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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 212 24 "Breaking Vigenere Cipher
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 77 "Initialize from reading the \+
necessary commands from the publisher's web-site:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 64 "with(LinearAlgebra): with(linalg): with(numt
heory): with(plots):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "numb:=tabl
e([\" \"=0,\"a\"=1, \"b\"=2, \"c\"=3, \"d\"=4, \"e\"=5, \"f\"=6, \"g\"
=7, \"h\"=8, \"i\"=9, \"j\"=10, \"k\"=11, \"l\"=12, \"m\"=13, \"n\"=14
, \"o\"=15, \"p\"=16, \"q\"=17, \"r\"=18, \"s\"=19, \"t\"=20, \"u\"=21
, \"v\"=22, \"w\"=23, \"x\"=24, \"y\"=25, \"z\"=26]):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 194 "alph:=table([0=\" \",1=\"a\",2=\"b\",3=\"c\",4=
\"d\",5=\"e\",6=\"f\",7=\"g\",8=\"h\",9=\"i\",10=\"j\",11=\"k\",12=\"l
\",13=\"m\",14=\"n\",15=\"o\",16=\"p\",17=\"q\",18=\"r\",19=\"s\",20=
\"t\",21=\"u\",22=\"v\",23=\"w\",24=\"x\",25=\"y\",26=\"z\"]):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "shift:=proc(txt,n) " }}{PARA 0 "> "
 0 "" {MPLTEXT 1 0 16 "   local i, z;  " }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "   z :=NULL;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "   for i fr
om 1 while i<= length(txt) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "  \+
   z:=cat(z,(alph[(numb[substring(txt,i)]+n-1 mod 26)+1]));" }}{PARA 0
 "> " 0 "" {MPLTEXT 1 0 10 "   end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "   return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "end: " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "allshifts:= proc(txt)" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "    local i;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "    for i from 0 while i<26 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "    print(shift(txt,i));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " \+
   end do;   " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 27 "affinecrypt:= proc(txt,m,n)" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 14 "    local i,z;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "    z:=NULL;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "for i from 1 wh
ile i<=length(txt) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "     z:=ca
t(z,(alph[((numb[substring(txt,i)]-1)*m+n mod 26)+1]));" }}{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 11 "    end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "    return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "vigenere:= proc(txt,v)" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 14 "    local i,z;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "    z:=NULL;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "for i from 1 wh
ile i<=length(txt) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "    z:=cat
(z,alph[(numb[substring(txt,i)]+v[(i-1 mod nops(v))+1]-1 mod 26)+1]);"
 }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "    end do;" }}{PARA 0 "> " 0 ""
 {MPLTEXT 1 0 14 "    return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "
end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "choose:=proc(txt,m,n)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "    local i,z;" }}{PARA 0 "> " 0 ""
 {MPLTEXT 1 0 12 "    z:=NULL;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " \+
for i from n by m while i<= length(txt) do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "     z:=cat(z,substring(txt,i));" }}{PARA 0 "> " 0 ""
 {MPLTEXT 1 0 9 "  end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "retur
n(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "frequency:=proc(txt)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 78 "   local i,j,k,v,z;  z:=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "  for i from 1 wh
ile i<= length(txt) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "   j:=num
b[substring(txt,i)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "   z:=subso
p(j=z[j]+1,z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "   end do;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "return(z);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "vigvec:= pr
oc(txt,m,n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "  local w,z,i;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "  z:=choose(txt,m,n);" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 31 "  w:=frequency(z)/length(z)*1.;" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 11 " return(w);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "alfreq:=[.082, .015, \+
