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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 11 "Secure mail" }}{PARA 
258 "" 0 "" {TEXT -1 38 "\251 Mike May, S. J., 2002, maymk@slu.edu" }}
}{EXCHG {PARA 259 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 
260 "" 0 "" {TEXT -1 225 "We want to look at sending a collection of c
oncepts we have been working on in class for an application like sendi
ng and receiving secured mail.  We will use DES as our symmetric block
 cipher and RSA as our public key cipher." }}{PARA 261 "" 0 "" {TEXT 
-1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 309 "The intent is to be able to \+
send an encrypted message over an open channel in such a way that it i
s secure from eavesdropping, and such that the intended recipient know
s who sent the message and that it has not been tampered with.  (The r
ecipient should be assured to both message integrity and authenticity.
)" }}}{EXCHG {PARA 263 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 
264 "" 0 "" {TEXT -1 22 "Encrypting the message" }}{EXCHG {PARA 265 "
" 0 "" {TEXT -1 48 "We start with a message that we will be sending." 
}}}{EXCHG {PARA 266 "> " 0 "" {MPLTEXT 1 0 591 "message := \"This is a
n attempt to look at a reasonable way to send a message\nin such a way
 that it is encrypted, but that the receiver can also revify that\nthe
 message is really from me, and that no one has tampered with it after
 I\nsigned the message.  There are several pieces to deal with.  I nee
d to hash\nthe message down to a digest of reasonable length.  We will
 do that with DES.\nAfter we have a hashed digest, we sign it with RSA
.  Then, since I want to have \nthe message decrypted by the intended \+
recipient alone, I encrypt the session key\nwith RSA and the receiver'
s public key. x\":" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 431 "We want \+
to encrypt the message with DES used in Cipher Block Chaining mode.  Y
ou can either rerun the DES constants and DES functions worksheets to \+
load the constants and commands, or you can read them in from a file. \+
 To read the DES.m file, you need to copy the file to the current dire
ctory.  On a Macintosh, that is the directory with the Maple applicati
on.  The current directory can be determined by the currentdir() comma
nd." }}}{EXCHG {PARA 268 "> " 0 "" {MPLTEXT 1 0 13 "currentdir();" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#Q)C:\\maple6\"" }}}{EXCHG {PARA 269 "
" 0 "" {TEXT -1 158 "Either copy DES.m to the current directory before
 proceeding or create it on your own machine by running the DESConstan
ts.mws and DESFunctions.mws worksheets." }}}{EXCHG {PARA 270 "> " 0 "
" {MPLTEXT 1 0 13 "read `DES.m`;" }}}{EXCHG {PARA 271 "" 0 "" {TEXT 
-1 276 "To prepare the message for encryption with DES, we want to bre
ak it into hex words of 64 bits.  Each word corresponds to 8 ASCII cha
racters, so we pad the message out with null characters so that the nu
mber of characters is divisible by 8.  We also record the number of wo
rds." }}}{EXCHG {PARA 272 "> " 0 "" {MPLTEXT 1 0 104 "messLength := le
ngth(message);\nmessWords := ceil(messLength/8);\nmessPadding := 8*mes
sWords - messLength;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+messLengthG
\"$x&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*messWordsG\"#t" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%,messPaddingG\"\"(" }}}{EXCHG {PARA 273 ">
