macros.tex 7.69 KB
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\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
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\newtheorem{dfn}[theorem]{Definition}
\newtheorem{hypothesis}{Hypothesis}
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\newcommand\invisiblesection[1]{%
  \refstepcounter{section}
\sectionmark{#1}}

\newenvironment{proof}[1][Proof]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
  \newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
  \newenvironment{example}[1][Example]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
  \newenvironment{remark}[1][Remark]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}

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\newcommand{\qed}{\nobreak \ifvmode \relax \else
  \ifdim\lastskip<1.5em \hskip-\lastskip
  \hskip1.5em plus0em minus0.5em \fi \nobreak
\vrule height0.75em width0.5em depth0.25em\fi}

  \newcommand{\sref}[1]{Section~\ref{#1}}
  \newcommand{\tref}[1]{Theorem~\ref{#1}}
  \newcommand{\lref}[1]{Lemma~\ref{#1}}
  \newcommand{\fref}[1]{Figure~\ref{#1}}
  \newcommand{\aref}[1]{Algorithm~\ref{#1}}
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  \usepackage{soul}\let\strikethrough\st\let\st\undefined
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% \DeclareMathOperator*{\argmin}{arg\,min}
% \DeclareMathOperator*{\Vol}{Vol}
% \DeclareMathOperator*{\Supp}{Supp}
% \newcommand{\cR}{\ensuremath{\mathcal R}}
% \newcommand{\cS}{\ensuremath{\mathcal S}}
%
% \newcommand{\CVPDf}{\ensuremath{\algo{CVP}_{\tilde{D}_4}}}
% \newcommand{\CVPDfZf}{\ensuremath{\algo{CVP}_{D_4/\ZZ^4}}}
% \newcommand{\LDEncode}{\algo{Encode}}
% \newcommand{\LDDecode}{\algo{Decode}}
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\newcommand{\N}{\ensuremath{\mathbb{N}}\xspace}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}\xspace}
\newcommand{\K}{\ensuremath{\mathbb{K}}\xspace}
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% \renewcommand\L{\mathcal{L}}
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\renewcommand{\L}{\ensuremath{\mathbb{L}}\xspace}
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\newcommand{\corr}{\,\hat{=}\,}
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% \newcommand{\B}{\ensuremath{\mathbb{B}}\xspace}
% \newcommand{\E}{\ensuremath{\mathbb{E}}\xspace}
\newcommand{\Oinf}{\ensuremath{\mathcal{O}}\xspace}
\newcommand{\F}[1]{\ensuremath{\mathbb{F}_{#1}}\xspace}
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% \newcommand{\RR}{\ensuremath{\mathbb{R}}}
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\newcommand{\mbf}{\ensuremath{\mathbf}}
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% \newcommand{\rando}{\ensuremath{\xleftarrow{\$}}}
% \newcommand{\la}{\ensuremath{\leftarrow}}

% \newcommand{\MD}{\ensuremath{\mathcal{D}}\xspace}
% \newcommand{\MS}{\ensuremath{\mathcal{D}}\xspace}
% \newcommand{\MA}{\ensuremath{\mathcal{A}}\xspace}
% \newcommand{\MB}{\ensuremath{\mathcal{B}}\xspace}
% \newcommand{\MP}{\ensuremath{\mathcal{P}}\xspace}
% \newcommand{\tA}{\ensuremath{t_{\mathcal{A}}}}
% \newcommand{\eA}{\ensuremath{\varepsilon_{\mathcal{A}}}}
% \newcommand{\tS}{\ensuremath{t_{\mathcal{D}}}}
% \newcommand{\eS}{\ensuremath{\varepsilon_{\mathcal{D}}}}

