| 1 |
2 |
arif_endro |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
| 2 |
10 |
arif_endro |
% $Id: mini_aes.tex,v 1.2 2005-12-26 04:18:33 arif_endro Exp $
|
| 3 |
2 |
arif_endro |
%
|
| 4 |
|
|
% Title : Mini AES 128
|
| 5 |
|
|
%
|
| 6 |
|
|
% Author : "Arif E. Nugroho" <arif_endro@yahoo.com>
|
| 7 |
|
|
%
|
| 8 |
|
|
% Description : Master Documentation File.
|
| 9 |
|
|
%
|
| 10 |
|
|
% Copyright (C) 2005 Arif E. Nugroho <arif_endro@yahoo.com>
|
| 11 |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
| 12 |
|
|
|
| 13 |
|
|
\documentclass[a4paper,12pt]{report}
|
| 14 |
|
|
\usepackage[english]{babel}
|
| 15 |
|
|
\usepackage[dvips,english,none,light,portrait]{draftcopy}
|
| 16 |
|
|
\usepackage{fancyvrb} % enable custom verbatim env.
|
| 17 |
|
|
\usepackage{float} % enable floating images
|
| 18 |
|
|
\usepackage{graphicx} % enable graphics in this document
|
| 19 |
|
|
\usepackage{titlesec} % enable customization title
|
| 20 |
|
|
\usepackage{fancyhdr} % enable customization header e.g. page number
|
| 21 |
|
|
\usepackage{setspace} % Custom line spacing
|
| 22 |
|
|
\usepackage{palatino}
|
| 23 |
|
|
%\usepackage{times} % Default font for report
|
| 24 |
|
|
\usepackage{indentfirst} % to make identation after sectioning
|
| 25 |
|
|
\usepackage[pdftitle={Mini AES 128},
|
| 26 |
|
|
pdfauthor={Copyright (C) 2005 Arif E. Nugroho},
|
| 27 |
|
|
pdfsubject={Mini AES 128},
|
| 28 |
|
|
pdfkeywords={AES},
|
| 29 |
|
|
colorlinks=false, bookmarksnumbered=false, ps2pdf,
|
| 30 |
|
|
pdfpagemode=none
|
| 31 |
|
|
]{hyperref}
|
| 32 |
|
|
|
| 33 |
|
|
\setlength{\topmargin} {0cm}
|
| 34 |
|
|
\setlength{\headheight} {1cm}
|
| 35 |
|
|
\setlength{\textheight} {21cm}
|
| 36 |
|
|
\setlength{\textwidth} {16cm}
|
| 37 |
|
|
\setlength{\oddsidemargin} {0cm}
|
| 38 |
|
|
\setlength{\evensidemargin}{0cm}
|
| 39 |
|
|
\setlength{\columnsep} {0.125in}
|
| 40 |
|
|
\setlength{\columnseprule} {0.5pt}
|
| 41 |
|
|
\setlength{\footskip} {1cm}
|
| 42 |
|
|
\renewcommand{\headrulewidth}{0.4pt}
|
| 43 |
|
|
\renewcommand{\footrulewidth}{0.4pt}
|
| 44 |
|
|
|
| 45 |
|
|
\setlength{\parindent}{1cm} % set paragraph indentation 1cm almost
|
| 46 |
|
|
% equal to 5 character
|
| 47 |
|
|
|
| 48 |
|
|
\lhead{\scriptsize{\textsf{\rightmark}}}
|
| 49 |
|
|
\rhead{\thepage}
|
| 50 |
|
|
\chead{}
|
| 51 |
|
|
\lfoot{}
|
| 52 |
|
|
\rfoot{}
|
| 53 |
|
|
\cfoot{Arif E. Nugroho\\www.opencores.org}
|
| 54 |
|
|
|
| 55 |
|
|
\titlelabel{\thetitle.\quad}
|
| 56 |
|
|
|
| 57 |
|
|
% Chapter heading layout
|
| 58 |
|
|
\titleformat{\chapter}[display]
|
| 59 |
|
|
{\normalfont\Large\filcenter\bfseries}
|
| 60 |
|
|
{ \vspace{1pc} \LARGE\thechapter}
|
| 61 |
|
|
{1pc} { \vspace{1pc} \Huge}
|
| 62 |
|
|
|
| 63 |
|
|
\onehalfspacing
|
| 64 |
|
|
|
| 65 |
|
|
\makeatletter
|
| 66 |
|
|
|
| 67 |
|
|
% numbering in equation by chapter
|
| 68 |
|
|
\renewcommand\theequation{\arabic{chapter}-\arabic{equation}}
