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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "DES functions" }}{PARA 
19 "" 0 "" {TEXT -1 23 "\251 Mike May, S. J., 2002" }}{PARA 19 "" 0 "
" {TEXT -1 13 "maymk@slu.edu" }}{PARA 256 "" 0 "" {TEXT 256 38 "A coll
ection of procedures used in DES" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "To execute D
ES we need to define quite a number of functions.  It seems best to co
llect them on one worksheet so they can all be loaded in at once." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 182 "The first 4 sections of functions
 are needed to be able to step through a single round of DES.  They de
al with form conversion, applying permutations, using XOR, and reading
 s-boxes." }}{PARA 0 "" 0 "" {TEXT -1 223 "The next section of functio
ns produces the f function, so that a round may be done in closer to a
 single step.  These first 5 sections let you through most of the DES \+
Example worksheet that looks at encoding a single block." }}{PARA 0 "
" 0 "" {TEXT -1 416 "The last three sections of functions are designed
 to do operations as a single procedure, so that you can focus on mode
s of operating DES rather than on the functioning with a single block.
  Of those 3 sections, the first deals with key expansion, the second \+
deals with encrypting and decrypting with DES, and the third deals wit
h converting a longer message between an ASCII string and a vector of \+
8-byte hex words." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT 
257 39 "Conversion between different data types" }}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 101 " The first section of code contains functions to co
nvert to hex or binary and keep the correct length" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 1465 "  #When we convert a decimal equivalent t
o hex, we want 2-digit hex\nhex2digit := x -> if x < 16 then cat(`0`,c
onvert(x,hex))\n                  else convert(x,hex) fi:\n  #We want \+
to convert an ASCII string of up to 8 characters to a \n  #64 bit bina
ry string.\nbin64 := proc(shortstring)\n  local temp,l1,missing,i, bin
str:\n  temp := convert(shortstring,bytes):\n  l1 := max(1,length(shor
tstring)):\n  binstr := convert(convert( cat(seq(hex2digit(temp[i]),i=
1..l1)), \n                      decimal,hex),binary):\n  missing := 6
4 -length(binstr):\n  cat(seq(`0`,i=1..missing),binstr):\nend:\n  #We \+
want to convert an ASCII string of up to 8 characters to a \n  #16 cha
racter hex string.\nASCII2hex16 := proc(shortstring)\n  local temp,l1,
missing,i, hexstr:\n  temp := convert(shortstring,bytes):\n  l1 := max
(1,length(shortstring)):\n  hexstr := cat(seq(hex2digit(temp[i]),i=1..
l1)):\n  missing := 16 -length(hexstr):\n  cat(seq(`0`,i=1..missing),h
exstr):\nend:\n  #We want to convert an hex string of up to 16 charact
ers to a \n  #64 bit binary string.\nbin64hex := proc(hexstring)\n  lo
cal temp,l1,missing,i, binstr:\n  l1 := 16 - max(1,length(hexstring)):
\n  temp := cat(seq(\"0\",i=1..l1),hexstring):\n  binstr := convert(co
nvert( temp,decimal,hex),binary):\n  missing := 64 -max(1,length(binst
r)):\n  cat(seq(\"0\",i=1..missing),binstr):\nend:\n  #The contents of
 s-boxes should be converted to 4 bit binary\nfourbitbin := decnum ->
\n     substring(convert(convert(decnum+16,binary),string),2..5):" }}}
}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }{TEXT 258 0 "" }{TEXT -1 30 "S
tring permutations and XORing" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "W
e want functions to do the various permutation expansions." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 388 "PC1onKey := binstr -> cat(seq(subs
tring(binstr,PC1[i]),i=1..56)):\nPC2onKey := binstr -> cat(seq(substri
ng(binstr,PC2[i]),i=1..48)):\nexpander := binstr -> cat(seq(substring(
binstr,E[i]),i=1..48)):\nInitPerm := binstr -> cat(seq(substring(binst
r,IP[i]),i=1..64)):\nFinalPerm := binstr -> cat(seq(substring(binstr,I
PI[i]),i=1..64)):\nPPerm := binstr -> cat(seq(substring(binstr,P[i]),i
=1..32)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 145 "We need to be able \+
to do XOR on 64, 48, and 32 bit strings.\nWe would also like to be abl
e to XOR two 64 bit strings that are given in hex format." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 561 "XOR := (a,b) -> if (a=b) then \"0
\" else \"1\" fi:\nxorNbits := proc(a,b,N) \n  local aString, bString:
