> read(`public/Maple/RSA.mpl`);

`convert/toASCII` :=

  proc(string)
  local addr,lst,op3,code,i;
      if string = `.` then RETURN(46) fi;
      for i to 128 do
          if substring(ctrlstring,i .. i) = string then RETURN(i-1)
          fi
      od;
      print(`Try to convert unprintable character to ASCII`);
      RETURN(0)
  end

Warning, string contains newline character. Close strings with ` quote.


ctrlstring :=

..........
..................... !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKL\
MNOPQRSTUVWXYZ(\)^_`abcdefghijklmnopqrstuvwxyz{|}~.


`convert/fromASCII` :=

    proc(ascii_val)
        substring(ctrlstring,ascii_val+1 .. ascii_val+1)
    end


encode :=

   proc(ClearText,PublicKey)
   local b,i,ints,codedints;
       b := blocking_factor(PublicKey);
       ints := pack(ClearText,b);
       codedints := [];
       for i to nops(ints) do
           codedints := [op(codedints),scramble(ints[i],PublicKey)]
       od;
       RETURN(codedints)
   end

Warning, `publickey` is implicitly declared local


decode :=

 proc(CodedInts,PrivateKeys)
 local b,i,ints,P,Q,magicexp,publickey;
     P := PrivateKeys[1];
     Q := PrivateKeys[2];
     magicexp := iquo(2*(P-1)*(Q-1)+1,3);
     publickey := P*Q;
     ints := [];
     for i to nops(CodedInts) do
         ints :=
             [op(ints),unscramble(CodedInts[i],magicexp,publickey)]
     od;
     b := blocking_factor(publickey);
     RETURN(unpack(ints,b))
 end


find_key := proc(Start)
            local int;
                int := Start;
                if irem(int,2) = 0 then int := int+1 fi;
                if irem(int,3) = 0 then int := int+2 fi;
                if irem(int,3) = 1 then int := int+4 fi;
                while not isprime(int) do  int := int+6 od;
                RETURN(int)
            end


blocking_factor :=

    proc(Key) iquo(trunc(evalf(log(Key)/log(2))),8) end


pack :=

  proc(text,b)
  local chars,len,i,j,k,ints,code,c;
      len := round(length(text)/b+1/2);
      chars := text.`                                     `.
          `                                     `.
          `                                     `;
      j := 0;
      ints := [];
      for i to len do
          code := 0;
          for k to b do
              j := j+1;
              code :=
                  256*code+convert(substring(chars,j .. j),toASCII)
          od;
          ints := [op(ints),code]
      od;
      RETURN(ints)
  end

Warning, `k` is implicitly declared local


unpack :=

    proc(intlist,b)
    local len,i,j,block,text,k;
        len := nops(intlist);
        text := ``;
        for i to len do
            block := ``;
            j := intlist[i];
            for k to b do
                block := cat(convert(irem(j,256),fromASCII),block);
                j := iquo(j,256)
            od;
            text := cat(text,block)
        od;
        RETURN(text)
    end


scramble :=

  proc(Int,PublicKey) irem(irem(Int^2,PublicKey)*Int,PublicKey) end


unscramble := proc(CodedInt,MagicExp,PublicKey)
                  power_mod(CodedInt,MagicExp,PublicKey)
              end


power_mod := proc(a,e,m)
             local half;
                 if e = 0 then RETURN(1) fi;
                 if e = 1 then RETURN(irem(a,m)) fi;
                 half := power_mod(a,iquo(e,2),m);
                 if type(e,even) then RETURN(Expand(half^2) mod m)
                 else RETURN(Expand(half^2*a) mod m)
                 fi
             end

--------------------------------------------------------------------------------
> convert(`H`, toASCII);

                                       72
--------------------------------------------------------------------------------
> convert(", binary);

                                     1001000
--------------------------------------------------------------------------------
> P := find_key(1047309741920874129087);

                           P := 1047309741920874129143
--------------------------------------------------------------------------------
> Q := find_key(174512903490182374);

                             Q := 174512903490182447
--------------------------------------------------------------------------------
> K := P*Q;\


                  K := 182769063916165392636054393131309752921
--------------------------------------------------------------------------------
> convert(K, binary);

1000100110000000000010101001001101010001000111010010100000011000111001011000101\
0010001011011101100101100011000000110001001011001
--------------------------------------------------------------------------------
> evalf(log[2](K));

                                   127.1032895
--------------------------------------------------------------------------------
> blocking_factor(K);

