AES:Advanced Encryption Standard symmetric-key NIST standard,replacied DES (NoV2001) 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 Network Security 8-16
Network Security 8-16 AES: Advanced Encryption Standard symmetric-key NIST standard, replacied 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
Public Key Cryptography symmetric key crypto public key crypte requires sender, radically different receiver know shared approach [Diffie- secret key Hellman76,RSA78] Q:how to agree on key sender,receiver do not in first place share secret key (particularly if never public encryption key “met")? known to all private decryption key known only to receiver Network Security 8-17
Network 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
Public key cryptography Bob's public key @学K Bob's private B key plaintext encryption ciphertext decryption plaintext message,m algorithm K含m algorithm message m-Kg(Kg(m) Network Security 8-18
Network 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 -
Public key encryption aigorithms requirements: (1) need Kg(and K(such that KgKg(m》)=m 2 given public key Kg it should be impossible to compute private key KB RSA:Rivest,Shamir,Adelson algorithm Network Security 8-19
Network 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 - + + -
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 mod10=6 Network Security 8-20
Network 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 xd = 142 = 196 xd mod 10 = 6