|
| 69 |
|
|
\@addtoreset{equation}{chapter}
|
| 70 |
|
|
|
| 71 |
|
|
% numbering in figure by section
|
| 72 |
|
|
\renewcommand\thefigure{\arabic{chapter}-\arabic{figure}}
|
| 73 |
|
|
\@addtoreset{figure}{chapter}
|
| 74 |
|
|
|
| 75 |
|
|
% numbering in table by section
|
| 76 |
|
|
\renewcommand\thetable{\arabic{chapter}-\arabic{table}}
|
| 77 |
|
|
\@addtoreset{table}{chapter}
|
| 78 |
|
|
|
| 79 |
|
|
\makeatother
|
| 80 |
|
|
|
| 81 |
|
|
\title{\\Large\textbf{Mini AES 128}\\}
|
| 82 |
|
|
\author{Arif E. Nugroho\\
|
| 83 |
|
|
Department of Electrical Engineering\\
|
| 84 |
|
|
Institut Teknologi Bandung, Indonesia\\
|
| 85 |
|
|
e-mail: arif\_endro@yahoo.com}
|
| 86 |
|
|
\date{}
|
| 87 |
|
|
|
| 88 |
|
|
\begin{document}
|
| 89 |
|
|
|
| 90 |
|
|
\begin{titlepage}
|
| 91 |
|
|
\tt
|
| 92 |
|
|
\thispagestyle{empty}
|
| 93 |
|
|
\center
|
| 94 |
|
|
{\Large\textbf{Mini AES 128\\}}
|
| 95 |
|
|
\vspace{2.0cm}
|
| 96 |
|
|
|
| 97 |
|
|
%\begin{figure}[H]
|
| 98 |
|
|
%\center
|
| 99 |
|
|
%\includegraphics[width=4.0cm,height=4.0cm]{oc_logo.eps}
|
| 100 |
|
|
%\end{figure}
|
| 101 |
|
|
|
| 102 |
|
|
\vspace{4.5cm}
|
| 103 |
|
|
\normalsize
|
| 104 |
|
|
\textbf{Arif E. Nugroho}\\
|
| 105 |
|
|
$\overline{\textbf{arif\_endro@opencores.org}}$\\
|
| 106 |
|
|
\vspace{1.50cm}
|
| 107 |
|
|
%Progress: 60\%
|
| 108 |
|
|
\vspace{2.00cm}
|
| 109 |
|
|
\begin{figure}[H]
|
| 110 |
|
|
\center
|
| 111 |
|
|
\includegraphics[width=3.0cm,height=3.0cm]{oc_logo.eps}
|
| 112 |
|
|
\end{figure}
|
| 113 |
|
|
|
| 114 |
|
|
\vspace{1.50cm}
|
| 115 |
|
|
\textbf{
|
| 116 |
|
|
\begin{tabular}{p{4.0cm}p{10cm}}
|
| 117 |
|
|
& VLSI Research Group\\
|
| 118 |
|
|
& LabTek VIII Institut Teknologi Bandung\\
|
| 119 |
|
|
& Jl.~Ganesha 10 Bandung 40141\\
|
| 120 |
|
|
& West Java, Indonesia\\
|
| 121 |
|
|
\end{tabular}
|
| 122 |
|
|
}
|
| 123 |
|
|
|
| 124 |
|
|
\end{titlepage}
|
| 125 |
|
|
|
| 126 |
|
|
\pagenumbering{roman}
|
| 127 |
|
|
|
| 128 |
|
|
\tableofcontents
|
| 129 |
|
|
%\listoffigures
|
| 130 |
|
|
|
| 131 |
|
|
\pagestyle{fancy}
|
| 132 |
|
|
\chapter{AES 128}
|
| 133 |
|
|
|
| 134 |
|
|
\pagenumbering{arabic}
|
| 135 |
|
|
\vspace{2cm}
|
| 136 |
|
|
|
| 137 |
|
|
\section{Introduction}
|
| 138 |
|
|
|
| 139 |
|
|
The National Institute of Standards and Technology (NIST) choose the
|
| 140 |
|
|
Rijndael algorithm as the new Advanced Encryption Standard (AES) in
|
| 141 |
|
|
2001. Rijndael algorithm is a symmetric block cipher that can process
|
| 142 |
|
|
data block of 128 bits, using cipher keys with length of 128, 192, and
|
| 143 |
|
|
256 bits. The algorithm can be used on different key length and may be
|
| 144 |
|
|
referred to as "AES-128", "AES-192", and "AES-256". This crypto core is
|
| 145 |
|
|
a hardware implementation of Rijndael algorithm that process 128 bit
|
| 146 |
|
|
block of data using 128 bit key or ussually called as AES-128.
