UCB Security Jean Walrand EECS Outline UCB Threats Cryptography Basic Mechanisms Secret Key Public Key Hashing Security Systems Integrity Key Management Identification UCB Threats Against Type Protection Computers Physical Infection Intrusion Physical security lock Virus detection Firewall passport control Users Identity Privacy Signature password watermark Encryption relay Documents Integrity Confidentiality Message authentication code Encryption UCB Cryptography Basic Mechanism P E C D P Decryption function Cyphertext Sent Encrypted Text Encryption Plaintext function UCB Cryptography continued Basic Mechanism continued P E C D P D is the inverse of E E should be a one way function Easy to compute Hard to invert Looking at E P it should be hard to get P Looking at many E P it should be hard to figure out the function D or Knowing many pairs P E P it should be hard to figure out the function D Cryptography UCB continued Secret Key E E K D D K where K is a shared secret Key distribution Alice P E K Bob C K D K P UCB Cryptography continued Secret Key EXAMPLE 1 One Time PAD C P K addition bit by bit modulo 2 no carry K random string of bits 50 0 50 1 If used only once this is a perfect code C is perfectly random and no information about P Application Top Secret transmissions K is stored in a CD ROM that is delivered securely ahead of time UCB Cryptography continued Secret Key EXAMPLE 2 Data Encryption Standard DES P Key K DES Algorithm C Algorithm is known but the key is secret K 40 bits Weak 56 bits Marginal 128 bits Safe UCB Cryptography continued Note Modes of Encryption 6 4 b its 6 4 b its 6 4 b its E 6 4 b its 6 4 b its 6 4 b its E R n 1 C n 1 R Cn 1nE 1 E Pn Pn R R n E C D Pn Pn n n Z C n Z n 1 P P n n 1 Cn n UCB Cryptography continued Public Key Bob use E Bob to talk to me Only Bob knows D Bob Trapdoor one way function Example Rivest Shamir Adleman p q prime n pq z p 1 q 1 and e coprime d s t ed 1 mod z If P in 0 1 n 1 and C P e mod n then C d mod n P e n public d n private Finding d from e n is believed to be hard UCB Cryptography continued Hashing H P short e g 160 bits Hard to find P and P s t H P H P UCB Security Systems Integrity Alice sends P H P where H P is protected by a Authentic channel b Message Authentication Code Note that E H P K with K secret may not be secure For instance Z H P R is not secure since then Eve can compute H P from P and R from Z H P and then Eve can send P and H P R Secure H K2 H K1 P where K1 and K2 are secret to Alice and Bob since Eve cannot compute H K1 P UCB Security Systems Integrity continued continued Alice sends P H P where H P is protected by c Digital Signature Alice sends C D P Alice and Bob recovers P E C Alice However if Eve constructs C and computes P E C Alice Bob will think that Alice sent D P Alice Instead Alice should send D P H P Alice because it is unlikely that Eve can find some C so that E C Alice has the form P H P for some P UCB Security Systems continued Key Management To share a secret K a Hand delivery b Encrypt and distribute K using some other secret key e g Kerberos Shared Key with Kerberos Get Loggin Key Get Session Key c Use a public key to distribute secret key K e g PGP UCB Security Systems continued d Public key agreement Diffie Hellman Alice and Bob agree on public z p Alice chooses a and Bob chooses b Alice computes A z a mod p and sends it to Bob Bob computes A b mod p Bob computes B z b mod p and sends it to Alice Alice computes B a mod p One can show that A b mod p B a mod p z ab mod p K Indeed A z a mp so that A b z a mp b z ab mod p However D H is not robust to a person in the middle attack Imagine Eve gets in the middle and plays the role of Alice Solution Signing the exchange Alice sends A to Bob and Bob sends B to Alice Alice signs A B and sends it to Bob Bob signs A B and sends it to Alice Eve cannot fake these signatures UCB Security Systems continued Identification Bob wants to ascertain the identity of Alice a Passwords Alice has a secret password K and sends Alice K Bob maintains H K to verify Alice However can be intercepted b Challenge Response Bob sends string X to Alice who computes f X K where K is a secret that Alice and Bob share However Bob must know K c Public Key Bob chooses X and sends E X Alice to Alice who computes X and sends it back to Bob d Digital signature Bob sends X to Alice who signs it and returns it to Bob
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