RSA

1
RSA

• Rivest, Shamir and Adleman
• 1978 - 1979

2
Rivest Shamir Adleman
3
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, 10000000000000001
• Remember the security depends on factoring n p q

10
Computation

• 600 digits raised to 600 digits is a lot of
  multiplication!
• Montgomerys 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