% \newcommand{\vX}{\mathcal X}
% \newcommand{\vY}{\mathcal Y}


% \newcommand{\MR}{\ensuremath{\mathcal{R}}\xspace}
% \newcommand{\tR}{\ensuremath{t_{\mathcal{R}}}}
% \newcommand{\eR}{\ensuremath{\varepsilon_{\mathcal{R}}}}
%
% \newcommand{\tD}{\ensuremath{t_{\mathcal{D}}}}
% \newcommand{\eD}{\ensuremath{\varepsilon_{\mathcal{D}}}}
% \newcommand{\sis}{\textsf{SIS}\xspace}
% \newcommand{\isis}{\textsf{ISIS}\xspace}
% \newcommand{\lwe}{\textsf{LWE}\xspace}
% \newcommand{\dlwe}{\textsf{LWE}\xspace}
% \newcommand{\rdlwe}{\textsf{R-LWE}\xspace}
%
% \newcommand{\ee}{\ensuremath{\varepsilon}}
%
% \newcommand{\sS}{\ensuremath{\sigma}}
% \newcommand{\sE}{\ensuremath{\sigma}}
% \newcommand{\DS}{\ensuremath{D_{\sS}}}
% \newcommand{\DE}{\ensuremath{D_{\sE}}}
% %\newcommand{\Dy}{\ensuremath{D_y}}
% \newcommand{\Dy}{\ensuremath{[-B, B]}}
% \newcommand{\Dysc}{\ensuremath{D_{y,\mat{Sc}}}}
% \newcommand{\Dz}{\ensuremath{D_z}}
% \newcommand{\bit}{\ensuremath{\{0,1\}}}
% \newcommand{\eqdef}{\stackrel{\mathrm{def}}=}
% \newcommand{\rand}{\getsr}

% \newcommand{\rounddq}[1]{\ensuremath{\lfloor #1 \rceil_{d,q}}}
% \newcommand{\roundd}[1]{\ensuremath{\lfloor #1 \rceil_d}}
% \newcommand{\norm}[1]{\ensuremath{||#1||}}

% \newcommand{\KeyGen}{\keygen}
% \newcommand{\Sign}{\sign}
% \newcommand{\Verify}{\verify}
% \newcommand{\keygen}{\ensuremath{\mathsf{KeyGen}}}
% \newcommand{\sign}{\ensuremath{\mathsf{Sign}}}
% \newcommand{\verify}{\ensuremath{\mathsf{Verify}}}
% \newcommand{\start}{\underline{\ensuremath{\mathsf{Start}}}\xspace}
% \newcommand{\randO}{\ensuremath{\underline{\mathsf{Rand}}^{O_c}}\xspace}
% \newcommand{\signO}{\ensuremath{\underline{\mathsf{Sign}}^{O_c}}\xspace}
% \newcommand{\finishO}{\ensuremath{\underline{\mathsf{Finish}}^{O_c}}}
% \newcommand{\instance}{\underline{\ensuremath{\mathsf{Instance}}}}
% \newcommand{\Sample}{\ensuremath{\mathsf{Sample}}}

% \newcommand{\keygenQ}{\ensuremath{\mathsf{KeyGen}}}
% \newcommand{\signQ}{\ensuremath{\mathsf{Sign}}}
% \newcommand{\verifyQ}{\ensuremath{\mathsf{Verify}}}
% \newcommand{\CHgen}{\ensuremath{\mathsf{ChGen}}}

% \newcommand{\inputtext}{\textsf{INPUT:}\;}
% \newcommand{\outputtext}{\textsf{OUTPUT:}\;}
% \newcommand{\iftext}{\mathbf{if\;}}
% \newcommand{\elsetext}{\mathbf{else\;}}
% \newcommand{\then}{\mathbf{then\;}}
% \newcommand{\return}{\mathbf{return\;}}