 " 0 "" {MPLTEXT 1 0 88 "messList := convert(message, bytes):\nmessLis
t := [op(messList),seq(0,i=1..messPadding)]:" }}}{EXCHG {PARA 274 "> \+
" 0 "" {MPLTEXT 1 0 63 "intTo2Hex := intVal -> substring(convert(intVa
l+256,hex),2..3):" }}}{EXCHG {PARA 275 "> " 0 "" {MPLTEXT 1 0 119 "mes
sHexList := map(intTo2Hex,messList):\nmessHexWordList := [seq(cat(seq(
messHexList[8*i+j],j=1..8)),i=0..messWords-1)];" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%0messHexWordListG7eo%15468697320697320G%1616E20617474
656DG%1707420746F206C6FG%16F6B206174206120G%1726561736F6E6162G%16C6520
7761792074G%16F2073656E642061G%1206D657373616765G%10A696E2073756368G%1
2061207761792074G%16861742069742069G%17320656E63727970G%17465642C20627
574G%12074686174207468G%16520726563656976G%165722063616E2061G%16C736F2
072657669G%1667920746861740AG%1746865206D657373G%16167652069732072G%16
5616C6C79206672G%16F6D206D652C2061G%16E64207468617420G%16E6F206F6E6520
68G%161732074616D7065G%17265642077697468G%12069742061667465G%17220490A
7369676EG%1656420746865206DG%16573736167652E20G%12054686572652061G%172
65207365766572G%1616C207069656365G%17320746F20646561G%16C20776974682E2
0G%12049206E65656420G%1746F20686173680AGF8%161676520646F776EG%120746F2
061206469G%167657374206F6620GF*%16C65206C656E6774G%1682E202057652077G%
1696C6C20646F2074G%16861742077697468G%1204445532E0A4166G%1746572207765
2068G%16176652061206861G%17368656420646967G%16573742C20776520G%1736967
6E20697420G%17769746820525341G%12E20205468656E2CG%12073696E63652049G%1
2077616E7420746FG%12068617665200A74G%16865206D65737361G%16765206465637
279G%17074656420627920G%174686520696E7465G%16E64656420726563G%16970696
56E742061G%16C6F6E652C204920G%1656E637279707420G%17468652073657373G%16
96F6E206B65790AGFX%120616E6420746865G%12072656365697665G%1722773207075
626CG%16963206B65792E20G%17800000000000000G" }}}{EXCHG {PARA 276 "" 0 
"" {TEXT -1 195 "To encrypt this message with DES in CBC mode I need a
 key and an initial value.  We choose the key at random.  (This ignore
s the fine point that every eighth bit of a key should be a parity bit
.)" }}}{EXCHG {PARA 277 "> " 0 "" {MPLTEXT 1 0 59 "randKey := substrin
g(convert(2^64+rand(2^64)(),hex),2..17);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%(randKeyG%17778EEFFF432E596G" }}}{EXCHG {PARA 278 "" 0 "" 
{TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT -1 130 "In order to reproduce res
ults we record the key as 7778EEFFF432E596.  We expand this key with t
he command from the DES worksheets." }}}{EXCHG {PARA 279 "> " 0 "" 
{MPLTEXT 1 0 59 "randKey := \"7778EEFFF432E596\":\nkey := keyexpander(
randKey):" }}}{EXCHG {PARA 280 "" 0 "" {TEXT -1 63 "Our initial value \+
will be the zero word encrypted with our key." }}}{EXCHG {PARA 281 "> \+
" 0 "" {MPLTEXT 1 0 81 "allZeroes := substring(convert(2^64+0,hex),2..
17);\nIV := qdDEShex(allZeroes,key);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%*allZeroesG%10000000000000000G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#IVGQ104844CB2337C0CC26\"" }}}{EXCHG {PARA 282 "" 0 "" {TEXT -1 180 
"We now encrypt the message with with DES in CBC mode.  The first word
 uses the initial value and the first word of the message.  The rest o
f the message in then encrypted in a loop" }}}{EXCHG {PARA 283 "> " 0 
"" {MPLTEXT 1 0 176 "cipherTable[1] := qdDEShex(xor64hex(IV,messHexWor
