1. Rivest, Shamir and Adleman 1978 - 1979
RSA
Rivest, Shamir and Adleman

2. Rivest Shamir Adleman

3. Depends on the difficulty of factoring really large numbers.
Security
Depends on the difficulty of factoring really large numbers.

4. Key Pair
Choose 2 random large (300 to 600 digits) prime numbers, p and q.
p and q should be of equal length
Compute
n = pq
Randomly choose e such that
e and (p – 1)(q – 1)
are relatively prime
Compute d such that
ed = 1 mod ((p – 1)(q - 1))

5. Keys e is the encryption key d is the decryption key
d = e-1 mod ((p – 1)(q – 1))
e and n are the public key
d is the private key
Throw p and q away (securely)

6. Message Preparation
The message m must be divided into blocks smaller than n.
For 2048 bit keys message blocks should be around 1024 bytes.
Pad with zeros

7. Encryption
Message block mi
Cipher text ci
ci = mi e mod n

8. Decryption
Message block mi
Cipher text ci
mi = ci d mod n

9. Common Public Keys 3, 17, and 65537 (216 + 1)
11, 1001,
Remember the security depends on factoring n = p q

10. Computation
600 digits raised to 600 digits is a lot of multiplication!
Montgomery’s method depends on the binary representation of e.
Using all of the tricks RSA is about 10,000 to 100,000 times more computationally intensive than DES or AES