|
| 147 |
|
|
|
| 148 |
|
|
\section{Circuit Architecture}
|
| 149 |
|
|
|
| 150 |
|
|
The architecture of this implementation is based on the paper described
|
| 151 |
|
|
by P. Chodowiec \cite{chodowiec}, the schematic diagram of circuit
|
| 152 |
|
|
implementation is as follows:
|
| 153 |
|
|
|
| 154 |
|
|
\begin{figure}[H]
|
| 155 |
|
|
\center
|
| 156 |
|
|
\includegraphics[width=15cm,height=10cm]{circuit_schematic.eps}
|
| 157 |
|
|
\caption{Circuit schematic}
|
| 158 |
|
|
\label{circuit_schematic}
|
| 159 |
|
|
\end{figure}
|
| 160 |
|
|
|
| 161 |
|
|
\section{Simulation}
|
| 162 |
|
|
|
| 163 |
|
|
Simulation is done by ModelSim 6.0 SE, the simulation is performed to
|
| 164 |
|
|
verify the correctness of design. The encryption and decrption units has
|
| 165 |
|
|
been verified using Electronic Codebook (ECB) method and passed 128 test
|
| 166 |
|
|
vector verification phase of Tables Known Answer Test (KAT).
|
| 167 |
|
|
|
| 168 |
|
|
\section{Synthesize}
|
| 169 |
|
|
|
| 170 |
|
|
This design has been synthesized using ISE Xilinx 6.3i, here is the
|
| 171 |
|
|
summary of the area utilization in FPGA Xilinx:
|
| 172 |
|
|
|
| 173 |
|
|
\begin{table}[H]
|
| 174 |
|
|
\center
|
| 175 |
|
|
\includegraphics[width=8cm,height=2.5cm]{area.eps}
|
| 176 |
|
|
\caption{Area utilizations summary}
|
| 177 |
|
|
\label{area}
|
| 178 |
|
|
\end{table}
|
| 179 |
|
|
|
| 180 |
10 |
arif_endro |
The maximum clock frequency is 50.594 MHz (Minimum period 19.765ns)
|
| 181 |
2 |
arif_endro |
|
| 182 |
|
|
\section{Circuit Explanation}
|
| 183 |
|
|
|
| 184 |
|
|
\begin{figure}[H]
|
| 185 |
|
|
\center
|
| 186 |
|
|
\includegraphics[width=5cm,height=4cm]{aes128block.eps}
|
| 187 |
|
|
\caption{AES 128 Input - Output Pin}
|
| 188 |
|
|
\label{aes128block}
|
| 189 |
|
|
\end{figure}
|
| 190 |
|
|
|
| 191 |
|
|
The AES 128 is composed from four subcircuit, these subcircuit are :
|
| 192 |
|
|
\begin{itemize}
|
| 193 |
|
|
\item ShiftRow
|
| 194 |
|
|
\item SubByte
|
| 195 |
|
|
\item MixColumn
|
| 196 |
|
|
\item KeyScheduler
|
| 197 |
|
|
\end{itemize}
|
| 198 |
|
|
%These subcircuit is the main component that build AES 128.
|
| 199 |
|
|
|
| 200 |
|
|
\subsection{ShiftRow}
|
| 201 |
|
|
|
| 202 |
|
|
ShiftRow transformation is performed by arranging the sequence of input
|
| 203 |
|
|
data to be processed, these transformation is performed this way:
|
| 204 |
|
|
|
| 205 |
|
|
\begin{displaymath}
|
| 206 |
|
|
\left\{
|
| 207 |
|
|
\begin{array}{lcl}
|
| 208 |
|
|
input & & output \\
|
| 209 |
|
|
0,5,a,f & => & 0,1,2,3\\
|
| 210 |
|
|
4,9,e,3 & => & 4,5,6,7\\
|
| 211 |
|
|
8,d,2,7 & => & 8,9,a,b\\
|
| 212 |
|
|
c,1,6,b & => & c,d,e,f\\
|
| 213 |
|
|
\end{array}
|
| 214 |
|
|
\right\}
|
| 215 |
|
|
\end{displaymath}
|
| 216 |
|
|
|
| 217 |
|
|
the InvShiftRow transformations operations is performed using the
|
| 218 |
|
|
following sequence of input data:
|
| 219 |
|
|
|
| 220 |
|
|
\begin{displaymath}
|
| 221 |
|
|
\left\{
|
| 222 |
|
|
\begin{array}{lcl}
|
| 223 |
|
|
input & & output \\
|
| 224 |
|
|
0,d,a,7 & => & 0,1,2,3\\
|
| 225 |
|
|
4,1,e,b & => & 4,5,6,7\\
|
| 226 |
|
|
8,5,2,f & => & 8,9,a,b\\
|
| 227 |
|
|
c,9,6,3 & => & c,d,e,f\\
|
| 228 |
|
|
\end{array}
|
| 229 |
|
|
\right\}
|
| 230 |
|
|
\end{displaymath}
|
| 231 |
|
|
|
| 232 |
|
|
\subsection{SubByte}
|
| 233 |
|
|
|
| 234 |
|
|
SubByte transformation is implemented using dedicated block RAM, SubByte
|
| 235 |
|
|
transformation occupy 4 Kb Block RAM in 512x8 configurations.
