{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 
{CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 
0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 
0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out
put" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "
" 3 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Codage RSA :" }}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 19 "Choix des nombres :" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 44 "p:=389;q:=167;k:=17;n:=p*q;phi:=(p-1)*(q-1);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"$*Q" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"qG\"$n\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG
\"#<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"&j\\'" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$phiG\"&3W'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "(phi mod k)*[1,2,3,4,5,6,7,8] mod k;alpha:=(7*phi+1)/
k;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*\"#7\"\"(\"\"#
\"#9\"\"*\"\"%\"#;\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"&
@l#" }}}}{SECT 1 {PARA 256 "" 0 "" {TEXT -1 37 "Proc\351dures de passa
ge lettre/nombre :" }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 79 "a <=> 1 : b
 <=> 2 : c <=> 3 : d <=> 4          ...     ...           \347 <=> 113
." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 263 16 "Proc\351dures RSA :" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 258 94 "Coder : c = m^k mod [n].         \+
                               D\351coder : c^alpha mod [n] = m." }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Exemples :" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 91 "codersa(`Bonjour tout le monde! Voici une appl
ication du syst\350me de codage RSA.`,17,64963);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%bo|dyR8j|`z-33/cCZXk=vD|_yc@|_zFgq|cyPk|_u#i^|dz&:9ku
\"XP<n'|cu\"pAxXM|byO+t|fywJFKD[z;J*v|^y|[y|fyMaG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 25 "decodersa(%,26521,64963);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%aoBonjour~tout~le~monde!~Voici~une~application~du~sy
st|cyme~de~codage~RSA.G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 88 "Temps
 de codage : 4 secondes.               Temps de d\351codage : 1 minute
 et 31 secondes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "coders
a(`Plus les nombres sont grands, plus il sera difficile de \"pirater\"
 le message.`,26521,64963);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%houZ|h
r*0[q9[JiPnYa!c6|^u|^u_fez!|dy|gzn_pj|fzb\"et|ir)CL5|_y[|iy|cy|fyTDY|j
yxrhX|`vUA|_uS1h!KDpL1|iym|]yD9:e\"J.G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "decodersa(%,17,64963);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%hoPlus~les~nombres~sont~grands,~plus~il~sera~difficile~de~\"pir
ater\"~le~message.G" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Piratag
e :" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Exemples :" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 260 49 " Pour casser le RSA, il suffit de factor
iser \"n\"." }}{PARA 0 "" 0 "" {TEXT 256 80 "On avait n = 64 963 : la \+
factorisation donne instantan\351ment p et q : 389 et 167." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ifactor(334464374000377840101700070
2389103);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%!G6#\"2hB,+++%o_\"\"
\"-F%6#\"2Bo0+++&[jF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 83 "Temps d
e calcul : 2 minutes et 45 secondes         (pour un nombre de 34 chif
fres)." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Nombres premiers :" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "nextprime(12785496834578965
847*10^180+12548968687535489658);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
\"cw$f!\\Nvoo*[D,+++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++++++++++++++++++++++q%e'*yX$o\\&y7" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 262 84 "Temps de calcul : 1 minute et 54 secondes          (pour
 un nombre de 200 chiffres)." }}}}}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 
1803 }