.028, .043, .127, .022, .020, .061, .070, .002, .008, .040, .024, .067
, .075, .019, .001, .060, .063, .091, .028, .010, .023, .001, .020, .0
01]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "corr:=proc(v)" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "   local i,j,w,z;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "   w:=augment(matrix(1,26,v),matrix(1,26,v));" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "   z:=seq(sum(alfreq[i]*w[1,i+j-1],
i=1..26),j=1..26);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 " return(z);" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 18 "coinc:=proc(txt,s)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "  lo
cal i,w,z;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "  z:=0;" }}{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 42 "  for i from 1 while i <= length(txt)-s do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "  " }{TEXT 213 1 " " }{MPLTEXT 1 0 
64 "if substring(txt,i)=substring(txt,i+s) then z:=z+1 else z:=z fi;" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "  end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 " return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "lfsr:=proc(c,k,n) " }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "  local f,i,j,r,z;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "  z:=matrix(1,nops(k),k);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "   for i from 1 while i<= n-nops(c) do" }}{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 68 "z:=augment(z,matrix(1,1,[sum(z[1,j+i-1]*c[j],j
=1..nops(c)) mod 2]));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "   end do
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "  z:=row(z,1);z:=[seq(z[i],i=1
..n)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "  end:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "lfsrlength:=proc(v,n)" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 19 "  local w,z,i,j,k; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "  f
or k from 1 while k<=n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "  w:=a
rray(1..k,1..k);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "  for i from 1 \+
while i<= k do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "  for j from 1 wh
ile j<= k do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "   w[i,j]:=v[i+j-1]
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 " end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " print(
[k,det(w) mod 2]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " end do;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " end:" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "lfsrsolve:=proc(v,n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "  l
ocal w1,w,z,i,j,k;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "  w1:=array(1
..n,1..1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "  w:=array(1..n,1..n)
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "  for i from 1 while i<= n do"
 }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "  for j from 1 while j<= n do" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "   w[i,j]:=v[i+j-1];" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 " end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
 end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " for i from 1 while i<=
 n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " w1[i,1]:=v[i+n]; " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "   end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 " z:=evalm(det(w)*transpose(evalm(inverse(w)&*w1)));" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "z:=map(x->x mod 2,z); z:=[seq(z[1
,i],i=1..n)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 " z;" }}{PARA 0 "> "
 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "  tex
t2num:=proc(txt)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "   local i,z; z
:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "   for i from 1 while i<=le
ngth(txt) do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "   z:=100*z+numb[su
bstring(txt,i)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "  end do;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "  return(z);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "  end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "num2text:
=proc(n)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 " local i,w,z; z:=NULL;w
:=n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "   for i from 1 while 100^(
i-1)<n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "   z:=cat(alph[w mod 1
00],z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "   w:=floor(w/100);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "  end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "  return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "  e
nd:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "cards:=[200514,10010311,1721
050514,11091407,10305]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with(com
binat,randperm):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "khide:=proc();2
*rand()+101;end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "shuffle:=proc(k
)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " local z; " }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 90 "z:=randperm(\{cards[1]&^k,cards[2]&^k,cards[3]&^k,c
ards[4]&^k,cards[5]&^k\}mod 24691313099);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "return(z); end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 
"reveal:=proc(c) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "  local  k1,z;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "  k1:= k&^(-1) mod 24691313098;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "  z:=[c[1]&^k1,c[2]&^k1,c[3]&^k
1,c[4]&^k1,c[5]&^k1] mod 24691313099;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 80 "z:=[num2text(z[1]),num2text(z[2]),num2text(z[3]),num2text(z[4]),
num2text(z[5])];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "  return(z); " 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 15 "advise:=proc(v)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " local \+
i,w,z;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " w:=1; " }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 " for i from 1 while w=1 do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "  w:=v[i]&^((24691313099-1)/2) mod 24691313099;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 " return(i-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "en
d: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "addell:=proc(p1,p2,a,b,n)" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "  local z,z1,m,x3,y3,p3;" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "  z:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "  z1:=1;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "  if p1=[\"infinity
\",\"infinity\"] then p3:=p2; z:=1 else end if;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 " if z=1 then NULL else " }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 75 "  if p2=[\"infinity\",\"infinity\"] then p3:=p1; z:=1 else en
d       if end if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if z=1 then \+
NULL else " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "  if p1[1]=p2[1] and \+
p1[2]=0 then   p3:=[\"infinity\",\"infinity\"]; z:=1 else end if" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "  end if;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 " if z=1 then NULL else" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 39 "  if p1[1]=p2[1] and p1[2]<>p2[2] then " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "  p3:=[\"infinity\",\"infinity\"]; z:=1 else end if e
nd if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if z=1 then NULL else " 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "  if p1=p2 and gcd(p1[2],n)<>1 an
d gcd(p1[2],n)<>n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "   then z1:=gc
d(p1[2],n); z:=1 else end if end if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 23 " if z=1 then NULL else " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 " \+
   if p1=p2 then m:=((3*p1[1]^2+a)*((2*p1[2])&^(-1) mod n)) mod n; z:=
1; x3:=(m^2-p1[1]-p2[1]) mod n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "
 y3:=(m*(p1[1]-x3)-p1[2]) mod n;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"p3:=[x3,y3];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "else end if end if
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " if z=1 then NULL else " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "  if gcd(p2[1]-p1[1],n)<>1 then z:=
1;z1:=gcd(p2[1]-p1[1],n) else end if end if;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 " if z=1 then NULL else " }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 56 "  m:= ((p2[2]-p1[2])*((p2[1]-p1[1])&^(-1) mod n)) mod n;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "  x3:=(m^2-p1[1]-p2[1]) mod n; y3:=