dList[1]),key);\nfor i from 2 to messWords do\ncipherTable[i] := qdDES
hex(xor64hex(cipherTable[i-1],messHexWordList[i]),key):\nod:" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%,cipherTableG6#\"\"\"%1CFE5523C29D556BFG
" }}}{EXCHG {PARA 284 "" 0 "" {TEXT -1 112 "Time for a technical adjus
tment.  We want to convert the format of the encrypted message from a \+
table to a list." }}}{EXCHG {PARA 285 "> " 0 "" {MPLTEXT 1 0 40 "ciphe
rList := convert(cipherTable,list);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#>%+cipherListG7eo%1CFE5523C29D556BFG%196F0272D4A3A54E4G%17EB9FE4EDA6B
B7F5G%197AE9F3B9962C5A5G%11347D0568C88B728G%1C623BCA4F38195DCG%1F933A4
B073ED3112G%1B91012489AC26DAEG%1EFD8057D6FD221BDG%11295F50C701D1D2AG%1
6F6DFA21417FAA4AG%17141B83C93FD20B6G%1E69DCE99E7250748G%1FE176522609FF
31BG%14A4C6F06D3777871G%1AF0F92A74F6BEC46G%162FD8DDE9EE32D60GQ10CB6D35
244F2E4426\"%16A967981EA02B712G%172CC1609326E70E8G%1B0DED0ECA222C388G%
1752B36EFD2577F58G%1453BB651C1E38943G%1281EAA993BC733C8G%1266339ECE05A
EC2BG%1F042F363E0407FC0G%1399568B48B4DEE1BG%16795E99D5464A384G%1BC17EA
AC8D5E4668G%1D1350C559437085CG%18A713C993AC9797FG%1409D82BB0A4E31E9G%1
DB5C8F9438DD8E47G%1F0FAB6F37EC1D37EG%12ABA3EB9FD4F2880G%146416F72365B3
D50G%1B85739A2776D053FG%184FC96A4F62FAC39G%15ABF5E07AA8AD34EG%1A0FDF34
99984D67FG%1F3FCD3D6AC6AEF93G%1A14644D8C85838D1G%1E7D72469150DBA19G%12
E1D829A60388C20G%16718F326DB8347C4G%13E0135B8172EB1DCG%1B0628989325F47
F9G%14F43A4AE9F3A3E8AG%19B734D47D058A4FAG%110D0EC2185334AA9G%157DD05A5
68A1298AG%1F3950DBD3FD36DD1GQ10001188AEE7CE1F2F8%1919E055417230178G%16
5E51F33A12038C2G%19CAB5B56319968D5G%1541D06B4F4BED47AG%137CB3A45D19969
8EGQ1077BAFF5CA62F4B8F8%1E75D714902E9AF89G%1A587EDFFCD7870A1G%113D9E02
08439CA65G%18FA36034F7CFB55DG%15FE1295449ED3D04GQ1074B76973A2AD3CAF8%1
3240DED15561C814G%19700F1A93DB61F1EGQ10B1A9419B9D4DEDEF8%1C7541B456A78
272FG%1B6919537C24376E3G%1D3EC4451D3A8B3B6G%129D4B2C2FF8D4A48G%17C54E0
8D43AEC1AFG" }}}{EXCHG {PARA 286 "" 0 "" {TEXT -1 35 "Thus we have enc
rypted the message." }}}}{SECT 0 {PARA 287 "" 0 "" {TEXT -1 47 "Signin
g the hash and encrypting the session key" }}{EXCHG {PARA 288 "" 0 "" 
{TEXT -1 115 "For the purpose of digital signatures, we will consider \+
the last word of the message to be the hash of the message." }}}
{EXCHG {PARA 289 "> " 0 "" {MPLTEXT 1 0 30 "hash := cipherList[messWor
ds];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%hashG%17C54E08D43AEC1AFG" }
}}{EXCHG {PARA 290 "" 0 "" {TEXT -1 286 "We want to use RSA for two fu
nctions.  We want to encrypt the session key so our recipient can decr
ypt the message.  We also want to sign the hash.  To sign the hash wit
h RSA we produce our primes and our public n.  We then set 2^16 + 1 as
 our standard encryption key, and we compute d." }}}{EXCHG {PARA 291 "
> " 0 "" {MPLTEXT 1 0 63 "p := nextprime(rand(10^80)());;\nq := nextpr
ime(rand(10^80)());;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"[ptSh0
Vgo<7uHs&3AA1K!Q0$QvYn(*=(e%eNcVhDuuptI$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"qG\"[pJT$))\\g\\nr0V)3gTfp\"RqX!\\zrzjr[v+JbE&>\")f#4u.!)" }
}}{EXCHG {PARA 292 "> " 0 "" {MPLTEXT 1 0 286 "Senderp := 330736974742
56143563558458718976746753830538032062222085722974121768604305614073:
\nSenderq := 800374092598119526553100754871637971794904570391695941600
88430571674960498834131:\nSendern := Senderp*Senderq;\nSendere := 2^16
