\documentclass[dvipsnames,14pt,t]{beamer}
\usepackage{../slides}
\usepackage{../langs}
\usepackage{../data}
\usepackage{../graphics}
\usepackage{soul}
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% beamer stuff
\renewcommand{\slidecaption}{AFL 09, King's College London}
\newcommand{\bl}[1]{\textcolor{blue}{#1}}
\begin{document}
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\begin{frame}[t]
\frametitle{%
\begin{tabular}{@ {}c@ {}}
\\[-3mm]
\LARGE Automata and \\[-2mm]
\LARGE Formal Languages (9)\\[3mm]
\end{tabular}}
\normalsize
\begin{center}
\begin{tabular}{ll}
Email: & christian.urban at kcl.ac.uk\\
Office: & S1.27 (1st floor Strand Building)\\
Slides: & KEATS (also home work is there)\\
\end{tabular}
\end{center}
\end{frame}
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\begin{frame}[c,fragile]
\frametitle{Functional Programming}
\footnotesize
\begin{textblock}{13}(0.9,3)
\lstset{emph={def,if,then,else},emphstyle=\color{codepurple}}
\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
def fib(n) = if n == 0 then 0
else if n == 1 then 1
else fib(n - 1) + fib(n - 2);
def fact(n) = if n == 0 then 1 else n * fact(n - 1);
def ack(m, n) = if m == 0 then n + 1
else if n == 0 then ack(m - 1, 1)
else ack(m - 1, ack(m, n - 1));
def gcd(a, b) = if b == 0 then a else gcd(b, a % b);
\end{lstlisting}
\end{textblock}
\end{frame}
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\mode<presentation>{
\begin{frame}[c]
\begin{center}
\bl{\begin{tabular}{@{}lcl@{}}
\textit{Exp} & $\rightarrow$ & \textit{Var} $|$ \textit{Num}\\
& $|$ & \textit{Exp} \texttt{+} \textit{Exp} $|$ ... $|$ ( \textit{Exp} )\\
& $|$ & \texttt{if}\; \textit{BExp} \;\texttt{then}\; \textit{Exp} \;\texttt{else}\; \textit{Exp}\\
& $|$ & \texttt{write}\;\textit{Exp}\\
& $|$ & \textit{Exp}\;\texttt{;}\;\textit{Exp}\\
& $|$ & \textit{FunName} \texttt{(}\textit{Exp},...,\textit{Exp}\texttt{)}\medskip\\
\textit{BExp} & $\rightarrow$ & \ldots\medskip\\
\textit{Decl} & $\rightarrow$ & \textit{Def} \;\texttt{;}\; \textit{Decl}\\
& $|$ & \textit{Exp}\medskip\\
\textit{Def} &
$\rightarrow$ & \texttt{def} \textit{FunName}\texttt{(}\textit{x}$_1$,..., \textit{x}$_n$\texttt{)} \texttt{=} \textit{Exp}\\
\end{tabular}}
\end{center}
\end{frame}}
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\begin{frame}[c, fragile]
\frametitle{Abstract Syntax Tree}
\footnotesize
\begin{textblock}{13}(0.3,2)
\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
abstract class Exp
abstract class BExp
abstract class Decl
case class
Def(name: String, args: List[String], body: Exp)
extends Decl
case class Main(e: Exp) extends Decl
case class Call(name: String, args: List[Exp]) extends Exp
case class If(a: BExp, e1: Exp, e2: Exp) extends Exp
case class Write(e: Exp) extends Exp
case class Var(s: String) extends Exp
case class Num(i: Int) extends Exp
case class Aop(o: String, a1: Exp, a2: Exp) extends Exp
case class Sequ(e1: Exp, e2: Exp) extends Exp
case class Bop(o: String, a1: Exp, a2: Exp) extends BExp
\end{lstlisting}
\end{textblock}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Mathematical Functions}
Compilation of some mathematical functions:
\begin{center}
\begin{tabular}{lcl}
\texttt{Aop("+", a1, a2)} & $\Rightarrow$ & \texttt{...iadd}\\
\texttt{Aop("-", a1, a2)} & $\Rightarrow$ & \texttt{...isub}\\
\texttt{Aop("*", a1, a2)} & $\Rightarrow$ & \texttt{...imul}\\
\texttt{Aop("/", a1, a2)} & $\Rightarrow$ & \texttt{...idiv}\\
\texttt{Aop("\%", a1, a2)} & $\Rightarrow$ & \texttt{...irem}\\
\end{tabular}
\end{center}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Boolean Expressions}
Compilation of boolean expressions:
\begin{center}
\begin{tikzpicture}[node distance=2mm and 4mm,
block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},
