Hi,

The decrypted value is 614. I did not do this by hand; certainly the RSA algorithm is not meant to be done by hand. What is needed once e, d and n are specified is a way to compute x^{m} mod n (encryption m=e and decryption m=d).

Here is C code to do exactly this. The first is recursive and the second is non-recursive. With enough patience you can do these algorithms by hand to arrive at 614, but I'm too lazy.

Code:

/* Recursive computation of x^m mod n (so n != 0) where m>0.
Of course ints involved must be all < MAX_INT and also n^2 < MAX_INT
Algorithm works because x^m=(x^(m/2))^2*x^(m%2). At each step the result
is reduced mod n.
*/
int powmod(int x,int m,int n) {
int temp;
if (m==1) {
return(x%n);
}
temp=powmod(x,m/2,n);
temp*=temp;
if (m&1==1) {
temp%=n;
temp*=x;
}
return(temp%n);
}
/* Computes x^m mod n as in recursivePowmod. Same caveats as there. The validity
of this technique can be verified by considering m written in binary. This is more
efficient than the above because it takes away the log(m) function calls, but practically
there is little difference in efficiency.
*/
int powmod1(int x,int m,int n) {
int z=1,y=x;
while (m>0) {
if (m&1==1) {
z=z*y%n;
}
y=y*y%n;
m>>=1;
}
return(z);
}