep 17 00:00:00 2001 From: Ian Sweet Date: Sat, 1 Apr 2017 15:06:46 -0400 Subject: [PATCH 14/35] Fix remaining issues from PR #167, namely equation 105 --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 7d3311ad..6bf4302c 100644 --- a/Paper.tex +++ b/Paper.tex @@ -755,7 +755,7 @@ \section{Message Call} \label{ch:call} 0 & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ g^{**} & \text{otherwise} \end{cases} \\ -(\boldsymbol{\sigma}^{**}, g^{**}, \mathbf{s}, \mathbf{o}) & \equiv & \begin{cases} +\qquad (\boldsymbol{\sigma}^{**}, g^{**}, A, \mathbf{o}) & \equiv & \begin{cases} \Xi_{\mathtt{ECREC}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 1 \\ \Xi_{\mathtt{SHA256}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 2 \\ \Xi_{\mathtt{RIP160}}(\boldsymbol{\sigma}_1, g, I) & \text{if} \quad r = 3 \\ From 672cf55be6f4e1b536beb404258c725d60d962b8 Mon Sep 17 00:00:00 2001 From: Justin Date: Mon, 10 Apr 2017 12:33:33 +0100 Subject: [PATCH 15/35] Fix typo: T_t should be T_\mathbf{t} Also cleanup nomenclature around byte sequences. --- Paper.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Paper.tex b/Paper.tex index 7d3311ad..06dfadab 100644 --- a/Paper.tex +++ b/Paper.tex @@ -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}. @@ -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} @@ -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:}\\ From 026e7efeabaed97788e0dc810f0ab60674bab2b6 Mon Sep 17 00:00:00 2001 From: Justin Date: Wed, 12 Apr 2017 11:19:02 +0100 Subject: [PATCH 16/35] Fix typo (the => that) --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 6bf4302c..ba81b803 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1274,7 +1274,7 @@ \section{Hex-Prefix Encoding}\label{app:hexprefix} Thus the high nibble of the first byte contains two flags; the lowest bit encoding the oddness of the length and the second-lowest encoding the flag $t$. The low nibble of the first byte is zero in the case of an even number of nibbles and the first nibble in the case of an odd number. All remaining nibbles (now an even number) fit properly into the remaining bytes. \section{Modified Merkle Patricia Tree}\label{app:trie} -The modified Merkle Patricia tree (trie) provides a persistent data structure to map between arbitrary-length binary data (byte arrays). It is defined in terms of a mutable data structure to map between 256-bit binary fragments and arbitrary-length binary data, typically implemented as a database. The core of the trie, and its sole requirement in terms of the protocol specification is to provide a single value that identifies a given set of key-value pairs, which may be either a 32 byte sequence or the empty byte sequence. It is left as an implementation consideration to store and maintain the structure of the trie in a manner the allows effective and efficient realisation of the protocol. +The modified Merkle Patricia tree (trie) provides a persistent data structure to map between arbitrary-length binary data (byte arrays). It is defined in terms of a mutable data structure to map between 256-bit binary fragments and arbitrary-length binary data, typically implemented as a database. The core of the trie, and its sole requirement in terms of the protocol specification is to provide a single value that identifies a given set of key-value pairs, which may be either a 32 byte sequence or the empty byte sequence. It is left as an implementation consideration to store and maintain the structure of the trie in a manner that allows effective and efficient realisation of the protocol. Formally, we assume the input value $\mathfrak{I}$, a set containing pairs of byte sequences: \begin{equation} From 2fc5b8288b269ab26f165bfdd86e22786de8b1e1 Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Fri, 25 Nov 2016 12:12:27 +0100 Subject: [PATCH 17/35] EIP170: max code size --- Paper.tex | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/Paper.tex b/Paper.tex index 6bf4302c..50ac2d1b 100644 --- a/Paper.tex +++ b/Paper.tex @@ -695,14 +695,16 @@ \section{Contract Creation} \label{ch:create} \begin{align} \quad g' &\equiv \begin{cases} -0 & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ +0 & \text{if} \quad F \\ g^{**} - c & \text{otherwise} \\ \end{cases} \\ \quad \boldsymbol{\sigma}' &\equiv \begin{cases} -\boldsymbol{\sigma} & \text{if} \quad \boldsymbol{\sigma}^{**} = \varnothing \\ +\boldsymbol{\sigma} & \text{if} \quad F \\ \boldsymbol{\sigma}^{**} \quad \text{except:} & \\ \quad\boldsymbol{\sigma}'[a]_c = \texttt{\small KEC}(\mathbf{o}) & \text{otherwise} -\end{cases} +\end{cases} \\ +\nonumber \text{where} \\ +F &\equiv \big(\boldsymbol{\sigma}^{**} = \varnothing \ \vee\ g^{**} < c \ \vee\ |\mathbf{o}| \ge 24576\big) \end{align} The exception in the determination of $\boldsymbol{\sigma}'$ dictates that $\mathbf{o}$, the resultant byte sequence from the execution of the initialisation code, specifies the final body code for the newly-created account. From 36d95c1040065bdac8f4a2d874f2adf2790d8abb Mon Sep 17 00:00:00 2001 From: Yoichi Hirai Date: Wed, 21 Jun 2017 16:30:39 +0200 Subject: [PATCH 18/35] An abbreviation abbreviates but does not imply --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 37c1b196..21ee68f8 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1934,7 +1934,7 @@ \subsection{Instruction Set} &&&& $\mathbf{i} \equiv \boldsymbol{\mu}_\mathbf{m}[ \boldsymbol{\mu}_\mathbf{s}[1] \dots (\boldsymbol{\mu}_\mathbf{s}[1] + \boldsymbol{\mu}_\mathbf{s}[2] - 1) ]$ \\ &&&& $(\boldsymbol{\sigma}', \boldsymbol{\mu}'_g, A^+) \equiv \begin{cases}\Lambda(\boldsymbol{\sigma}^*, I_a, I_o, L(\boldsymbol{\mu}_g), I_p, \boldsymbol{\mu}_\mathbf{s}[0], \mathbf{i}, I_e + 1) & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[0] \leqslant \boldsymbol{\sigma}[I_a]_b \;\wedge\; I_e < 1024\\ \big(\boldsymbol{\sigma}, \boldsymbol{\mu}_g, \varnothing\big) & \text{otherwise} \end{cases}$ \\ &&&& $\boldsymbol{\sigma}^* \equiv \boldsymbol{\sigma} \quad \text{except} \quad \boldsymbol{\sigma}^*[I_a]_n = \boldsymbol{\sigma}[I_a]_n + 1$ \\ -&&&& $A' \equiv A \Cup A^+$ which implies: $A'_\mathbf{s} \equiv A_\mathbf{s} \cup A^+_\mathbf{s} \quad \wedge \quad A'_\mathbf{l} \equiv A_\mathbf{l} \cdot A^+_\mathbf{l} \quad \wedge \quad A'_\mathbf{r} \equiv A_\mathbf{r} + A^+_\mathbf{r}$ \\ +&&&& $A' \equiv A \Cup A^+$ which abbreviates: $A'_\mathbf{s} \equiv A_\mathbf{s} \cup A^+_\mathbf{s} \quad \wedge \quad A'_\mathbf{l} \equiv A_\mathbf{l} \cdot A^+_\mathbf{l} \quad \wedge \quad A'_\mathbf{r} \equiv A_\mathbf{r} + A^+_\mathbf{r}$ \\ &&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv x$ \\ &&&& where $x=0$ if the code execution for this operation failed due to an exceptional halting \\ &&&& $Z(\boldsymbol{\sigma}^*, \boldsymbol{\mu}, I) = \top$ or $I_e = 1024$ \\ From 8bc426ca1e30cfdbe65307a10f4378b8612e5075 Mon Sep 17 00:00:00 2001 From: Gav Wood Date: Wed, 5 Jul 2017 12:02:36 +0200 Subject: [PATCH 19/35] Fix off-by-one. Should be strictly greater than the limit, the limit itself is acceptable. --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 50ac2d1b..a9175e3f 100644 --- a/Paper.tex +++ b/Paper.tex @@ -704,7 +704,7 @@ \section{Contract Creation} \label{ch:create} \quad\boldsymbol{\sigma}'[a]_c = \texttt{\small KEC}(\mathbf{o}) & \text{otherwise} \end{cases} \\ \nonumber \text{where} \\ -F &\equiv \big(\boldsymbol{\sigma}^{**} = \varnothing \ \vee\ g^{**} < c \ \vee\ |\mathbf{o}| \ge 24576\big) +F &\equiv \big(\boldsymbol{\sigma}^{**} = \varnothing \ \vee\ g^{**} < c \ \vee\ |\mathbf{o}| \gt 24576\big) \end{align} The exception in the determination of $\boldsymbol{\sigma}'$ dictates that $\mathbf{o}$, the resultant byte sequence from the execution