 (m*(p1[1]-x3)-p1[2]) mod n; p3:= [x3,y3] end if;" }}{PARA 0 "> " 0 ""
 {MPLTEXT 1 0 59 "if z1=1 then return(p3) else return([\"factor=\",z1]
) end if;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 26 "multsell:=proc(p1,m,a,b,n)" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 " local i,z;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " z:
=[[1,p1]];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " for i from 2 while i
<=m and z[-1][2][1]<>\"factor=\" do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
55 " z:=[op(z),[1+nops(z),addell(p1,z[nops(z)][2],a,b,n)]];" }}{PARA 0
 "> " 0 "" {MPLTEXT 1 0 9 "  end do;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 " return(z);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}{PARA 0
 "> " 0 "" {MPLTEXT 1 0 24 "multell:=proc(p,m,a,b,n)" }}{PARA 0 "> " 0
 "" {MPLTEXT 1 0 18 " local i,j,q,y,z1;" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 28 " y:=[\"infinity\",\"infinity\"];" }}{PARA 0 "> " 0 "" {MPLTEXT
 1 0 6 " q:=p;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " z1:=m; " }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 48 " for i from 1 while z1<>0 and y[1]<>\"fac
tor=\" do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "  for j from 1 while z
1 mod 2 = 0  and q[1]<>\"factor=\" do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 42 "   z1:=z1/2; q:=addell(q,q,a,b,n); end do;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "  z1:=z1-1; y:=addell(q,y,a,b,n); end do;         " }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "  if q[1]=\"factor=\" then y:=q el
se NULL end if; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}{PARA 0 "> 
" 0 "" {MPLTEXT 1 0 11 " return(y);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
4 "end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gaul:= \"gaulisdividedin
tothreeparts\":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "ycve:= \"ycvejqw
vhqtdtwvwu\":\n" }{MPLTEXT 1 0 40 "edsg:= \"edsgickxhuklzveqzvkxwkzukc
vuh\":\n" }{MPLTEXT 1 0 151 "tcab:= \"tcabtiqmfheqqmrmvmtmaq\": lcll:=
\"lcllewljazlnnzmvyiylhrmhza\":            DNA:= \"GAATTCGCGGCCGCAATTA
ACCCTCACTAAAGGGATCTCTAGAACT\":                " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "xkju:= \"xkjurowmllpxwznpimbvbqjcnowxpcchhvvfvsllfvxh
azityxohulxqojaxelxzxmyjaqfs\\\n" }{MPLTEXT 1 0 80 "tsrulhhucdskbxknjq
idallpqslluhiaqfpbpcidsvcihwhwewthbtxrljnrsncihuvffuxvoukjlj\\\n" }
{MPLTEXT 1 0 80 "swmaqfvjwjsdyljogjxdboxajultucpzmpliwmlubzxvoodybafds
kxgqfadshxnxehsaruojaqfpf\\\n" }{MPLTEXT 1 0 80 "kndhsaafvulluwtaqfrup
wjrszxgpfutjqiynrxnyntwmhcukjfbirzsmehhsjshyonddzzntzmpli\\\n" }
{MPLTEXT 1 0 27 "lrwnmwmlvuryonthuhabwnvw\":\n" }{MPLTEXT 1 0 82 "ocwy
:= \"ocwyikoooniwugpmxwktzdwgtssayjzwyemdlbnqaaavsuwdvbrflauplooubfgqh
gcscmgz\\\n" }{MPLTEXT 1 0 80 "latoedcsdeidpbhtmuovpiekifpimfnoamvlpqf
xejsmxmpgkccaykwfzpyuavtelwhrhmwkbbvgtg\\\n" }{MPLTEXT 1 0 80 "uvtefjl
odfefkvpxsgrsorvgtajbsauhzrzalkwuowhgedefnswmrciwcpaaavogpdnfpktdbalsi
s\\\n" }{MPLTEXT 1 0 80 "urlnpsjyeatcuceesohhdarkhwotikbroqrdfmzghguce
bvgwcdqxgpbgqwlpbdaylooqdmuhbdqgm\\\n" }{MPLTEXT 1 0 8 "yweuik\":" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "hdsf:= \"hdsfgvmkoowafweetcmfthskuc
aqbilgjofmaqlgspvatvxqbiryscpcfrmvswrvnqlszd\\\n" }{MPLTEXT 1 0 80 "mg
aoqsakmlupsqforvtwvdfcjzvgsoaoqsacjkbrsevbelvbksarlscdcaarmnvrysywxqgv
ellcyl\\\n" }{MPLTEXT 1 0 80 "uwwveoafgclazowafojdlhssfiksepsoywxafowl
bfcsocylngqsyzxgjbmlvgrggokgfgmhlmejab\\\n" }{MPLTEXT 1 0 80 "sjvgmlnr
vqzcrggcrghgeupcyfgtydycjkhqluhgxgzovqswpdvbwsffsenbxapasgazmyuhgsfhmf
\\\n" }{MPLTEXT 1 0 43 "tayjxmwznrsofrsoaopgauaaarmftqsmahvqecev\":\n"
 }{MPLTEXT 1 0 80 "vvhq:= \"vvhqwvvrhmusgjgthkihtssejchlsfcbgvwcrlryqt
fsvgahwkcuhwauglqhnslrljshbl\\\n" }{MPLTEXT 1 0 80 "tspisprdxljsveeghl
qwkasskuwepwqtwvspgoelkcqyfnsvwljsniqkgnrgybwlwgoviokhkazkqk\\\n" }
{MPLTEXT 1 0 80 "xzgyhcecmeiujoqkwfwvefqhkijrclrlkbienqfrjljsdhgrhlsfq
twlauqrhwdmwlgusgikkflryv\\\n" }{MPLTEXT 1 0 80 "cwvspgpmlkassjvoqxegg
veyggzmljcxxljsvpaivwikvrdrygfrjljslveggveyggeiapuuisfpbt\\\n" }
{MPLTEXT 1 0 30 "gnwwmuczrvtwglrwugumnczvile\":\n" }{MPLTEXT 1 0 78 "L
100:= [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, \+
1, 0, \n" }{MPLTEXT 1 0 79 "      1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, \+
0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, \n" }{MPLTEXT 1 0 79 "      0, 0, \+