+1;\nSenderd := (1/Sendere) mod ((Senderp-1)*(Senderq-1)):" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%(SendernG\"[ujbKEX$fepG264V)3x3M([O>l%pIc*
)pWwLSfq%[eC]NtQ2]%>o_M$y-#ygTk8`!oJ^[B#H^j^9twa&yC#[gI8ZE" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(SendereG\"&Pb'" }}}{EXCHG {PARA 293 "" 0 
"" {TEXT -1 111 "We publish (Sendern, Sendere) as our public key.  To \+
sign the hash we encrypt the hash with our decryption key." }}}{EXCHG 
{PARA 294 "> " 0 "" {MPLTEXT 1 0 127 "digestNum := convert(hash, decim
al, hex);\nsignature := Power(digestNum,Senderd) mod Sendern;\nsigHex \+
:= convert(signature, hex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*dige
stNumG\"4ZgHxgXK!f*)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*signatureG
\"[uq5Ht7()Q!o0(*f$*H-1;Hz#zK_0WscF&fp'R$*[.I]FaM%4s`OV=1WicIEm&)>#yMh
+GXtHLU$[d(oBO*3;Tz-P)fC" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'sigHexG
%`s2CCA706E7E7864A48915A4B0A2A3EF20D56C920BD79B48B15B66B982576BEB36884
15EECC0474C48649ED7AC322A9DFD7E811221FFB0DA8EC67B66EF51C721323BD3EG" }
}}{EXCHG {PARA 295 "" 0 "" {TEXT -1 86 "To encrypt the session key, we
 need the receiver's public key, (Receivern, Receivere)." }}}{EXCHG 
{PARA 296 "> " 0 "" {MPLTEXT 1 0 63 "p := nextprime(rand(10^80)());;\n
q := nextprime(rand(10^80)());;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"pG\"[prMw!fb\")>2j[Yh3IN0^*\\t%\\i?zI&RJSkh%>qu`k\"zX?" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"qG\"[pj$)yqknt%4NZXowLH)fnu$*4g(>7)*31gsK(4^
Ga_4Pn#*" }}}{EXCHG {PARA 297 "> " 0 "" {MPLTEXT 1 0 306 "Receiverp :=
 204579164537470194616440313953079206249473499510535300861464863071981
55590763471:\nReceiverq := 9267370952542851097327260060898121976009937
4675982933766845473509473676470788363:\nReceivern := Receiverp*Receive
rq;\nReceivere := 2^16+1:\nReceiverd := (1/Receivere) mod ((Receiverp-
1)*(Receiverq-1));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*ReceivernG\"[
utzGK%GU3/]tIh?9rgsVXVvk1X`&fu_yo\"4yb*=$***)Rl*p^wQ.$3%R\"4VgC&RxZ=QG
fs0%)ywHbk86#e.Ip+6f*=" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*Receiverd
G\"[uLQ3MsX*Qz%>pA=vXeGC!*o+'G!p.ivJCzPs9f&\\#Q!*[T,&oD1*\\!*oDVVKAa:@
rSn?6NH%))R0ToyVUBuyF)yV$p\"" }}}{EXCHG {PARA 298 "> " 0 "" {MPLTEXT 
1 0 138 "keyNum := convert(randKey, decimal, hex);\nencryptKey := Powe
r(keyNum, Receivere) mod Receivern:\nencryptKeyHex := convert(encryptK
ey, hex);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'keyNumG\"4]0v*zqM*)3')
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%.encryptKeyHexG%`s10F36CDAE57F66
5A367984588EC59ACACFD57D31338F7C119F57E5AFE25B13E06BB669508542CE257DB9
55EE4BD8840830EE5C728A470EEC8E267BBCB113000F29C5EG" }}}}{SECT 0 {PARA 
299 "" 0 "" {TEXT -1 11 "The message" }}{EXCHG {PARA 300 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 301 "" 0 "" {TEXT -1 44 "Putting thi
ngs together we have our message." }}{PARA 302 "" 0 "" {TEXT -1 0 "" }
}{PARA 303 "" 0 "" {TEXT -1 1453 "cipherList := [CFE5523C29D556BF, \"9
6F0272D4A3A54E4\", \"7EB9FE4EDA6BB7F5\", \"97AE9F3B9962C5A5\", \"1347D
0568C88B728\", C623BCA4F38195DC, F933A4B073ED3112, B91012489AC26DAE, \+
\"88AC794BF81A3613\", \"027979270A6CE25E\", \"1FF04858A850FB18\", \"72
B6F715E5F0B050\", \"302DA487928942DD\", \"400825FF341D62FF\", \"25BAB3
DFAA300C6E\", DF6548D262CCDB76, \"155112EEC2A35653\", \"3626EB94C95083
87\", F923D7D04BA91C3C, \"4541DD7ED88DF681\", B80954BD64B25BD1, E5DDE2