point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},
skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]
\node (A1) [point] {};
\node (b) [block, right=of A1] {code of \bl{$b$}};
\node (A2) [point, right=of b] {};
\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};
\node (A3) [point, right=of cs1] {};
\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};
\node (A4) [point, right=of cs2] {};
\only<1>{
\draw (A1) edge [->, red, line width=1mm] (b);
\draw (b) edge [->, red, line width=1mm] (A2);
\draw (A2) edge [skip loop] (A3);
\draw (A3) edge [->, red, line width=1mm] (cs2);
\draw (cs2) edge [->,red, line width=1mm] (A4);
\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}
\end{tikzpicture}
\end{center}
\begin{center}
\begin{tabular}{lcl}
\texttt{Bop("==", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpne...}\\
\texttt{Bop("!=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpeq...}\\
\texttt{Bop("<", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpge...}\\
\texttt{Bop("<=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpgt...}\\
\end{tabular}
\end{center}
\end{frame}
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\begin{frame}[t, fragile]
\frametitle{Sequences}
Compiling \texttt{arg1 ; arg2}:
\begin{textblock}{7}(2,5)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
...arg1...
pop
...arg1...
\end{lstlisting}
\end{minipage}
\end{textblock}
\end{frame}
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\begin{frame}[t, fragile]
\frametitle{Write}
Compiling \texttt{write(arg)}:
\begin{textblock}{7}(2,4)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
...arg...
dup
invokestatic XXX/XXX/write(I)V
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{7}(2,8)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
case Write(a1) => {
compile_exp(a1, env) ++
List("dup\n",
"invokestatic XXX/XXX/write(I)V\n")
}
\end{lstlisting}
\end{minipage}
\end{textblock}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Functions}
\begin{textblock}{7}(1,2)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
.method public static write(I)V
.limit locals 5
.limit stack 5
iload 0
getstatic java/lang/System/out Ljava/io/PrintStream;
swap
invokevirtual java/io/PrintStream/println(I)V
return
.end method
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{10}(1,9.8)
\small We will need for definitions\\[-8mm]\mbox{}\footnotesize
\begin{center}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
.method public static f (I...I)I
.limit locals ??
.limit stack ??
??
.end method
\end{lstlisting}
\end{center}
\end{textblock}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Stack Estimation}
\footnotesize
\begin{center}
\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
def max_stack_exp(e: Exp): Int = e match {
case Call(_, args) => args.map(max_stack_exp).sum
case If(a, e1, e2) => max_stack_bexp(a) +
(List(max_stack_exp(e1), max_stack_exp(e1)).max)
case Write(e) => max_stack_exp(e) + 1
case Var(_) => 1
case Num(_) => 1
case Aop(_, a1, a2) =>
max_stack_exp(a1) + max_stack_exp(a2)
case Sequ(e1, e2) =>
List(max_stack_exp(e1), max_stack_exp(e2)).max
}
def max_stack_bexp(e: BExp): Int = e match {
case Bop(_, a1, a2) =>
max_stack_exp(a1) + max_stack_exp(a2)
}
\end{lstlisting}
\end{center}
\end{frame}
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\begin{frame}[fragile]
\frametitle{Successor}
\begin{textblock}{7}(1,2.5)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
.method public static suc(I)I
.limit locals 1
.limit stack 3
iload 0
ldc 1
iadd
ireturn
.end method
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{7}(6,8)
\begin{bubble}[5cm]\small
\begin{lstlisting}[language=Lisp,
basicstyle=\ttfamily,
numbers=none,
xleftmargin=1mm]
def suc(x) = x + 1;
\end{lstlisting}
\end{bubble}
\end{textblock}
\end{frame}
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\begin{frame}[fragile]
\frametitle{Addition}
\begin{textblock}{7}(1,1.5)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
.method public static add(II)I
.limit locals 2
.limit stack 6
iload 0
ldc 0
if_icmpne If_else_2
iload 1
goto If_end_3
If_else_2:
iload 0
ldc 1
isub
iload 1
invokestatic defs/defs/add(II)I
invokestatic defs/defs/suc(I)I
If_end_3:
ireturn
.end method
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{7}(6,6.2)
\begin{bubble}[7cm]\small
\begin{lstlisting}[language=Lisp,
basicstyle=\ttfamily,
numbers=none,
xleftmargin=1mm]
def add(x, y) =
if x == 0 then y
else suc(add(x - 1, y));
\end{lstlisting}
\end{bubble}
\end{textblock}
\end{frame}
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\begin{frame}[fragile]
\frametitle{Factorial}
\begin{textblock}{7}(1,1.5)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]
.method public static facT(II)I
.limit locals 2
.limit stack 6
iload 0
ldc 0
if_icmpne If_else_2
iload 1
goto If_end_3
If_else_2:
iload 0
ldc 1
isub
iload 0
iload 1
imul
invokestatic fact/fact/facT(II)I
If_end_3:
ireturn
.end method
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{7}(6,7)
\begin{bubble}[7cm]\small
\begin{lstlisting}[language=Lisp,
basicstyle=\ttfamily,
numbers=none,
xleftmargin=1mm]
def facT(n, acc) =
if n == 0 then acc
else facT(n - 1, n * acc);
\end{lstlisting}
\end{bubble}
\end{textblock}
\end{frame}
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\begin{frame}[fragile]
\begin{textblock}{7}(1,-0.2)\footnotesize
\begin{minipage}{6cm}
\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]
.method public static facT(II)I
.limit locals 2
.limit stack 7
(*@\hl{facT\_Start:} @*)
iload 0
ldc 0
if_icmpne If_else_2
iload 1
goto If_end_3
If_else_2:
iload 0
ldc 1
isub
iload 0
iload 1
imul
(*@\hl{istore 1} @*)
(*@\hl{istore 0} @*)
(*@\hl{goto facT\_Start} @*)
If_end_3:
ireturn
.end method
\end{lstlisting}
\end{minipage}
\end{textblock}
\begin{textblock}{7}(6,7)
\begin{bubble}[7cm]\small
\begin{lstlisting}[language=Lisp,
basicstyle=\ttfamily,
numbers=none,
xleftmargin=1mm]
def facT(n, acc) =
if n == 0 then acc
else facT(n - 1, n * acc);
\end{lstlisting}
\end{bubble}
\end{textblock}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Tail Recursion}
A call to \texttt{f(args)} is usually compiled as\medskip
{\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
args onto stack
invokestatic .../f
\end{lstlisting}}\pause
A call is in tail position provided:\medskip
{\small\begin{itemize}
\item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}
\item \texttt{Exp ; \hl{Exp}}
\item \texttt{Exp op Exp}
\end{itemize}}\medskip
then a call \texttt{f(args)} can be compiled as\medskip\small
\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]
prepare environment
jump to start of function
\end{lstlisting}
\end{frame}
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\begin{frame}[c, fragile]
\frametitle{Tail Recursive Call}
\footnotesize
\begin{textblock}{13}(-0.3,2)
\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]
def compile_expT(a: Exp, env: Mem, name: String): Instrs =
...
case Call(n, args) => if (name == n)
{
val stores = args.zipWithIndex.map
{ case (x, y) => "istore " + y.toString + "\n" }
args.flatMap(a => compile_expT(a, env, "")) ++
stores.reverse ++
List ("goto " + n + "_Start\n")
}
else
{
val is = "I" * args.length
args.flatMap(a => compile_expT(a, env, "")) ++
List ("invokestatic XXX/XXX/" + n + "(" + is + ")I\n")
}
\end{lstlisting}
\end{textblock}
\end{frame}
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\mode<presentation>{
\begin{frame}[c]
\large\bf
Using a compiler, \\how can you mount the\\ perfect attack against a system?
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
{\large\bf
What is a \alert{perfect} attack?}\bigskip
\begin{enumerate}
\item you can potentially completely take over a target system
\item your attack is (nearly) undetectable
\item the victim has (almost) no chance to recover
\end{enumerate}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\begin{center}
\begin{tikzpicture}[scale=1]
\onslide<1->{
\node (A) at (0,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=17mm] {};
\node [below right] at (A.north west) {\footnotesize\begin{tabular}{@{}l@{}}
\only<1,2>{clean}\only<3->{\alert{hacked}}\\compiler\end{tabular}};}
\onslide<2->{
\node (B) at (-2,2) [draw=black, rectangle, very thick, minimum height=10mm, minimum width=12mm] {};
\node [below right] at (B.north west) {\footnotesize\begin{tabular}{@{}l@{}}login\\(src)\end{tabular}};
\node (C) at (2,2) [draw=black, rectangle, very thick, minimum height=10mm, minimum width=12mm] {};
\node [below right] at (C.north west) {\footnotesize\begin{tabular}{@{}l@{}}login\\(bin)\end{tabular}};
\draw[->, line width=2mm] (B) -- (C);
}
\onslide<3->{\node [above left=-1.5mm] at (C.south east) {\footnotesize \alert{$\blacksquare$}};}
\end{tikzpicture}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}[c]
\begin{center}
\begin{tikzpicture}[scale=1]
\onslide<1->{
\node (A) at (0,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (A.north west) {\small V0.01};
\node [below right] (A1) at (A.south west) {\small Scala};
\node [below right] (A1) at (A1.south west) {\small\textcolor{gray}{host language}};
\node [above right] at (A.north west) {my compiler (src)};}
\onslide<2->{
\node (B) at (1.8,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (B.north west) {\small V0.02};
\node [below right] at (B.south west) {\small Scala};
\node at (3,0) {\ldots};
\node (C) at (5,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (C.north west) {\small V1.00};
\node [below right] at (C.south west) {\small Scala};}
\onslide<3->{
\node (D) at (6.8,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (D.north west) {\small V1.00};
\node (E) at (6.8,2) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (E.north west) {\small V1.01};}
\onslide<4->{
\node (F) at (8.6,0) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (F.north west) {\small V1.01};
\node (G) at (8.6,2) [draw=black, rectangle, very thick, minimum height=18mm, minimum width=14mm] {};
\node [below right] at (G.north west) {\small V1.02};
\node at (9.8,0) {\ldots};
\node at (9.8,2) {\ldots};
\node at (8,-2) {\textcolor{gray}{\begin{tabular}{@{}l@{}}no host language\\needed\end{tabular}}};
}
\end{tikzpicture}
\end{center}
\end{frame}}
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\mode<presentation>{
\begin{frame}<1-3>
\frametitle{\LARGE\begin{tabular}{c}Hacking Compilers
\end{tabular}}
%Why is it so paramount to have a small trusted code base (TCB)?
\bigskip\bigskip
\begin{columns}
\begin{column}{2.7cm}
\begin{minipage}{2.5cm}%
\begin{tabular}{c@ {}}
\includegraphics[scale=0.2]{../pics/ken-thompson.jpg}\\[-1.8mm]
\footnotesize Ken Thompson\\[-1.8mm]
\footnotesize Turing Award, 1983\\
\end{tabular}
\end{minipage}
\end{column}
\begin{column}{9cm}
\begin{tabular}{l@ {\hspace{1mm}}p{8cm}}
& Ken Thompson showed how to hide a Trojan Horse in a
compiler \textcolor{red}{without} leaving any traces in the source code.\\[2mm]
& No amount of source level verification will protect
you from such Thompson-hacks.\\[2mm]
& Therefore in safety-critical systems it is important to rely
on only a very small TCB.
\end{tabular}
\end{column}
\end{columns}
\only<2>{
\begin{textblock}{6}(4,2)
\begin{tikzpicture}
\draw (0,0) node[inner sep=3mm,fill=cream, ultra thick, draw=red, rounded corners=2mm]
{\normalsize
\begin{minipage}{8cm}
\begin{quote}
\includegraphics[scale=0.05]{../pics/evil.png}
\begin{enumerate}
\item[1)] Assume you ship the compiler as binary and also with sources.
\item[2)] Make the compiler aware when it compiles itself.
\item[3)] Add the Trojan horse.
\item[4)] Compile.
\item[5)] Delete Trojan horse from the sources of the compiler.
\item[6)] Go on holiday for the rest of your life. ;o)\\[-7mm]\mbox{}
\end{enumerate}
\end{quote}
\end{minipage}};
\end{tikzpicture}
\end{textblock}}
\end{frame}}
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\end{document}
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