1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, \n" 
}{MPLTEXT 1 0 79 "      0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0
, 0, 1, 0, 0, 0, 1, 0, 0, \n" }{MPLTEXT 1 0 22 "      1, 0, 0, 0, 0]:
\n" }{MPLTEXT 1 0 80 "L011:= [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0
, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0,\n" }{MPLTEXT 1 0 79 "       0, 1, 0, 0
, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1,\n" }
{MPLTEXT 1 0 14 "       0, 1]:\n" }{MPLTEXT 1 0 59 "L101:= [1, 0, 1, 0
, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1,\n" }{MPLTEXT 1 0 60 "      0,
 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1,\n" }{MPLTEXT 1 0 
79 "      1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, \+
0, 1, 1, 1, \n" }{MPLTEXT 1 0 79 "      0, 1, 0, 1, 1, 0, 1, 0, 0, 1, \+
1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, \n" }{MPLTEXT 1 0 28 "      \+
0, 1, 1, 1, 0, 0, 0]:\n" }{MPLTEXT 1 0 80 "rsan:= 11438162575788886766
923577997614661201021829672124236256256184293570693\\\n" }{MPLTEXT 1 
0 60 "5245733897830597123563958705058989075147599290026879543541:\n" }
{MPLTEXT 1 0 13 "rsae:= 9007:\n" }{MPLTEXT 1 0 80 "rsaci:= 96869613754
62206147714092225435588290575999112457431987469512093081629\\\n" }
{MPLTEXT 1 0 60 "82251457083569314766228839896280133919905518299451578
15154:\n" }{MPLTEXT 1 0 73 "rsap:= 34905295108476509491478496199038981
33417764638493387843990820577:\n" }{MPLTEXT 1 0 74 "rsaq:= 32769132993
266709549961988190834461413177642967992942539798288533:\n" }{MPLTEXT 
1 0 67 "naive:= 152415787501905985701881832150835089037858868621211004
433:\n" }{MPLTEXT 1 0 68 "cnaive:= 14107746176556950024119950561785467
3388398574333341423525:\n" }{MPLTEXT 1 0 1441 "n1:=8834884587090814646
372459890377418962766907:                           sigpairm1:=4187265
53997094258577980055061305150940547956: sigpairs1:=7491426496415481015
20133634736865752883277237: sigpairm2:=1482376523249871234451241871713
0930: sigpairs2:=43176121628465441340112418672065063:      signa:=1710
24704183616109700818066925197841516671277: signb:=83907354273436935926
0871355939062622747633109:  sigpb:=98763457697834568934613: sigqb:=849
5789457893457345793:          golay:=matrix(12,24,[1,0,0,0,0,0,0,0,0,0
,0,0,1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0
,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0
,0,0,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1
,0,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,0,0,0
,1,0,0,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,0
,0,1,0,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0
,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0
,1,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,1,1,1,1,1]): \+
golayb:=matrix(12,12,[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,
1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,
0,1,0,0,0,1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,1,0,0,0,1,0,1,1,
0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,1,1,1,0,0,0,
1,0,1,0,1,1,1,1,1,1,1,1,1,1,1]): hammingpc:=matrix(4,15,[0,0,0,0,1,1,1
,1,1,1,1,1,0,0,0,\n" }{MPLTEXT 1 0 61 "1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0
,1,1,1,0,1,1,0,0,1,1,0,0,1,0,\n" }{MPLTEXT 1 0 32 "1,0,1,1,1,0,1,0,1,0
,1,0,0,0,1]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "XXXX:= \"DON'T FO
RGET TO HIT RETURN TO LOAD THE ABOVE COMMANDS BEFORE STARTING YOUR WOR
K. PUT THE CURSOR HERE, OR HIGHER, BEFORE HITTING RETURN.\":" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 208 62 "We start from defining a plaintte
xt in the appropriate format:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 1120 "plaintext:=\"youdontknowaboutmewithoutyouhavereadabookbythenam
eoftheadventuresoftomsawyerbutthataintnomatterthatbookwasmadebymrmarkt
wainandhetoldthetruthmainlytherewasthingswhichhestretchedbutmainlyheto
ldthetruththatisnothingineverseenanybodybutliedonetimeoranotherwithout
itwasauntpollyorthewidowormaybemaryauntpollytomsauntpollysheisandmarya
ndthewidowdouglasisalltoldaboutinthatbookwhichismostlyatruebookwithsom
estretchersasisaidbeforenowthewaythatthebookwindsupisthistomandmefound
themoneythattherobbershidinthecaveanditmadeusrichwegotsixthousanddolla
rsapieceallgolditwasanawfulsightofmoneywhenitwaspiledupwelljudgethatch
erhetookitandputitoutatinterestanditfetchedusadollaradayapiecealltheye
arroundmorethanabodycouldtellwhattodowiththewidowdouglasshetookmeforhe