\n  aString := convert(a,string):\n  bString := convert(b,string): \n \+
 cat(seq(XOR(substring(aString,i), substring(bString,i)),i=1..N)):\nen
d:\nxor64 := (a,b) -> xorNbits(a,b,64):\nxor48 := (a,b) -> xorNbits(a,
b,48):\nxor32 := (a,b) -> xorNbits(a,b,32):\n\nxor64hex := proc(a,b)\n
  local binab, hexab, i, l:\n  binab := xor64(bin64hex(a),bin64hex(b))
:\n  hexab := convert(convert(parse(binab),decimal,binary),hex):\n  l \+
:= 16 - length(hexab):\n  cat(seq(\"0\",i=1..l),hexab):\nend:" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 25 "SBoxes and the f function" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 236 "To do the s-box substitutions, we
 want to be able to cut the 48 bit word into a vector of 6 bit words. \+
 Since we have made the SBox a list of tables with 4 bit entries index
ed by 6 bit strings, looking up SBox values is straightforward." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "prodbs := proc(binstr)\n  l
ocal bvec,i: \n  bvec := linalg[vector](8):\n  for i from 1 to 8 do\n \+
   bvec[i] := substring(binstr,i*6-5..i*6):\n  od:\n  convert(bvec,lis
t):\nend:   " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 351 "We now want a si
ngle function that corresponds to the f function discussed in class an
d in the text.  It should takes a round key and a half word, expand th
e half word and xor with the round key, then cut the 48 bit result int
o 8 6 bit strings that are used for SBox look ups.  The results are co
ncatenated together and permuted according to the rule." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 227 "fcomb := proc(ri, ki)\n  local t1,
t2, t3, vec1, vec2, i:\n  t1 := xor48(ki,expander(ri)):\n  vec1 := pro
dbs(t1):\n  vec2 := linalg[vector](8,[seq(SBox[i][vec1[i]],i=1..8)]):
\n  t2 := cat(seq(vec2[i],i=1..8)):\n  t3 := PPerm(t2):\nend:" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 17 "One line commands" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 164 "When we are ready to look at using DES o
n more than 64 bits of information at a time we want to be able to do \+
key expansion and DES encryption with single commands." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "keyexpander takes a \+
hex string as input and produces a list of the 16 subkeys." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 794 "keyexpander := proc(hexstring)\n  \+
local keybin, binlength, keybin64, PC1key, c, d, key, i:  \n  keybin:=
 convert(convert(hexstring,decimal,hex),binary):\n  binlength := lengt
h(keybin):\n  keybin64 := cat(seq(`0`,i=1..(64-binlength)),keybin):\n \+
 PC1key := PC1onKey(keybin64):\n  c := linalg[vector](17): d := linalg
[vector](17):\n  key := linalg[vector](16):\n  c[1] := substring(PC1ke
y,1..28): d[1]:=substring(PC1key,29..56):\n  for i from 2 to 17 do\n  \+
   c[i] := cat(substring(c[i-1],keyshifts[i-1]+1..28),\n              \+
   substring(c[i-1],1..keyshifts[i-1])):\n     d[i] := cat(substring(d
[i-1],keyshifts[i-1]+1..28),\n                 substring(d[i-1],1..key
shifts[i-1])):\n  od:\n  for i from 1 to 16 do\n    key[i] := convert(
PC2onKey(cat(c[i+1],d[i+1])),string);\n  od:\n  key := convert(key,lis
t):\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 155 "The command qdDEShe
x (qd for quick and dirty) uses DES and a vector of subkeys to encode \+
a hex input.  The input should be no more than 16 hex digits long." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 86 "The comma
nd qdDESASCII encodes an ASCII string that is no more than 8 character
s long." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
42 "The command unDEShex decodes a hex string." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 1537 "qdDEShex := proc(hexstring,keyvec)\n local b
in2, R, i, keytriv,code1,code2, code3, l1:\n keytriv := cat(seq(`0`,j=
1..48));\n bin2 := InitPerm(bin64hex(hexstring));\n R := linalg[vector
](18):\n R[2] := substring(bin2,33..64);\n R[1] := substring(bin2,1..3
2);\n for i from 1 to 16 do\n   R[i+2] := xor32(R[i],fcomb(R[i+1],keyv
ec[i]));\n od:\n code1 := cat(R[18],R[17]);\n code2 := FinalPerm(code1
);\n code3 := convert(convert(parse(code2),decimal,binary),hex);\n l1 \+
:= length(code3);\n cat(seq(\"0\",i=1..(16-l1)),code3);\nend:\nunDEShe
x := proc(hexstring,keyvec)\n local bin2, R, i, keytriv,code1,code2, c
ode3, l1:\n keytriv := cat(seq(\"0\",j=1..48));\n bin2 := InitPerm(bin
