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

Rivest Shamir Adleman

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

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))

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)

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

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

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

Common Public Keys 3, 17, and 65537 (216 + 1) 11, 1001, 10000000000000001 Remember the security depends on factoring n = p q

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