rsonandallowedshewouldsivilizemebutitwasroughlivinginthehouseallthetim
econsideringhowdismalregularanddecentthewidowwasinallherwaysandsowheni
couldntstanditnolongerilitoutigotintomyoldragsandmysugarhogsheadagaina
ndwasfreeandsatisfiedbuttomsawyerhehuntedmeupandsaidhewasgoingtostarta
bandofrobbersandimightjoinifiwouldgobacktothewidowandberespectablesoiw
entback\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q]`oyoudontknowaboutmewith
outyouhavereadabookbythenameoftheadventuresoftomsawyerbutthataintnomat
terthatbookwasmadebymrmarktwainandhetoldthetruthmainlytherewasthingswh
ichhestretchedbutmainlyhetoldthetruththatisnothingineverseenanybodybut
liedonetimeoranotherwithoutitwasauntpollyorthewidowormaybemaryauntpoll
ytomsauntpollysheisandmaryandthewidowdouglasisalltoldaboutinthatbookwh
ichismostlyatruebookwithsomestretchersasisaidbeforenowthewaythattheboo
kwindsupisthistomandmefoundthemoneythattherobbershidinthecaveanditmade
usrichwegotsixthousanddollarsapieceallgolditwasanawfulsightofmoneywhen
itwaspiledupwelljudgethatcherhetookitandputitoutatinterestanditfetched
usadollaradayapiecealltheyearroundmorethanabodycouldtellwhattodowithth
ewidowdouglasshetookmeforhersonandallowedshewouldsivilizemebutitwasrou
ghlivinginthehouseallthetimeconsideringhowdismalregularanddecentthewid
owwasinallherwaysandsowhenicouldntstanditnolongerilitoutigotintomyoldr
agsandmysugarhogsheadagainandwasfreeandsatisfiedbuttomsawyerhehuntedme
upandsaidhewasgoingtostartabandofrobbersandimightjoinifiwouldgobacktot
hewidowandberespectablesoiwentback6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
 208 49 "Compute the ciphertext using the vigenere command" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "ciphertext:=vigenere(plaintext,[3,1
2,21,7,4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q]`obapksqffuszmwvywyzdmw
tjbxbapoeyqmlegmwvsnntalhzvtirrooidpqlrwgmlwrrovqvmrfiunpaxkmohmqfivqd
folvwtvafrafdevyvkiekhyqddfaaduihrgtzasopooiwdpalpmdupbfclvhivzxkuinwz
tdjlkqnavhfxoignpaqduisckqovpgfclxugooxkmopwqaoomqsduiyqmzihzvuceayffx
fgpigailxlyzvvdzjalhdrpxkapamwivzexzowsoxtvvwtzdmgarvvpmtiipmmfexzowso
xtaspevbrwbjspbeclmvmikqddthrgfclalpjdhrgbsevunhpofjshdnjbxlzooewnjvoz
tdjllehvwwxthxugzisrwrpxkejtivfmlxftzywdedzelpwljrdzuszfcladkooewfclfr
afdmqpnbtleoomvfjteqphljrgikxkqhvrhkooewfclvrnwlvvtdkmqfclgdhzhrguoteg
qpzvlocdijaozmafcvyvmikhrxghvvmkpifqvspjagkmwivzeqmrmyoednlwaatsqqtdlh
zdaadekpphppwahxgqygszaldfxoiutzasrwdaeqpkbxlfjbxdfduxhdzzxdzypxiqojlh
ppzegagseumyhcdbdlghmgsxkqtleudjbrgyjyiwtvueeayfgrggkxhxgdldfovhridalw
tzdmgarksxsghwvtzasrwhljrdclvvaihrgmgsszqyzlhijbpgedcmouulqhnpamwivzvr
gboplhduklzooikapzidxgalhfdtifaizmgqmprjtjdhlehhpuqbbpddvuhgqxlrwfclal
pjdadedueoxclvzmtzeqpnvakqipgrggkrweohrguousoainiuugpxrgopkrfduxrytvpg
dvnwdzytcvgbhvkabzlhmyhkduihrgivzjuqzhrgevamvrdlhegoaspevdchdcllxzolhp
qpweqpnhmgtzdevsjprjfjzxddohfdzyvjuawiiuevuhlydnlwvjprlrddsxxynsemxrxr
fclalpjdeqpwlvheklgwmwsivaddiqfwhgn6\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 208 91 "Now we assume that we have ciphertext only and we want t
o brake the cipher and find the key" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
208 113 "Finction \"coinc\" counts number of coincidences between the \+
ciphertext and the displaced ciphertexrt. For example," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "coinc(ciphertext,7);" }}{PARA 11 ""
 1 "" {XPPMATH 20 "\"#K" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 70 "We th
en compute the numbers of coincidences for different replacements" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f:=x->coinc(ciphertext,x);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF
%F%-I&coincGF%6$I+ciphertextGF%9$F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "map(f,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "72\"#\\\"#T\"#X\"#M\"#_\"#N\"#K\"#O\"#[
\"#n\"#Z\"#W\"#`F)\"#rF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 113 "So \+
the length of the key is 5 as the spikes are at positions 5,10,15, etc
. We can now proceed to finding the key!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "choose(ciphertext,5,1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "Qixbqzwwbygnhrdwrvukqdwrveddgowpbhkzkhgdkgukqqyhexgldhkwxowgppxopw
bvdglrvodlwzlwurkvfdlrzdwrqlvqrkhwrvqdggljavrvfjwqowqhdhhgdurqldhdihgu
dhkugwerhdrwgxvrrvgzhgohwrllkdhfgjludgwldozqkrwgourrrgdvkhdgugvephxpqg
vjdduulwlxerlqhwvqn6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f
req:=frequency(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7<\"\"\"\"\"%\"\"!
