May 2
Continue discussion of RSA algorithm.
algorithmic tricks in
primes folder
- how to find a**b mod c in O(log(b)) steps
- how to find big primes
- wikipedia "miller-rabin"
- aside: Sieve of Eratosthenes
And the basic number theory behind RSA :
Choose p, q (big) primes.
Set n = p * q .
Find e, d such that
e and (p-1)(q-1) have no common factors.
(Typically e is set to 65537.)
e * d = 1 mod (p-1)(q-1).
Then
(e, n) are the public key.
(d, n) are the private key.
Then for each message 'word' m, the codeword c is
c = m ** e mod n
and it can be decoded via
m = c ** d mod n
... hopefully Matt can discuss some pieces of this.
These crypto 'challenges' look interesting :