260FA80D54, \"553431C417C63262\", \"238AEC42B48D39F9\", \"001F68168A03
DC79\", F0F26735387BEAFE, ABF29815E6EEF280, \"1CE591E013397E46\", AE25
3A8F2CB920F5, \"6CDD5CF57DB814E9\", \"538EDF12831AAF07\", D16DA28C099F
BCD2, \"16EA042321E8C07C\", \"4B4E3A3A240CD134\", \"008A4839BB5A902A\"
, \"1D9EF4F67B9D790F\", \"315D4ABFE6FD552A\", \"5B8EC53DB56BE2F0\", \"
8764D129BE79A2AE\", E468BD18F31EFC89, \"041B1B2EDD8609F2\", \"94084157
231C1D69\", \"7592C6C37E571E88\", \"1AE32E4143FDBD02\", \"4F46C82DF30E
8C7B\", C4CEC8AC4B918453, \"43B15827F8831008\", F47E5AA003E98FEC, \"5B
2581BC8F0D5FD8\", \"2463B68E42F65963\", \"614F5FEFF34EECE6\", \"1F5FBB
2D65D5D1B0\", EE611B55060418A9, \"78EDFE10B983D58F\", E0DCBAE6A02405A2
, \"089157D36419A8A8\", A82D7722C7302B21, \"755443BF881CDAA8\", \"9F9A
275493C95772\", \"673AF1ED886F45FA\", \"1666C6E7E5F342ED\", C44E2FB386
806250, EC429290D9DE3961, D69AFA699BC1B350, A558FC5AD6134C13, \"3836A7
16B9D63336\", FAA592E49F503D7B, \"793C737ADDBD5ECE\", \"00912BAFAE5F4E
4F\", \"1C297C183126E230\", \"6A69015002985748\", \"01A14542FEBCBC8E\"
, D058ADE681825447];\nhash := D058ADE681825447;" }}{PARA 304 "" 0 "" 
{TEXT -1 299 "sigHex := \"151746B988F8A7879A20548871F96A4D40CE8CBFB826
381F26183F2209C8D4E75460CC3617781B018BEF0DB767E18ECE809551514E0479C54F
188697160FCD867C088\"\nencryptKeyHex := \"10F36CDAE57F665A367984588EC5
9ACACFD57D31338F7C119F57E5AFE25B13E06BB669508542CE257DB955EE4BD8840830
EE5C728A470EEC8E267BBCB113000F29C5E\";" }}{PARA 305 "" 0 "" {TEXT -1 
188 "Sendern := 264713306048224785547673145163512922348513168053136441
6078202783345268194500738733550245848470594033764469895630694651936487
340877088430911072869585934526325563\nSendere := 65537" }}}{EXCHG 
{PARA 306 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 307 "" 0 "" 
{TEXT -1 19 "Reading the message" }}{EXCHG {PARA 308 "" 0 "" {TEXT -1 
198 "To put ourselves in the position of the receiver, we restart to c
lear the memory.  The receiver knows the public key of the sender and \+
the receiver's private key.  The receiver also has our message." }}}
{EXCHG {PARA 309 "> " 0 "" {MPLTEXT 1 0 22 "restart;\nread `DES.m`:" }
}}{EXCHG {PARA 310 "> " 0 "" {MPLTEXT 1 0 540 "Receivern := 1895911006
9300358211136455297678840572592838184777395246043091394083033876516996
5398999318955780916878527459553450664754345437260711420613073500408422
8432287973:\nReceiverd := 16934378827787423424378684105398842935112067
4071211554223243432568904990625685014148903824955914723779243175620369
0286006890242858457518226919479389457234083833:\nSendern := 2647133060
4822478554767314516351292234851316805313644160782027833452681945007387
3355024584847059403376446989563069465193648734087708843091107286958593
4526325563:\nSendere := 65537:" }}}{EXCHG {PARA 311 "> " 0 "" 
{MPLTEXT 1 0 1728 "cipherList := [CFE5523C29D556BF, \"96F0272D4A3A54E4
\", \"7EB9FE4EDA6BB7F5\", \"97AE9F3B9962C5A5\", \"1347D0568C88B728\", \+
C623BCA4F38195DC, F933A4B073ED3112, B91012489AC26DAE, \"88AC794BF81A36
13\", \"027979270A6CE25E\", \"1FF04858A850FB18\", \"72B6F715E5F0B050\"
, \"302DA487928942DD\", \"400825FF341D62FF\", \"25BAB3DFAA300C6E\", DF
6548D262CCDB76, \"155112EEC2A35653\", \"3626EB94C9508387\", F923D7D04B
A91C3C, \"4541DD7ED88DF681\", B80954BD64B25BD1, E5DDE2260FA80D54, \"55
3431C417C63262\", \"238AEC42B48D39F9\", \"001F68168A03DC79\", F0F26735
387BEAFE, ABF29815E6EEF280, \"1CE591E013397E46\", AE253A8F2CB920F5, \"
