# This script untangles the Scientific American 1977 challenge
# load power_mod
read(`RSA.mpl`);

# 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;

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

# 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(");