% \newcommand{\mat}[1]{\mathbf{#1}}
% \renewcommand{\vec}[1]{\mathbf{#1}}
% \newcommand{\modq}{\ensuremath{\; (\bmod \; q)}}
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%\newcommand{\modq}{\ensuremath{\; (q)}}
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% \newcommand{\ip}[2]{\ensuremath{\langle {#1},{#2}\rangle}}
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% \newcommand{\adv}{\ensuremath{\mathcal{A}}}
% \newcommand{\secpar}{\ensuremath{\lambda}}
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% \newcommand{\sk}{\ensuremath{\mathsf{sk}}\xspace}
% \newcommand{\pk}{\ensuremath{\mathsf{vk}}\xspace}
% \newcommand{\sst}{\ensuremath{\mathsf{st}}\xspace}
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% \newcommand{\CH}{\ensuremath{\mathcal{CH}}}
% \newcommand{\ch}{\ensuremath{\mathsf{CH}}}
% \newcommand{\Mek}{\ensuremath{\mathsf{M_{ek}}}}
% \newcommand{\Yek}{\ensuremath{\mathsf{Y_{ek}}}}
% \newcommand{\Rek}{\ensuremath{\mathsf{R_{ek}}}}
% \newcommand{\ek}{\ensuremath{\mathsf{ek}}}
% \newcommand{\td}{\ensuremath{\mathsf{td}}}
% \newcommand{\Gen}{\ensuremath{\mathsf{Gen}}}
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% \newcommand{\negl}{\ensuremath{\mathsf{negl}}}
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% \newcommand{\R}{\mathcal{R}}
% \newcommand{\Rp}{\mathcal{R}_p}
% \newcommand{\Rq}{\mathcal{R}_q}
% \newcommand{\Rqk}[1]{\mathcal{R}_{q,#1}}
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% \def\getsr{\stackrel{{\scriptscriptstyle \$}}{\leftarrow}}
% \def\gets{{\leftarrow}}
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% \newcommand{\Uniform}{\mathcal{U}}
% \newcommand{\UniRk}[1]{\Rqk{#1}}
% \newcommand{\UniRq}{\Rq}
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\newcommand{\zeropo}{{\bf 0}}
\newcommand{\Apo}{{\bf A\xspace}}
\newcommand{\Bpo}{{\bf B\xspace}}
\newcommand{\Ipo}{{\bf I\xspace}}
\newcommand{\apo}{{\bf a\xspace}}
\newcommand{\bpo}{{\bf b\xspace}}
\newcommand{\cpo}{{\bf c\xspace}}
\newcommand{\Cpo}{{\bf C\xspace}}
\newcommand{\dpo}{{\bf d\xspace}}
\newcommand{\epo}{{\bf e\xspace}}
\newcommand{\ppo}{{\bf p\xspace}}
\newcommand{\fpo}{{\bf f\xspace}}
\newcommand{\gpo}{{\bf g\xspace}}
\newcommand{\Gpo}{{\bf G\xspace}}
\newcommand{\hpo}{{\bf h\xspace}}
\newcommand{\kpo}{{\bf k\xspace}}
\newcommand{\Kpo}{{\bf K\xspace}}
\newcommand{\lpo}{{\bf l\xspace}}
\newcommand{\Lpo}{{\bf L\xspace}}
\newcommand{\mpo}{{\bf m\xspace}}
\newcommand{\rpo}{{\bf r\xspace}}
\newcommand{\spo}{{\bf s\xspace}}
\newcommand{\tpo}{{\bf t\xspace}}
\newcommand{\upo}{{\bf u\xspace}}
\newcommand{\Upo}{{\bf U\xspace}}
\newcommand{\vpo}{{\bf v\xspace}}
\newcommand{\wpo}{{\bf w\xspace}}
\newcommand{\xpo}{{\bf x\xspace}}
\newcommand{\ypo}{{\bf y\xspace}}
\newcommand{\zpo}{{\bf z\xspace}}
\newcommand{\Zpo}{{\bf Z\xspace}}

\newcommand{\Spo}{{\bf S}}
\newcommand{\Ypo}{{\bf Y}}

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% \newcommand{\algo}[1]{\textsf{#1}}
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% \newcommand{\PeikertDBL}{\algo{dbl}}
% \newcommand{\PeikertREC}{\algo{rec}}
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% \newcommand{\PowMul}{{\text{\sf PowMul}}}
% \newcommand{\PowMulPsi}{{\text{\sf PowMul}_{\psi}}}
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\newcommand{\ie}{{\textit{i.e.}}\;}
\newcommand{\eg}{{\textit{e.g.}}\;}
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\newcommand{\p}{\ensuremath{2^{255}-19}}
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\newcommand{\Zfield}{\ensuremath{\mathbb{Z}_{\p}}}
\newcommand{\Ffield}{\ensuremath{\mathbb{F}_{\p}}}