64hex(hexstring));\n R := linalg[vector](18):\n R[17] := substring(bin
2,33..64);\n R[18] := substring(bin2,1..32);\n for i from 1 to 16 do\n
   R[17-i] := xor32(R[19-i],fcomb(R[18-i],keyvec[17-i]));\n od:\n code
1 := cat(R[1],R[2]);\n code2 := FinalPerm(code1);\n code3 := convert(c
onvert(parse(code2),decimal,binary),hex);\n l1 := length(code3);\n cat
(seq(\"0\",i=1..(16-l1)),code3);\nend:\nqdDESASCII := proc(ASCIIstring
,keyvec)\n local bin2, R, i, keytriv,code1,code2, code3, l1:\n keytriv
 := cat(seq(\"0\",j=1..48));\n bin2 := InitPerm(bin64(ASCIIstring));\n
 R := linalg[vector](18):\n R[2] := substring(bin2,33..64);\n R[1] := \+
substring(bin2,1..32);\n for i from 1 to 16 do\n   R[i+2] := xor32(R[i
],fcomb(R[i+1],keyvec[i]));\n od:\n code1 := cat(R[18],R[17]);\n code2
 := FinalPerm(code1);\n code3 := convert(convert(parse(code2),decimal,
binary),hex);\n l1 := length(code3);\n cat(seq(\"0\",i=1..(16-l1)),cod
e3);\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 26 "More data type co
nversions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 165 "If we are going to u
se DES on a longer message, we want to convert the message from an ASC
II string to a vector of hex words with each word being 16 characters \+
long." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1401 "  #When we conve
rt a decimal equivalent to hex, we want 2-digit hex\nhex2digit := x ->
 if x < 16 then cat(`0`,convert(x,hex))\n                  else conver
t(x,hex) fi:\nasciistrtohexword := proc(messagestring)\n  local string
ofhex, lenofstr, roundlen, padding, wordlen, temp, j, i, k:\n    #Firs
t we convert the ASCII string to a list of decimal equivalents\n    #T
hen we convert thedecimal numbers to 2 place hex equivalents\n  lenofs
tr := length(messagestring);\n  stringofhex := map(hex2digit, convert(
messagestring,bytes)):\n    #Time to compute the appropriate lengths\n
  roundlen := lenofstr + 7 - (lenofstr + 7 mod 8);\n  padding := round
len - lenofstr:\n  wordlen := roundlen/8:\n    #Now we put togehter he
x words\n  temp := linalg[vector](wordlen):\n  for i from 1 to (wordle
n -1) do\n    temp[i] := cat(seq(stringofhex[j],j=(i*8-7)..i*8)):\n  o
d:\n  temp[wordlen] :=cat(seq(stringofhex[j], j=(roundlen-7)..lenofstr
),\n                    seq(`00`,k=1..padding)):\n    #Finally we conv
ert the vector to a list\n  convert(temp,list):\nend:\nhexwordtoasciis
tr := proc(wordlist)\n  local l1, temp, i, j, vec1:\n  vec1 := convert
(wordlist,array):\n  l1 := linalg[vectdim](wordlist):\n  temp := linal
g[vector](8*l1):\n  for i from 1 to l1 do\n    for j from 1 to 8 do\n \+
     temp[j+8*(i-1)] := substring(wordlist[i],2*j-1..2*j):\n    od:\n \+
 od:\n  temp := convert(temp,list):\n  convert(map(convert,temp,decima
l,hex),bytes):\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 30 "Saving \+
constants and functions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 216 "Rather
 than rerunning the DES constants and DES functions worksheets each ti
me we can save the functions and constants in a file named DES.m.  Thi
s file will be created in the same directory as the Maple application.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 324 "save \nSBox, PC1, PC2,
 keyshifts, IP, E, P, IPI, \nhex2digit, bin64, ASCII2hex16, bin64hex, \+
fourbitbin,\nPC1onKey, PC2onKey, expander, InitPerm, FinalPerm, PPerm,
\nXOR, xorNbits, xor64, xor48, xor32, xor64hex,\nprodbs, fcomb, keyexp
ander, qdDEShex, unDEShex,\nqdDESASCII, \nhex2digit, asciistrtohexword
, hexwordtoasciistr,\n`DES.m`;" }}{PARA 7 "" 1 "" {TEXT -1 54 "Warning
, unassigned variable `SBox` in save statement\n" }}{PARA 7 "" 1 "" 
{TEXT -1 53 "Warning, unassigned variable `PC1` in save statement\n" }
}{PARA 7 "" 1 "" {TEXT -1 53 "Warning, unassigned variable `PC2` in sa
ve statement\n" }}{PARA 7 "" 1 "" {TEXT -1 59 "Warning, unassigned var
iable `keyshifts` in save statement\n" }}{PARA 7 "" 1 "" {TEXT -1 52 "
Warning, unassigned variable `IP` in save statement\n" }}{PARA 7 "" 1 
"" {TEXT -1 51 "Warning, unassigned variable `E` in save statement\n" 
}}{PARA 7 "" 1 "" {TEXT -1 51 "Warning, unassigned variable `P` in sav
e statement\n" }}{PARA 7 "" 1 "" {TEXT -1 53 "Warning, unassigned vari
able `IPI` in save statement\n" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
59 "Next you need to execute the worksheet on DES Key Expansion" }}}
{EXCHG {PARA 0 "> " 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 }