Mathematica Overflow[] error : Why and how-to bypass?

Question

I never had an overflow error in Mathematica, the following happened.

I demo-ed the principle of RSA-encryption as follows:

 n = 11*13
 m = EulerPhi[         


        

Answer 1

Try using PowerMod in the decyphering operation:

n = 252097800611*252097800629;
m = EulerPhi[n];
e = 7;
Print[GCD[e, m]];
d = PowerMod[e, -1, m];
Print[{"n" -> n, "m" -> m, "e" -> e, "d" -> d}];
Grid[
 Join[{
  {"Input", "Encrypted", "Decrypt with Mod", "Decrypt with PowerMod"}}, 
  Table[{i, (j = Mod[i^e, n]), Mod[j^d, n], PowerMod[j, d, n]}, {i, 40}]], 
 Frame -> All]