AES:Advanced Encryption Standard symmetric-key NIST standard,replaced DES (Nov2001) processes data in 128 bit blocks 128,192,or 256 bit keys brute force decryption(try each key)taking I sec on DES,takes 149 trillion years for AES Security 8-16
AES: Advanced Encryption Standard ▪ symmetric-key NIST standard, replaced DES (Nov 2001) ▪ processes data in 128 bit blocks ▪ 128, 192, or 256 bit keys ▪ brute force decryption (try each key) taking 1 sec on DES, takes 149 trillion years for AES Security 8-16
Public Key Cryptography symmetric key crypto public key crypto requires sender,receiver radically different know shared secret key approach [Diffie- Q:how to agree on key in Hellman76,RSA78] first place(particularly if never“met")2 sender,receiver do not share secret key public encryption key known to all private decryption key known only to receiver Security 8-17
Public Key Cryptography symmetric key crypto ▪ requires sender, receiver know shared secret key ▪ Q: how to agree on key in first place (particularly if never “ met ”)? public key crypto ▪ radically different approach [DiffieHellman76, RSA78] ▪ sender, receiver do not share secret key ▪ public encryption key known to all ▪ private decryption key known only to receiver Security 8-17
Public key cryptography Bob's public key Bob's private B key plaintext encryption ciphertext decryption plaintext message,m algorithm K言m algorithm message m=K名(Km) Security 8-18
Public key cryptography plaintext message, m encryption ciphertext algorithm decryption algorithm Bob’ s public key plaintext message K (m) B + K B + Bob’ s private key K B - m = K (K (m)) B + B - Security 8-18
Public key encryption algorithms requirements: need K)and K(such that B KaKgm》)=m 2 given public key Kg it should be impossible to compute private key KB RSA:Rivest,Shamir,Adelson algorithm Security 8-19
Public key encryption algorithms need K ( ) and K ( ) such that B B . . given public key K , it should be impossible to compute private key K B B requirements: 1 2 RSA: Rivest, Shamir, Adelson algorithm + - K (K (m)) = m B B - + + - Security 8-19
Prerequisite:modular arithmetic x mod n remainder of x when divide by n ■facts: [(a mod n)+(b mod n)]mod n=(a+b)mod n [(a mod n)-(b mod n)]mod n (a-b)mod n [(a mod n)*(b mod n)]mod n =(a*b)mod n ■thus (a mod n)d mod n=ad mod n example:x=14,n=10,d=2: (x mod n)d mod n =42 mod 10=6 xd=142=196 xd mod 10 =6 Security 8-20
Prerequisite: modular arithmetic ▪ x mod n = remainder of x when divide by n ▪ facts: [(a mod n) + (b mod n)] mod n = (a+b) mod n [(a mod n) - (b mod n)] mod n = (a-b) mod n [(a mod n) * (b mod n)] mod n = (a*b) mod n ▪ thus (a mod n)d mod n = ad mod n ▪ example: x=14, n=10, d=2: (x mod n)d mod n = 42 mod 10 = 6 x d = 142 = 196 xd mod 10 = 6 Security 8-20