6CDD5CF57DB814E9\", \"538EDF12831AAF07\", D16DA28C099FBCD2, \"16EA0423
21E8C07C\", \"4B4E3A3A240CD134\", \"008A4839BB5A902A\", \"1D9EF4F67B9D
790F\", \"315D4ABFE6FD552A\", \"5B8EC53DB56BE2F0\", \"8764D129BE79A2AE
\", E468BD18F31EFC89, \"041B1B2EDD8609F2\", \"94084157231C1D69\", \"75
92C6C37E571E88\", \"1AE32E4143FDBD02\", \"4F46C82DF30E8C7B\", C4CEC8AC
4B918453, \"43B15827F8831008\", F47E5AA003E98FEC, \"5B2581BC8F0D5FD8\"
, \"2463B68E42F65963\", \"614F5FEFF34EECE6\", \"1F5FBB2D65D5D1B0\", EE
611B55060418A9, \"78EDFE10B983D58F\", E0DCBAE6A02405A2, \"089157D36419
A8A8\", A82D7722C7302B21, \"755443BF881CDAA8\", \"9F9A275493C95772\", \+
\"673AF1ED886F45FA\", \"1666C6E7E5F342ED\", C44E2FB386806250, EC429290
D9DE3961, D69AFA699BC1B350, A558FC5AD6134C13, \"3836A716B9D63336\", FA
A592E49F503D7B, \"793C737ADDBD5ECE\", \"00912BAFAE5F4E4F\", \"1C297C18
3126E230\", \"6A69015002985748\", \"01A14542FEBCBC8E\", D058ADE6818254
47]:\nsigHex := \"151746B988F8A7879A20548871F96A4D40CE8CBFB826381F2618
3F2209C8D4E75460CC3617781B018BEF0DB767E18ECE809551514E0479C54F18869716
0FCD867C088\":\nencryptKeyHex := \"10F36CDAE57F665A367984588EC59ACACFD
57D31338F7C119F57E5AFE25B13E06BB669508542CE257DB955EE4BD8840830EE5C728
A470EEC8E267BBCB113000F29C5E\":" }}}{EXCHG {PARA 312 "" 0 "" {TEXT -1 
39 "Check first that the signature matches." }}}{EXCHG {PARA 313 "> " 
0 "" {MPLTEXT 1 0 145 "signature := convert(sigHex, decimal, hex):\nsi
gD := Power(signature,Sendere) mod Sendern;\nhashRecover := substring(
convert(2^64+sigD,hex),2..17);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%s
igDG\"5jQVmLcSH,:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,hashRecoverG%1
D058ADE681825447G" }}}{EXCHG {PARA 314 "" 0 "" {TEXT -1 76 "Next the r
eceiver recovers the session key using the receiver's private key;" }}
}{EXCHG {PARA 315 "> " 0 "" {MPLTEXT 1 0 163 "encryptKey := convert(en
cryptKeyHex,decimal,hex):\nkeyNum := Power(encryptKey, Receiverd) mod \+
Receivern:\nsessionKey := substring(convert(keyNum + 2^64, hex),2..17)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+sessionKeyG%17778EEFFF432E596G
" }}}{EXCHG {PARA 316 "" 0 "" {TEXT -1 90 "Now the receiver starts dec
rypting the message with the standard procedure for CBC mode.  " }}}
{EXCHG {PARA 317 "> " 0 "" {MPLTEXT 1 0 113 "key := keyexpander(sessio
nKey):\nallZeroes := substring(convert(2^64+0,hex),2..17):\nIV := qdDE
Shex(allZeroes,key);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#IVGQ104844C
B2337C0CC26\"" }}}{EXCHG {PARA 318 "> " 0 "" {MPLTEXT 1 0 41 "messWord
s := linalg[vectdim](cipherList);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%*messWordsG\"#t" }}}{EXCHG {PARA 319 "> " 0 "" {MPLTEXT 1 0 165 "plai
nTable[1] := xor64hex(unDEShex(cipherList[1],key), IV):\nfor i from 2 \+
to messWords do\nplainTable[i] := xor64hex(unDEShex(cipherList[i],key)
, cipherList[i-1]);\nod:" }}}{EXCHG {PARA 320 "> " 0 "" {MPLTEXT 1 0 
38 "plainList := convert(plainTable,list);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%*plainListG7eo%15468697320697320G%1616E20617474656DG%
1707420746F206C6FG%16F6B206174206120G%1726561736F6E6162G%16C6520776179
2074G%16F2073656E642061G%1206D657373616765GQ10D696E20737563686\"%12061
207761792074G%16861742069742069G%17320656E63727970G%17465642C20627574G
%12074686174207468G%16520726563656976G%165722063616E2061G%16C736F20726
57669G%1667920746861740DG%1746865206D657373G%16167652069732072G%165616
