# RSA encryption example

Suppose we pick the primes *p*=3457631 and
*q*=4563413. (In practice we might pick integers 100
or more digits each, numbers which are strong probable
primes for several bases.) Suppose we also choose the
exponent *e*=1231239 and calculate *d* so *e d* \equic 1 (mod φ(*n*)). We now publish the key
(*n*, *e*) = (15778598254603, 1231239).

To encrypt the message "George has green hair" we convert it to an integer. One simple idea (too simple for real use) is to let A be 1, B be 2, .... Then our message is

0705151807052 7080119270718 0505142718010 918.

For each of the four blocks (whose length was chosen so the blocks would represent integers no larger than
*n*) we compute *B*^{e} (mod
*n*) (using the binary exponentiation). This
gives the encrypted message:

1658228449402 5333403068473 7979527536648 13889903320423.

This message can be decrypted by raising each block to
the *d* = 1315443185039th power modulo *n*.

**See Also:** RSA