|
| 236 |
|
|
|
| 237 |
|
|
\subsection{MixColumn}
|
| 238 |
|
|
|
| 239 |
|
|
The MixColumn is implemented using matrix calculation of following equation:
|
| 240 |
|
|
|
| 241 |
|
|
\begin{equation}
|
| 242 |
|
|
c(x) =~'03'~x^3 +~'01'~x^2 +~'01'~x +~'02'.
|
| 243 |
|
|
\end{equation}
|
| 244 |
|
|
|
| 245 |
|
|
matrix form of above equation is:
|
| 246 |
|
|
|
| 247 |
|
|
\begin{displaymath}
|
| 248 |
|
|
\left[ \begin{array}{c} b_0\\ b_1\\ b_2\\ b_3\\ \end{array} \right]
|
| 249 |
|
|
=
|
| 250 |
|
|
\left[ \begin{array}{c} 02~03~01~01\\ 01~02~03~01\\ 01~01~02~03\\ 03~01~01~02\\ \end{array} \right]
|
| 251 |
|
|
\left[ \begin{array}{c} a_0\\ a_1\\ a_2\\ a_3\\ \end{array} \right]
|
| 252 |
|
|
\end{displaymath}
|
| 253 |
|
|
|
| 254 |
|
|
The InvMixColumn operations is performed using following equation:
|
| 255 |
|
|
|
| 256 |
|
|
\begin{equation}
|
| 257 |
|
|
d(x) =~'0b'~x^3 +~'0d'~x^2 +~'09'~x +~'0e'.
|
| 258 |
|
|
\end{equation}
|
| 259 |
|
|
|
| 260 |
|
|
in matrix representation is:
|
| 261 |
|
|
|
| 262 |
|
|
\begin{displaymath}
|
| 263 |
|
|
\left[ \begin{array}{c} d_0\\ d_1\\ d_2\\ d_3\\ \end{array} \right]
|
| 264 |
|
|
=
|
| 265 |
|
|
\left[ \begin{array}{c} 0e~0b~0d~09\\ 09~0e~0b~0d\\ 0d~09~0e~0b\\ 0b~0d~09~0e\\ \end{array} \right]
|
| 266 |
|
|
\left[ \begin{array}{c} c_0\\ c_1\\ c_2\\ c_3\\ \end{array} \right]
|
| 267 |
|
|
\end{displaymath}
|
| 268 |
|
|
|
| 269 |
|
|
The InvMixColumn can be implemented using resource sharing, by following
|
| 270 |
|
|
equation:
|
| 271 |
|
|
|
| 272 |
|
|
\begin{equation}
|
| 273 |
|
|
c(x) \otimes d(x) =~'01'
|
| 274 |
|
|
\end{equation}
|
| 275 |
|
|
|
| 276 |
|
|
then if we multiply both side with $d^2(x)$ then it become:
|
| 277 |
|
|
|
| 278 |
|
|
\begin{equation}
|
| 279 |
|
|
c(x) \otimes d^2(x) = d(x)
|
| 280 |
|
|
\end{equation}
|
| 281 |
|
|
|
| 282 |
|
|
above equation state that we can get the InvMixColumn using
|
| 283 |
|
|
multiplication of MixColumn operations and $d^2(x)$:
|
| 284 |
|
|
|
| 285 |
|
|
\begin{equation}
|
| 286 |
|
|
d^2(x) =~'04'~x^2 +~'05'.
|
| 287 |
|
|
\end{equation}
|
| 288 |
|
|
|
| 289 |
|
|
and matrix representation of above equation is:
|
| 290 |
|
|
|
| 291 |
|
|
\begin{displaymath}
|
| 292 |
|
|
\left[ \begin{array}{c} e_0\\ e_1\\ e_2\\ e_3\\ \end{array} \right]
|
| 293 |
|
|
=
|
| 294 |
|
|
\left[ \begin{array}{c} 05~00~04~00\\ 00~05~00~04\\ 04~00~05~00\\ 00~04~00~05\\ \end{array} \right]
|
| 295 |
|
|
\left[ \begin{array}{c} c_0\\ c_1\\ c_2\\ c_3\\ \end{array} \right]
|
| 296 |
|
|
\end{displaymath}
|
| 297 |
|
|
|
| 298 |
|
|
\subsection{KeyScheduler}
|
| 299 |
|
|
|
| 300 |
|
|
The KeyScheduler is implemented using the following schematic diagram:
|
| 301 |
|
|
|
| 302 |
|
|
\begin{figure}[H]
|
| 303 |
|
|
\center
|
| 304 |
|
|
\includegraphics[width=9cm,height=6cm]{key_scheduler.eps}
|
| 305 |
|
|
\caption{KeyScheduler Schematics}
|
| 306 |
|
|
\label{key_scheduler}
|
| 307 |
|
|
\end{figure}
|
| 308 |
|
|
|
| 309 |
|
|
\section{TODO}
|
| 310 |
|
|
|
| 311 |
|
|
\begin{itemize}
|
| 312 |
|
|
%\item Finish decryption circuit.
|
| 313 |
|
|
\item Optimize Key Scheduler storage allocations implementations.
|
| 314 |
|
|
\item Optimize folded register implementation.
|
| 315 |
|
|
\item Implement TriState Buffer for switching SubBytes utilization.
|
| 316 |
|
|
\item Update documentation.
|
| 317 |
|
|
\item CleanUp code.
|
| 318 |
|
|
\end{itemize}
|
| 319 |
|
|
|
| 320 |
|
|
\begin{thebibliography}{1}
|
| 321 |
|
|
|
| 322 |
|
|
\bibitem{chodowiec}
|
| 323 |
|
|
Pawel Chodowiec and Kris Gaj, \textbf{Very Compact FPGA Implementation
|
| 324 |
|
|
of the AES Algorithm}, CHES 2003, LNCS 2779, pp. 319-333
|
| 325 |
|
|
|
| 326 |
|
|
\bibitem{fips197}
|
| 327 |
|
|
Federal Information Processing Standards Publication 197,
|
| 328 |
|
|
\textbf{Advanced Encryption Standard (AES)}, National Institute of
|
| 329 |
|
|
Standards and Technology, 2001.
|
| 330 |
|
|
|
| 331 |
|
|
\bibitem{rijndael}
|
| 332 |
|
|
Daemen J. and Rijmen V., \textbf{AES Proposal: The Rijndael Block Cipher},\\
|
| 333 |
|
|
\href{http://www.esat.kuleuven.ac.be/~rijmen/rijndael/Rijndael.pdf}{http://www.esat.kuleuven.ac.be/\~~rijmen/rijndael/Rijndael.pdf}
|
| 334 |
|
|
|
| 335 |
|
|
%\bibitem{wada}
|
| 336 |
|
|
%Tom Wada, \textbf{2-D Product Code Iterative Decoder},\\
|
| 337 |
|
|
%\href{http://www.ie.u-ryukyu.ac.jp/\~\ wada/design06/spec\_e.html}
|
| 338 |
|
|
% {http://www.ie.u-ryukyu.ac.jp/\~\ wada/design06/spec\_e.html}\\
|
| 339 |
|
|
% October 1$^{st}$, 2005
|
| 340 |
|
|
|
| 341 |
|
|
\end{thebibliography}
|
| 342 |
|
|
|
| 343 |
|
|
\appendix
|
| 344 |
|
|
|
| 345 |
|
|
\chapter{Informations}
|
| 346 |
|
|
|
| 347 |
|
|
\section{Tools}
|
| 348 |
|
|
|
| 349 |
|
|
\begin{itemize}
|
| 350 |
|
|
\item \textbf{ModelSim 6.0} The Simulator
|
| 351 |
|
|
\item \textbf{Xilinx 6.3i} The Synthesizer
|
| 352 |
|
|
\item \textbf{VIM} (Vi IMproved) / \textbf{Emacs} The Editor
|
| 353 |
|
|
\item \textbf{\LaTeX}~~The Typesetter
|
| 354 |
|
|
\item \textbf{OpenOffice.org 2.0} The Drawer
|
| 355 |
|
|
\end{itemize}
|
| 356 |
|
|
|
| 357 |
|
|
\vspace{1cm}
|
| 358 |
|
|
\begin{tabbing}
|
| 359 |
|
|
\textbf{Version: 1.0}
|
| 360 |
|
|
\end{tabbing}
|
| 361 |
|
|
|
| 362 |
|
|
\end{document}
|