C6C79206672G%16F6D206D652C2061G%16E64207468617420G%16E6F206F6E652068G%
161732074616D7065G%17265642077697468G%12069742061667465G%17220490D7369
676EG%1656420746865206DG%16573736167652E20G%12054686572652061G%1726520
7365766572G%1616C207069656365G%17320746F20646561G%16C20776974682E20G%1
2049206E65656420G%1746F20686173680DGF9%161676520646F776EG%120746F20612
06469G%167657374206F6620GF*%16C65206C656E6774G%1682E202057652077G%1696
C6C20646F2074G%16861742077697468G%1204445532E0D4166G%17465722077652068
G%16176652061206861G%17368656420646967G%16573742C20776520G%17369676E20
697420G%17769746820525341G%12E20205468656E2CG%12073696E63652049G%12077
616E7420746FG%12068617665200D74G%16865206D65737361G%16765206465637279G
%17074656420627920G%174686520696E7465G%16E64656420726563G%1697069656E7
42061G%16C6F6E652C204920G%1656E637279707420G%17468652073657373G%1696F6
E206B65790DGFY%120616E6420746865G%12072656365697665G%1722773207075626C
G%16963206B65792E20G%17800000000000000G" }}}{EXCHG {PARA 321 "" 0 "" 
{TEXT -1 32 "Finally we convert back to text," }}}{EXCHG {PARA 322 "> \+
" 0 "" {MPLTEXT 1 0 101 "plainListBytes := map(x -> seq(convert(substr
ing(x,2*i+1..2*i+2),decimal,hex),i=0..7),\n   plainList):" }}}{EXCHG 
{PARA 323 "> " 0 "" {MPLTEXT 1 0 42 "received := convert(plainListByte
s,bytes);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)receivedGQ\\_mThis~is~
an~attempt~to~look~at~a~reasonable~way~to~send~a~message|.in~such~a~wa
y~that~it~is~encrypted,~but~that~the~receiver~can~also~revify~that|.th
e~message~is~really~from~me,~and~that~no~one~has~tampered~with~it~afte
r~I|.signed~the~message.~~There~are~several~pieces~to~deal~with.~~I~ne
ed~to~hash|.the~message~down~to~a~digest~of~reasonable~length.~~We~wil
l~do~that~with~DES.|.After~we~have~a~hashed~digest,~we~sign~it~with~RS
A.~~Then,~since~I~want~to~have~|.the~message~decrypted~by~the~intended
~recipient~alone,~I~encrypt~the~session~key|.with~RSA~and~the~receiver
's~public~key.~x6\"" }}}{EXCHG {PARA 324 "" 0 "" {TEXT -1 71 "This bec
omes easier to read if it is converted from a string to a name." }}}
{EXCHG {PARA 325 "> " 0 "" {MPLTEXT 1 0 24 "convert(received, name);" 
}}{PARA 12 "" 1 "" {XPPMATH 20 "6#%\\_mThis~is~an~attempt~to~look~at~a
~reasonable~way~to~send~a~message|.in~such~a~way~that~it~is~encrypted,
~but~that~the~receiver~can~also~revify~that|.the~message~is~really~fro
m~me,~and~that~no~one~has~tampered~with~it~after~I|.signed~the~message
.~~There~are~several~pieces~to~deal~with.~~I~need~to~hash|.the~message
~down~to~a~digest~of~reasonable~length.~~We~will~do~that~with~DES.|.Af
ter~we~have~a~hashed~digest,~we~sign~it~with~RSA.~~Then,~since~I~want~
to~have~|.the~message~decrypted~by~the~intended~recipient~alone,~I~enc
rypt~the~session~key|.with~RSA~and~the~receiver's~public~key.~xG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 326 "" 0 
"" {TEXT -1 10 "Exercises:" }}{EXCHG {PARA 327 "" 0 "" {TEXT -1 537 "1
)  The following message was sent to to a receiver with the following \+
private key:\nReceivern := 1457907094342636571934108159685862980326515
9149118248616433975229804975507362306154960468021868768356118367534405
25199587698019954839165932427842278373706998741;\nReceiverd := 3418029
8922096847472065507840720943425419102236324807359431775852717312155060
7778293183240178522095499109087453784896094825475099226794560236481979
918863102913;\nVerify that it was sent by sender, decrypt it, formulat