of the initialisation code, specifies the final body code for the newly-created account. From f915d074f610b9ba81d00bdf7648cdbd490f778e Mon Sep 17 00:00:00 2001 From: Gav Wood Date: Wed, 5 Jul 2017 12:08:57 +0200 Subject: [PATCH 20/35] Use actual latex. --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index a9175e3f..f5d86e31 100644 --- a/Paper.tex +++ b/Paper.tex @@ -704,7 +704,7 @@ \section{Contract Creation} \label{ch:create} \quad\boldsymbol{\sigma}'[a]_c = \texttt{\small KEC}(\mathbf{o}) & \text{otherwise} \end{cases} \\ \nonumber \text{where} \\ -F &\equiv \big(\boldsymbol{\sigma}^{**} = \varnothing \ \vee\ g^{**} < c \ \vee\ |\mathbf{o}| \gt 24576\big) +F &\equiv \big(\boldsymbol{\sigma}^{**} = \varnothing \ \vee\ g^{**} < c \ \vee\ |\mathbf{o}| > 24576\big) \end{align} The exception in the determination of $\boldsymbol{\sigma}'$ dictates that $\mathbf{o}$, the resultant byte sequence from the execution of the initialisation code, specifies the final body code for the newly-created account. From a75b5489a3a2e676ecb87e1c3cddd3205ca2c523 Mon Sep 17 00:00:00 2001 From: likang Date: Mon, 7 Aug 2017 18:04:08 +0800 Subject: [PATCH 21/35] modify (136) --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 8b6ce813..1a6bbaa4 100644 --- a/Paper.tex +++ b/Paper.tex @@ -937,7 +937,7 @@ \subsection{The Execution Cycle} O\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \equiv & (\boldsymbol{\sigma}', \boldsymbol{\mu}', A', I) \\ \Delta & \equiv & \mathbf{\alpha}_w - \mathbf{\delta}_w \\ \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert & \equiv & \lVert\boldsymbol{\mu}_\mathbf{s}\rVert + \Delta \\ -\quad \forall x \in [\mathbf{\alpha}_w, \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert): \boldsymbol{\mu}'_\mathbf{s}[x] & \equiv & \boldsymbol{\mu}_\mathbf{s}[x+\Delta] +\quad \forall x \in [\mathbf{\alpha}_w, \lVert\boldsymbol{\mu}'_\mathbf{s}\rVert): \boldsymbol{\mu}'_\mathbf{s}[x] & \equiv & \boldsymbol{\mu}_\mathbf{s}[x-\Delta] \end{eqnarray} The gas is reduced by the instruction's gas cost and for most instructions, the program counter increments on each cycle, for the three exceptions, we assume a function $J$, subscripted by one of two instructions, which evaluates to the according value: From 780f647208ad76fd228549bb25d09a3c50e33e1a Mon Sep 17 00:00:00 2001 From: Peng Wang Date: Wed, 9 Aug 2017 20:44:38 -0400 Subject: [PATCH 22/35] fixed a typo in equation (118): (\sigma, \mu', ...) -> (\sigma', \mu', ...) --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..f69b21f9 100644 --- a/Paper.tex +++ b/Paper.tex @@ -835,7 +835,7 @@ \subsection{Execution Overview} The empty sequence, denoted $()$, is not equal to the empty set, denoted $\varnothing$; this is important when interpreting the output of $H$, which evaluates to $\varnothing$ when execution is to continue but a series (potentially empty) when execution should halt. \begin{eqnarray} \Xi(\boldsymbol{\sigma}, g, I) & \equiv & (\boldsymbol{\sigma}'\!, \boldsymbol{\mu}'_g, A, \mathbf{o}) \\ -(\boldsymbol{\sigma}, \boldsymbol{\mu}'\!, A, ..., \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ +(\boldsymbol{\sigma}', \boldsymbol{\mu}'\!, A, ..., \mathbf{o}) & \equiv & X\big((\boldsymbol{\sigma}, \boldsymbol{\mu}, A^0\!, I)\big) \\ \boldsymbol{\mu}_g & \equiv & g \\ \boldsymbol{\mu}_{pc} & \equiv & 0 \\ \boldsymbol{\mu}_\mathbf{m} & \equiv & (0, 0, ...) \\ From 07fa9c35dd2eca70877addef208b33fed681bac7 Mon Sep 17 00:00:00 2001 From: midinpa Date: Wed, 6 Sep 2017 16:10:16 +0900 Subject: [PATCH 23/35] typo fixed (then => than) --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..e458bb7c 100644 --- a/Paper.tex +++ b/Paper.tex @@ -888,7 +888,7 @@ \subsubsection{Exceptional Halting} \end{array} \end{equation} -This states that the execution is in an exceptional halting state if there is insufficient gas, if the instruction is invalid (and therefore its $\delta$ subscript is undefined), if there are insufficient stack items, if a {\small JUMP}/{\small JUMPI} destination is invalid or the new stack size would be larger then 1024. The astute reader will realise that this implies that no instruction can, through its execution, cause an exceptional halt. +This states that the execution is in an exceptional halting state if there is insufficient gas, if the instruction is invalid (and therefore its $\delta$ subscript is undefined), if there are insufficient stack items, if a {\small JUMP}/{\small JUMPI} destination is invalid or the new stack size would be larger than 1024. The astute reader will realise that this implies that no instruction can, through its execution, cause an exceptional halt. \subsubsection{Jump Destination Validity} From 1ac4209f480b9afedd998afdbf7e77accd48026a Mon Sep 17 00:00:00 2001 From: 4000D Date: Tue, 12 Sep 2017 16:55:05 +0900 Subject: [PATCH 24/35] use parentheses for multiply --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..be8ff793 100644 --- a/Paper.tex +++ b/Paper.tex @@ -2078,7 +2078,7 @@ \subsection{Size of dataset and cache} \begin{equation} E_{prime}(x, y) = \begin{cases} x & \text{if} \quad x / y \in \mathbb{P} \\ -E_{prime}(x - 1 \cdot y, y) & \text{otherwise} +E_{prime}((x - 1) \cdot y, y) & \text{otherwise} \end{cases} \end{equation} \subsection{Dataset generation} From 560e7bf09b90ee4cb3da253af8b085c185104991 Mon Sep 17 00:00:00 2001 From: 4000D Date: Tue, 12 Sep 2017 16:55:33 +0900 Subject: [PATCH 25/35] account state order fixed --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index be8ff793..0e57e314 100644 --- a/Paper.tex +++ b/Paper.tex @@ -741,7 +741,7 @@ \section{Message Call} \label{ch:call} \end{equation} \begin{equation} \begin{cases} -\boldsymbol{\sigma}_1'[r] \equiv (v, 0, \mathtt{\tiny KEC}(()), \mathtt{\tiny TRIE}(\varnothing)) & \text{if} \quad \boldsymbol{\sigma}[r] = \varnothing \\ +\boldsymbol{\sigma}_1'[r] \equiv (0, v, \mathtt{\tiny TRIE}(\varnothing), \mathtt{\tiny KEC}(())) & \text{if} \quad \boldsymbol{\sigma}[r] = \varnothing \\ \boldsymbol{\sigma}_1'[r]_b \equiv \boldsymbol{\sigma}[r]_b + v & \text{otherwise} \end{cases} \end{equation} From 75a8f2e1a3306707e7438095f631f7edc1aafea5 Mon Sep 17 00:00:00 2001 From: 4000D Date: Wed, 13 Sep 2017 15:29:00 +0900 Subject: [PATCH 26/35] fix typo --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 0e57e314..549ebab7 100644 --- a/Paper.tex +++ b/Paper.tex @@ -2082,7 +2082,7 @@ \subsection{Size of dataset and cache} \end{cases} \end{equation} \subsection{Dataset generation} -In order the generate the dataset we need the cache $\mathbf{c}$, which is an array of bytes. It depends on the cache size $c_{size}$ and the seed hash $\mathbf{s} \in \mathbb{B}_{32}$. +In order to generate the dataset we need the cache $\mathbf{c}$, which is an array of bytes. It depends on the cache size $c_{size}$ and the seed hash $\mathbf{s} \in \mathbb{B}_{32}$. \subsubsection{Seed hash} The seed hash is different for every epoch. For the first epoch it is the Keccak-256 hash of a series of 32 bytes of zeros. For every other epoch it is always the Keccak-256 hash of the previous seed hash: \begin{equation} From c243d01d07ceeb99fed8bc046551dc417a7b02a9 Mon Sep 17 00:00:00 2001 From: Lane Rettig Date: Thu, 21 Sep 2017 14:05:29 -0400 Subject: [PATCH 27/35] fix small grammatical typo --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..76d7501f 100644 --- a/Paper.tex +++ b/Paper.tex @@ -817,7 +817,7 @@ \subsection{Execution Environment} \item $I_e$, the depth of the present message-call or contract-creation (i.e. the number of {\small CALL}s or {\small CREATE}s being executed at present). \end{itemize} -The execution model defines the function $\Xi$, which can compute the resultant state $\boldsymbol{\sigma}'$, the remaining gas $g'$, the accrued substate $A$ and the resultant output, $\mathbf{o}$, given these definitions. For the present context, we will defined it as: +The execution model defines the function $\Xi$, which can compute the resultant state $\boldsymbol{\sigma}'$, the remaining gas $g'$, the accrued substate $A$ and the resultant output, $\mathbf{o}$, given these definitions. For the present context, we will define it as: \begin{equation} (\boldsymbol{\sigma}', g', A, \mathbf{o}) \equiv \Xi(\boldsymbol{\sigma}, g, I) \end{equation} From 89d7b91f1fc44e75dde27e4c52ecc31644830ed2 Mon Sep 17 00:00:00 2001 From: Ayrat Badykov Date: Thu, 19 Oct 2017 11:59:06 +0300 Subject: [PATCH 28/35] fix ommer reference --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..a4ba01d7 100644 --- a/Paper.tex +++ b/Paper.tex @@ -290,7 +290,7 @@ \subsection{The Transaction} \label{ch:transaction} \subsection{The Block} \label{ch:block} -The block in Ethereum is the collection of relevant pieces of information (known as the block \textit{header}), $H$, together with information corresponding to the comprised transactions, $\mathbf{T}$, and a set of other block headers $\mathbf{U}$ that are known to have a parent equal to the present block's parent's parent (such blocks are known as \textit{ommers}\footnote{\textit{ommer} is the most prevalent (not saying much) gender-neutral term to mean ``sibling of parent''; see \url{http://nonbinary.org/wiki/Gender_neutral_language#Family_Terms}}). The block header contains several pieces of information: +The block in Ethereum is the collection of relevant pieces of information (known as the block \textit{header}), $H$, together with information corresponding to the comprised transactions, $\mathbf{T}$, and a set of other block headers $\mathbf{U}$ that are known to have a parent equal to the present block's parent's parent (such blocks are known as \textit{ommers}\footnote{\textit{ommer} is the most prevalent (not saying much) gender-neutral term to mean ``sibling of parent''; see \url{https://nonbinary.miraheze.org/wiki/Gender_neutral_language#Aunt.2FUncle}}). The block header contains several pieces of information: %\textit{TODO: Introduce logs} From 7fc31a65bdc3f50988d9b72f11487218b4b73b0d Mon Sep 17 00:00:00 2001 From: Nadir Akhtar Date: Thu, 26 Oct 2017 19:41:59 -0700 Subject: [PATCH 29/35] Changed one " to `` --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..0cc221ca 100644 --- a/Paper.tex +++ b/Paper.tex @@ -2160,7 +2160,7 @@ \subsubsection{Full dataset calculation} \label{dataset} \end{equation} \subsection{Proof-of-work function} -Essentially, we maintain a "mix" $J_{mixbytes}$ bytes wide, and repeatedly sequentially fetch $J_{mixbytes}$ bytes from the full dataset and use the $E_\text{\tiny FNV}$ function to combine it with the mix. $J_{mixbytes}$ bytes of sequential access are used so that each round of the algorithm always fetches a full page from RAM, minimizing translation lookaside buffer misses which ASICs would theoretically be able to avoid. +Essentially, we maintain a ``mix" $J_{mixbytes}$ bytes wide, and repeatedly sequentially fetch $J_{mixbytes}$ bytes from the full dataset and use the $E_\text{\tiny FNV}$ function to combine it with the mix. $J_{mixbytes}$ bytes of sequential access are used so that each round of the algorithm always fetches a full page from RAM, minimizing translation lookaside buffer misses which ASICs would theoretically be able to avoid. If the output of this algorithm is below the desired target, then the nonce is valid. Note that the extra application of \texttt{KEC} at the end ensures that there exists an intermediate nonce which can be provided to prove that at least a small amount of work was done; this quick outer PoW verification can be used for anti-DDoS purposes. It also serves to provide statistical assurance that the result is an unbiased, 256 bit number. From e9e7fc372cbc8119683e8265b943ed5321ad155f Mon Sep 17 00:00:00 2001 From: nicksavers Date: Sat, 18 Nov 2017 19:45:49 +0100 Subject: [PATCH 30/35] Fix minGasLimit to 5000 --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 37c1b196..2047d52a 100644 --- a/Paper.tex +++ b/Paper.tex @@ -463,7 +463,7 @@ \subsubsection{Block Header Validity} \begin{eqnarray} & & H_l < {P(H)_H}_l + \left\lfloor\frac{{P(H)_H}_l}{1024}\right\rfloor \quad \wedge \\ & & H_l > {P(H)_H}_l - \left\lfloor\frac{{P(H)_H}_l}{1024}\right\rfloor \quad \wedge \\ -& & H_l \geqslant 125000 +& & H_l \geqslant 5000 \end{eqnarray} $H_s$ is the timestamp of block $H$ and must fulfil the relation: From 67b9fc2cad3656c116fd4f230d53f04e6da4d8dc Mon Sep 17 00:00:00 2001 From: Jaycen Horton Date: Mon, 20 Nov 2017 00:05:05 -0700 Subject: [PATCH 31/35] Update Paper.tex Change ECDSARESTORE to ECDSARECOVER to keep consistent with the following (and previous) defined terms --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..7a703406 100644 --- a/Paper.tex +++ b/Paper.tex @@ -1397,7 +1397,7 @@ \section{Signing Transactions}\label{app:signing} It is assumed that the sender has a valid private key $p_r$, which is a randomly selected positive integer (represented as a byte array of length 32 in big-endian form) in the range \hbox{$[1, \mathtt{\tiny secp256k1n} - 1]$}. -We assert the functions $\mathtt{\small ECDSASIGN}$, $\mathtt{\small ECDSARESTORE}$ and $\mathtt{\small ECDSAPUBKEY}$. These are formally defined in the literature. +We assert the functions $\mathtt{\small ECDSASIGN}$, $\mathtt{\small ECDSARECOVER}$ and $\mathtt{\small ECDSAPUBKEY}$. These are formally defined in the literature. \begin{eqnarray} \mathtt{\small ECDSAPUBKEY}(p_r \in \mathbb{B}_{32}) & \equiv & p_u \in \mathbb{B}_{64} \\ \mathtt{\small ECDSASIGN}(e \in \mathbb{B}_{32}, p_r \in \mathbb{B}_{32}) & \equiv & (v \in \mathbb{B}_{1}, r \in \mathbb{B}_{32}, s \in \mathbb{B}_{32}) \\ From e64176805572049a4ae966f16fc1246a30780e02 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Thorkil=20V=C3=A6rge?= Date: Mon, 11 Dec 2017 11:28:41 +0100 Subject: [PATCH 32/35] Fix minor spelling errors Fix capitalization of some instances of the word "Greek" --- Paper.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Paper.tex b/Paper.tex index 1a6bbaa4..2925e169 100644 --- a/Paper.tex +++ b/Paper.tex @@ -153,13 +153,13 @@ \section{Conventions}\label{ch:conventions} The two sets of highly structured, `top-level', state values, are denoted with bold lowercase Greek letters. They fall into those of world-state, which are denoted $\boldsymbol{\sigma}$ (or a variant thereupon) and those of machine-state, $\boldsymbol{\mu}$. -Functions operating on highly structured values are denoted with an upper-case greek letter, \eg $\Upsilon$, the Ethereum state transition function. +Functions operating on highly structured values are denoted with an upper-case Greek letter, \eg $\Upsilon$, the Ethereum state transition function. For most functions, an uppercase letter is used, e.g. $C$, the general cost function. These may be subscripted to denote specialised variants, \eg $C_\text{\tiny SSTORE}$, the cost function for the {\tiny SSTORE} operation. For specialised and possibly externally defined functions, I may format as typewriter text, \eg the Keccak-256 hash function (as per the winning entry to the SHA-3 contest) is denoted $\texttt{KEC}$ (and generally referred to as plain Keccak). Also $\texttt{KEC512}$ is referring to the Keccak 512 hash function. Tuples are typically denoted with an upper-case letter, \eg $T$, is used to denote an Ethereum transaction. This symbol may, if accordingly defined, be subscripted to refer to an individual component, \eg $T_n$, denotes the nonce of said transaction. The form of the subscript is used to denote its type; \eg uppercase subscripts refer to tuples with subscriptable components. -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. +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. From eccb42b1086c63eaa4c90ef678da700eb0189ef4 Mon Sep 17 00:00:00 2001 From: Gav Date: Sat, 6 Jan 2018 16:19:03 +0100 Subject: [PATCH 33/35] Add license. --- LICENCE.md | 175 +++++++++++++++++++++++++++++++++++++++++++++++++++++ README.md | 9 ++- 2 files changed, 183 insertions(+), 1 deletion(-) create mode 100644 LICENCE.md diff --git a/LICENCE.md b/LICENCE.md new file mode 100644 index 00000000..22dc42ec --- /dev/null +++ b/LICENCE.md @@ -0,0 +1,175 @@ +## creative commons + +# Attribution-ShareAlike 4.0 International + +Creative Commons Corporation (“Creative Commons”) is not a law firm and does not provide legal services or legal advice. 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For the avoidance of doubt, this paragraph does not form part of the public licenses. + +Creative Commons may be contacted at [creativecommons.org](http://creativecommons.org/). +``` diff --git a/README.md b/README.md index fabebcb8..31f0fa54 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,14 @@ -# yellowpaper +# Ethereum Yellow Paper +[![License: CC BY-SA 4.0](https://img.shields.io/badge/License-CC%20BY--SA%204.0-lightgrey.svg)](https://creativecommons.org/licenses/by-sa/4.0/) [![Gitter](https://badges.gitter.im/ethereum/yellowpaper.svg)](https://gitter.im/ethereum/yellowpaper?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge) +The Yellow Paper is a formal definition of the Ethereum protocol, originally by Gavin Wood, currently maintained by Nick Savers and with contributions from many people around the world. + +It is free culture work, licensed under the Creative Commons Attribution Share-Alike (CC-BY-SA)i version 4.0. + +## Usage + The paper comes as a single ``latex`` file ``Paper.tex``. The latest version is generally available as a PDF at https://ethereum.github.io/yellowpaper/paper.pdf or just [yellowpaper.io](http://yellowpaper.io/) . In order to build, use the supplied build script (``build.sh``). Following the first time, you can use the standard `pdflatex` tools like http://latex.informatik.uni-halle.de/latex-online/latex.php for compiling/preview. It can be viewed in ``PDF`` format after building. From c298aa9996a91bbe99b6b8b9e3099f4e4a68bb91 Mon Sep 17 00:00:00 2001 From: Nick Savers Date: Sun, 7 Jan 2018 20:45:09 +0100 Subject: [PATCH 34/35] Remove accidental i from README --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 31f0fa54..0c6e11d3 100644 --- a/README.md +++ b/README.md @@ -5,7 +5,7 @@ The Yellow Paper is a formal definition of the Ethereum protocol, originally by Gavin Wood, currently maintained by Nick Savers and with contributions from many people around the world. -It is free culture work, licensed under the Creative Commons Attribution Share-Alike (CC-BY-SA)i version 4.0. +It is free culture work, licensed under the Creative Commons Attribution Share-Alike (CC-BY-SA) version 4.0. ## Usage From 72cc52e9416cd6139bc294483fda293bd284d65b Mon Sep 17 00:00:00 2001 From: Nick Savers Date: Sun, 7 Jan 2018 21:04:40 +0100 Subject: [PATCH 35/35] Fix minGasLimit to 5000 mentioned in #393 --- Paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Paper.tex b/Paper.tex index 41414fda..f6092bb0 100644 --- a/Paper.tex +++ b/Paper.tex @@ -490,7 +490,7 @@ \subsubsection{Block Header Validity} & & H_g \le H_l \quad \wedge \\ & & H_l < {P(H)_H}_l + \left\lfloor\frac{{P(H)_H}_l}{1024}\right\rfloor \quad \wedge \\ & & H_l > {P(H)_H}_l - \left\lfloor\frac{{P(H)_H}_l}{1024}\right\rfloor \quad \wedge \\ -& & H_l \geqslant 125000 \quad \wedge \\ +& & H_l \geqslant 5000 \quad \wedge \\ & & H_s > {P(H)_H}_s \quad \wedge \\ & & H_i = {P(H)_H}_i +1 \quad \wedge \\ & & \lVert H_x \rVert \le 32