                                       15
--------------------------------------------------------------------------------
> pack(`Hello, how are you today?`, 15);

  [375902487384808157144386877911098656, 630528547088015391132806231474839584]
--------------------------------------------------------------------------------
> unpack(", 15);

                         Hello, how are you today?
--------------------------------------------------------------------------------
> encode(`Hello, how are you today?`, K);

[106721224137614351582281885445412317874, 67467725784683723348414505373754317001

    ]
--------------------------------------------------------------------------------
> decode(", [P, Q]);

                         Hello, how are you today?
--------------------------------------------------------------------------------
> ints := pack(`Erich Kaltofen`, 15);

                 ints := [360589027655680158358836091235429920]
--------------------------------------------------------------------------------
> sgn := [unscramble(op(1,ints), (2*(P-1)*(Q-1)+1)/3, K)];

                sgn := [175447822430736748602544060112260396636]
--------------------------------------------------------------------------------
> lst := [scramble(op(1, sgn), K)];

                  lst := [360589027655680158358836091235429920]
--------------------------------------------------------------------------------
> unpack(lst, 15);

                                 Erich Kaltofen
--------------------------------------------------------------------------------
> # factors of RSA-129 found in 1994\
P := 3490529510847650949147849619903898133417764638493387843990820577;\
\
Q := 32769132993266709549961988190834461413177642967992942539798288533;\
\
# RSA-129\
K := P*Q;\
\
# encode(m) =  m^s mod K\
s := 9007;\
\
# decode(e) = e^t mod K, where t = s^(-1) mod phi(K)\
t := s^(-1) mod ((P-1)*(Q-1));\
\
# this procedure does the special number to text conversion used\
sciamer_unpack := proc(int)\
   local ctrlstring, text, pos, code;\
   ctrlstring := ` ABCDEFGHIJKLMNOPQRSTUVWXYZ`;\
   code := int;\
   text := ``;\
   while(code > 0) do\
      pos := code mod 100; code := iquo(code, 100);\
      text := cat(substring(ctrlstring, pos+1..pos+1), text);\
   od;\
   RETURN(text);\
end;\


      P := 3490529510847650949147849619903898133417764638493387843990820577

     Q := 32769132993266709549961988190834461413177642967992942539798288533

K :=

1143816257578888676692357799761466120102182967212423625625618429357069352457338\
97830597123563958705058989075147599290026879543541

                                    s := 9007

t :=

1066986143685780244428687713289201547807099066339378628012262244966310631259117\
74470873340168597462306553968544513277109053606095

sciamer_unpack :=

    proc(int)
    local ctrlstring,text,pos,code;
        ctrlstring := ` ABCDEFGHIJKLMNOPQRSTUVWXYZ`;
        code := int;
        text := ``;
        while 0 < code do
            pos := code mod 100;
            code := iquo(code,100);
            text := cat(substring(ctrlstring,pos+1 .. pos+1),text)
        od;
        RETURN(text)
    end

--------------------------------------------------------------------------------
> # test sciamer_unpack on example p. 123\
sciamer_unpack(09201900011212000718050511002015001305);\


                               ITS ALL GREEK TO ME
--------------------------------------------------------------------------------
> # this was the secret text on p. 121\
challenge :=                   9686961375462206;\
challenge := challenge*10^16 + 1477140922254355;\
challenge := challenge*10^16 + 8829057599911245;\
challenge := challenge*10^16 + 7431987469512093;\
challenge := challenge*10^16 + 0816298225145708;\
challenge := challenge*10^16 + 3569314766228839;\
challenge := challenge*10^16 + 8962801339199055;\
challenge := challenge*10^16 + 1829945157815154;\
\
power_mod(challenge, t, K);\
sciamer_unpack(");\


                          challenge := 9686961375462206

                  challenge := 96869613754622061477140922254355

          challenge := 968696137546220614771409222543558829057599911245

  challenge := 9686961375462206147714092225435588290575999112457431987469512093

challenge :=

96869613754622061477140922254355882905759991124574319874695120930816298225145708

challenge :=

9686961375462206147714092225435588290575999112457431987469512093081629822514570\
83569314766228839

challenge :=

9686961375462206147714092225435588290575999112457431987469512093081629822514570\
835693147662288398962801339199055

challenge :=

9686961375462206147714092225435588290575999112457431987469512093081629822514570\
8356931476622883989628013391990551829945157815154

 200805001301070903002315180419000118050019172105011309190800151919090618010705

                     THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE
--------------------------------------------------------------------------------
>