e a reply to sender that is encrypted and signed." }}}{EXCHG {PARA 
328 "" 0 "" {TEXT -1 2083 "Sendern := 26471330604822478554767314516351
2922348513168053136441607820278334526819450073873355024584847059403376
4469895630694651936487340877088430911072869585934526325563:\nSendere :
= 65537:\ncipherlist := [\"841DF241571484DA\", \"79793834C7DD81D0\", \+
\"48ABB98186432AE6\", \"81DBE80752EADAB6\", \"8B43C22E1099BC4E\", \"33
19DDD18A5216D7\", \"2C465263FCB169D7\", AD1DB4C8E76699AE, \"9F439228B3
264B02\", \"7D235364FC85B872\", \"2AEB9BBBB01BBE9A\", \"5BA93E6E539970
B1\", \"8FC41AEE50B953FA\", \"324B23BB22CCD112\", \"395513EC6C5F82D1\"
, D821C1549F0C8AC0, \"58FE6D0F4F6C8643\", \"4B5C7E74B3859EFD\", \"9907
A68B351101D3\", \"56424729A52A8889\", \"5D3AF3A93FD72238\", DEE853E94A
56B0BA, B0430A8817016724, \"6D9FD3FFBB3A4D50\", E81B5EE640F89D42, \"51
0DFC71FA25C40C\", \"3CC43FBB5B655D72\", \"630071DB2D013E9F\", \"6B2286
634C67C6DE\", \"58447F6CBD665E69\", E945777C507A99CE, \"0367FD0AC597D7
31\", \"616B270C7B713B66\", \"537B8E0728D3E8E9\", E4C57177141001F5, A5
F09AE750BE19FD, \"55D5BEAC66E71FC5\", \"4E33D27B5A5F7E09\", B9203D5C4E
F0068D, \"5DC41D5BA801444F\", \"8786352A029EE02D\", \"04B30B785A76F6DA
\", \"623F4AB38026661B\", \"48BC5F2C834D1F35\", F115C4747A0521E8, \"93
6C3DA21AD0D3ED\", AC52CC995163B0DF, E54536560E8CBA96, \"157912D2417927
71\", \"29C096048813A485\", CE70C7E14525124C, \"2B7D0241F09A6890\", \"
377D1B206D53823B\", \"1301320EF2E23257\", \"444DF372B826A9CF\", FC580B
4A75667C47, C310038925FB71DA, \"85E21A5B46FDE69A\", B328EC3944D128DE, \+
\"650D24EB4D657855\", D6CF942B2CFF4805, \"694BA546F05B9471\", \"5C0C7A
9B814E4D87\", C698D4BF4704ACFF, \"2BF5C15310CB94BF\", \"3FF942653F528F
B0\", \"7A0A0B17200F9BC7\", \"7B8C888CA6E7C992\", \"6FBE19BB8BB32031\"
, \"97C62DA7C96C134C\", \"8CC5430A980A3DDC\", EF150D80FD6B277E, \"2762
FAAA92DA27C6\", ABA7010CE599034D, \"1DBB5EE17CAB5788\", B769F09C13715F
D2, \"6D4AFC0B31B19123\", D7671D4064D46B27, \"9BC484AEE970D44A\", \"99
DA4B18A0B9D70D\", \"512AA8D5AEBA0CBF\"];\nsigHex := \"17E394C94FF7357C
A2B856A764D54911A64F45000EA103E0BA0971FE35371AE81CC2AB9413FA808218C904
9CC0AF7CFDD4DC04E4E600994A6BE02DDDA3221854DDC89\";\nencryptKeyHex := \+
\"120B390A6D5333E6D19BCC3FE367C27B3B5562F89344A2B1708307AF1593E956FE1D
1EECE000AF9EC6DB69913119B2886B6207C7908966B6EFAA0D6BA868E0DA65584\";" 
}}}{EXCHG {PARA 329 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 330 "
" 0 "" {TEXT -1 391 "2)  Create a 10 line message, a random DES key,  \+
and a pair of RSA keys, one for encryption and one for signing.  Encry
pt your message with DES is CBC mode, consider the last cipherword to \+
be a has of the message and sign the hash.  Encrypt your DES key with \+
RSA and post the composite message to the bulletin board.  (You will a
lso need to append the receiver's private key on this problem." }}}
{EXCHG {PARA 331 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 332 "" 0 
"" {TEXT -1 89 "3)  Pull your own message off the bulletin board and d
ecrypt it to be sure that it works." }}}{EXCHG {PARA 333 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 334 "" 0 "" {TEXT -1 112 "4)  Exchan
ge public RSA keys with someone in the class. Send a message and reply
 using this secured mail system." }}}{EXCHG {PARA 335 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 336 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }