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Make sure that divisions and modulo operations are not subject to mod 2^{256} #443

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Make sure that divisions and modulo operations are not subject to mod 2^{256} #443

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Make sure that divisions and modulo operations are not subject to mod…
pirapira Jun 21, 2017
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Copying build-related files from master
pirapira Jan 22, 2018
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1 change: 1 addition & 0 deletions .travis.yml
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,7 @@ sudo: required
before_install:
- sudo apt-get -qq update
- sudo apt-get install texlive texlive-latex3
- sudo apt install texlive-latex-extra
script:
- ./build.sh
deploy:
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6 changes: 4 additions & 2 deletions Paper.tex
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Expand Up @@ -1583,18 +1583,20 @@ \subsection{Instruction Set}
\midrule
0x04 & {\small DIV} & 2 & 1 & Integer division operation. \\
&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \begin{cases}0 & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] = 0\\ \lfloor\boldsymbol{\mu}_\mathbf{s}[0] \div \boldsymbol{\mu}_\mathbf{s}[1]\rfloor & \text{otherwise}\end{cases}$ \\
&&&& where division is not subject to modulo $2^{256}$. \\
\midrule
0x05 & {\small SDIV} & 2 & 1 & Signed integer division operation (truncated). \\
&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \begin{cases}0 & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] = 0\\ -2^{255} & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[0] = -2^{255} \wedge \quad \boldsymbol{\mu}_\mathbf{s}[1] = -1\\ \mathbf{sgn} (\boldsymbol{\mu}_\mathbf{s}[0] \div \boldsymbol{\mu}_\mathbf{s}[1]) \lfloor |\boldsymbol{\mu}_\mathbf{s}[0] \div \boldsymbol{\mu}_\mathbf{s}[1]| \rfloor & \text{otherwise}\end{cases}$ \\
&&&& Where all values are treated as two's complement signed 256-bit integers. \\
&&&& Where all values are treated as two's complement signed 256-bit integers and division is not subject to modulo $2^{256}.$ \\
&&&& Note the overflow semantic when $-2^{255}$ is negated.\\
\midrule
0x06 & {\small MOD} & 2 & 1 & Modulo remainder operation. \\
&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \begin{cases}0 & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] = 0\\ \boldsymbol{\mu}_\mathbf{s}[0] \bmod \boldsymbol{\mu}_\mathbf{s}[1] & \text{otherwise}\end{cases}$ \\
&&&& where $\mod$ is not subject to modulo $2^{256}$. \\
\midrule
0x07 & {\small SMOD} & 2 & 1 & Signed modulo remainder operation. \\
&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \begin{cases}0 & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[1] = 0\\ \mathbf{sgn} (\boldsymbol{\mu}_\mathbf{s}[0]) |\boldsymbol{\mu}_\mathbf{s}[0]| \bmod |\boldsymbol{\mu}_\mathbf{s}[1]| & \text{otherwise}\end{cases}$ \\
&&&& Where all values are treated as two's complement signed 256-bit integers. \\
&&&& Where all values are treated as two's complement signed 256-bit integers and $\mod$ is not subject to modulo $2^{256}$. \\
\midrule
0x08 & {\small ADDMOD} & 3 & 1 & Modulo addition operation. \\
&&&& $\boldsymbol{\mu}'_\mathbf{s}[0] \equiv \begin{cases}0 & \text{if} \quad \boldsymbol{\mu}_\mathbf{s}[2] = 0\\ (\boldsymbol{\mu}_\mathbf{s}[0] + \boldsymbol{\mu}_\mathbf{s}[1]) \mod \boldsymbol{\mu}_\mathbf{s}[2] & \text{otherwise}\end{cases}$ \\
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