\"#C\"\"&\"\"$\"#A\"#>F#F$\"#7\"#:F%\"\"#\"\")\"\"'\"#9\"#@F%F%\"#6F,F
1F/F-F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "corr(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6<$\"%jt!\"$$\"%ehF%$\"%!))*F%$\"&'G9F%$
\"%c#)F%$\"%!H'F%$\"%Z\")F%$\"%d))F%$\"%zsF%$\"%4!)F%$\"%1!*F%$\"%awF%
$\"%xwF%$\"%%e*F%$\"%B$*F%$\"%_))F%$\"%z&)F%$\"%V))F%$\"&,/\"F%$\"%9&)
F%$\"%/lF%$\"%zzF%$\"%\"e)F%$\"%^vF%$\"%(>)F%$\"&_/\"F%" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 208 41 "Therefore the first entry in the key is \+
3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "choose(ciphertext,5,2)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "Qhxafmytaqmnzrpgrmnmfftaykdutpdmfiu
tqfnuqfgmasqzafayzdaizxtammzxebemdfpgufnzntexgweftepdfkfapefpgqkfntfhu
qoafmxmqaimeaqzepxsftwpffdzqpambmqdytagxfitastwdamqieunighzaxfaqteqdqf
pexmpqgeuaugfydzgamuiqergedzqptsfdzaeyvrxmfppemaf6\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 19 "freq:=frequency(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "7<\"#A\"\"#\"\"!\"#7\"#;\"#E\"#6F$\"\"(F%\"\"$F%\"#>F*\"
\"\"\"#9\"#<\"\"%F0F.\"\"*F-F+F1\"\"'F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "corr(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6<$\"%J$*!\"
$$\"&^+\"F%$\"%]&)F%$\"%TlF%$\"%%3)F%$\"%+*)F%$\"%XuF%$\"%+tF%$\"%)f*F
%$\"%uuF%$\"%3iF%$\"%q\"*F%$\"&pP\"F%$\"%'>*F%$\"%YnF%$\"%v$)F%$\"%u#)
F%$\"%pwF%$\"%c%)F%$\"%b$*F%$\"%@uF%$\"%)R(F%$\"%Z*)F%$\"%#G*F%$\"%4))
F%$\"%s))F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 43 "Therefore the sec
ond entry in the key is 12" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "choose(ciphertext,5,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "Qhxpfwzjp
mwtvoqmorpoiovfvhfizopdcvidnxpiocooodmvygizjrpvotzrtmotvjcitcjbnjjojdh
tzrjmzdwzcocfnojhihocwdczopcocigkvgvrdatdkpgzxzdkjdzyopgydgtjjvyggodzr
gzhcigyjdupvbdopgdimjhbvxcjdctnigooigodtvybbyivzvdovcopnzjjoywvdjdyxcj
wkwdw6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "freq:=frequency
(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7<\"\"\"\"\"&\"#:\"#@\"\"!\"\"%
\"#8\"\"'F)\"#>F(F'F*F$\"#E\"#7F#F*F'\"#5F#\"#<\"\")F(\"\"*F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "corr(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6<$\"%$o(!\"$$\"%u*)F%$\"%&y*F%$\"%%\\)F%$\"%0sF%$\"%;\")
F%$\"%e!*F%$\"%z#)F%$\"%N#)F%$\"%?zF%$\"&s0\"F%$\"%?!*F%$\"%goF%$\"%)3
(F%$\"%u$*F%$\"%%\\*F%$\"%EzF%$\"%6$*F%$\"%kxF%$\"%OlF%$\"%dvF%$\"&>K
\"F%$\"%R))F%$\"%#=(F%$\"%.zF%$\"%F))F%" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 208 42 "Therefore the third entry in the key is 21" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "choose(ciphertext,5,4);" }}{PARA 11
 "" 1 "" {XPPMATH 20 "Qhxkuvdbolvatollvfahvladkyahaoaulznjaoasvlopouzu
fplvapazwvdvifwabslkhldshsbovjvhiptlyzluloldbotlkvollklhtzdzvkhpskzmnt
dapwqaoaabbuzpjzshlslbyufkdvadkhallhszbclazouozatzpdhbulldulzvpkhunppu
vnthzhhzhaladllwhdpzhviunpdnrldllsdh6\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "freq:=frequency(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
7<\"#@\"\"*\"\"\"\"#;\"\"!\"\"%F'\"#>\"\"$F*\"#5\"#JF%\"\"'\"#8F.F%F%F
$\"\"(F.F&F(F'F*\"#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "corr
(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6<$\"%i*)!\"$$\"%;yF%$\"%tnF%$\"
&?2\"F%$\"%FqF%$\"%.gF%$\"%X#)F%$\"&cW\"F%$\"%+()F%$\"%2pF%$\"%ByF%$\"
%/**F%$\"%+wF%$\"%RwF%$\"%0()F%$\"%0#)F%$\"%rrF%$\"%\"*yF%$\"&?.\"F%$
\"%)o)F%$\"%V\")F%$\"%)z)F%$\"&v-\"F%$\"%f))F%$\"%^lF%$\"%S!*F%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 208 42 "Therefore the fourth entry in the
 key is 7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "choose(ciphert
ext,5,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "Qhxssymxeesliirwqixmqvfeiqa
rsilpvxwlviqcpxxwmiicfixvlxmesvmviessrpmqrahephxeolwxsxixwejsaefmtmejx
revvmgrevimyhvipmeylslapaylisexxxxxleecgxeriegxlhlmswsjvrslpmqmvpkiili
mrhpphraaeveagrrsixkxpwcvlkrjrmhsclhemerxfjihlrssxaevgiig6\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "freq:=frequency(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "7<\"\"*\"\"!\"\"&F$\"#B\"\"%\"\"'F#\"#AF
%\"\"$\"#;\"#<F$\"\"\"\"#6F(F+\"#=F-F$\"#:\"\"(F&F'F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "corr(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6<$\"&n+\"!\"$$\"%(e(F%$\"%lpF%$\"%3$)F%$\"&<X\"F%$\"%N!)
F%$\"%llF%$\"%dzF%$\"%x%*F%$\"%hvF%$\"%)*yF%$\"%:*)F%$\"%qyF%$\"%S#)F%
$\"%O!)F%$\"%2$*F%$\"%y%)F%$\"%3$*F%$\"%N$)F%$\"&H-\"F%$\"%rzF%$\"%&*p
F%$\"%JvF%$\"%\">*F%$\"%R$)F%$\"%RvF%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
 208 41 "Therefore the fifth entry in the key is 4" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT 208 15 "Thus the key is" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "key:=[3,12,21,7,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "
7'\"\"$\"#7\"#@\"\"(\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 208 38 "And
 we can decipher the original text:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "vigenere(ciphertext,-key);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "Q]`oyoudontknowaboutmewithoutyouhavereadabookbythenameoft
headventuresoftomsawyerbutthataintnomatterthatbookwasmadebymrmarktwain
andhetoldthetruthmainlytherewasthingswhichhestretchedbutmainlyhetoldth
etruththatisnothingineverseenanybodybutliedonetimeoranotherwithoutitwa
sauntpollyorthewidowormaybemaryauntpollytomsauntpollysheisandmaryandth
ewidowdouglasisalltoldaboutinthatbookwhichismostlyatruebookwithsomestr
etchersasisaidbeforenowthewaythatthebookwindsupisthistomandmefoundthem
oneythattherobbershidinthecaveanditmadeusrichwegotsixthousanddollarsap
ieceallgolditwasanawfulsightofmoneywhenitwaspiledupwelljudgethatcherhe
tookitandputitoutatinterestanditfetchedusadollaradayapiecealltheyearro
undmorethanabodycouldtellwhattodowiththewidowdouglasshetookmeforherson
andallowedshewouldsivilizemebutitwasroughlivinginthehouseallthetimecon
sideringhowdismalregularanddecentthewidowwasinallherwaysandsowhenicoul
dntstanditnolongerilitoutigotintomyoldragsandmysugarhogsheadagainandwa
sfreeandsatisfiedbuttomsawyerhehuntedmeupandsaidhewasgoingtostartaband
ofrobbersandimightjoinifiwouldgobacktothewidowandberespectablesoiwentb
ack6\"" }}}}
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