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Network Security

Explore communication security, confidentiality, authentication, encryption methods, shared key establishment, public key crypto, RSA, DH, network security protocols, prime number generation, efficiency optimizations, crypto systems, certificates, and practical applications.

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Network Security

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  1. Network Security Review

  2. Secure channel • Communication security • Confidentiality • Message • Traffic • Authentication • Integrity • How to achieve? • Establish shared key • Encrypt • MAC • Left out: non-repudiation, etc.

  3. Shared Key Establishment • “Trusted third party” • Kerberos • Tickets • Public key methods • SSL • IPSEC • “Out-of-band”

  4. Public Key Crypto

  5. Diffie-Hellman RSAN=pq; ed  1 (mod (N))Public:e,N;Private:d,N Encrypt M: CMemodN DecryptC:MCdmodN Sign M: SMdmod N VerifyS: Se M (modN) Public Key techniques p, g Alice Bob a b magamod p mbgbmod p ma mb mbamod p =gabmod p= mabmod p ? shared secret key! • Discrete log: • Given y,p,b • Find x: bxmod p = y • Factoring: • Given N=pq • Find p,q

  6. Discrete log based schemes • DH (key establishment) • DSS/DSA (signatures) • El-Gamal (signatures, encryption) • Elliptic Curves Cryptography (ECC) • Why modulus (p) is so large? • Little-step/giant-step attack

  7. Factoring based • RSA • Square Roots (=Factoring) • Rabin (Encryption, Signature) • Fiat-Shamir (ID scheme, Signature)

  8. World mod N • How many objects?|Z*N|= (N); for all z Z*N, z (N) mod N=1 • If N=pq, then (N)= (p-1)(q-1)[If N=p, then (N)= p-1] • Blum integers: N=pq, pq3 (mod 4) • Thenx(p+1)/4mod p= y; y2x(p+1)/2x(p-1)/2 x±x mod p

  9. Chinese Remainder Theorem (CRT) • Given y2 x mod p; z2 x mod q; N=pq;Find s: s2 x mod N • More generally:Given a,A, b,B;Find x: x a mod A, x b mod B • Let u, v be s.t. uA 1 mod B, vB 1 modAThen x=uAb+vBa[indeed: x mod A = uAb+vBa = vBa = a; x mod B = uAb+vBa = uAb = b] • How to find u,v?

  10. Extended GCD • Euclid’s GCD algorithm(greatest common divisor):gcd(a,b) = gcd( b, a mod b) =…= gcd(a’,b’)=ca’=ib’+c, … , ax+by=c • If gcd(a,b)=1: ax 1 mod b

  11. Summary(factoring-based) • RSA • Given p,q; Can compute (N), for N=pq; • With Extended gcd, can compute e, d  1/e mod (N); • gcd(e, (N)) must be 1 • Rabin • Using Blum integers can compute SQRT mod p,q • Using CRT can combine them to SQRT mod N

  12. Prime number generation • Why? • How? • Exhaustive search • Too long • Miller-Rabin • Little Fermat’s Theorem (again) • Prime Number Theorem • #of primes between R and 2R is R/lnR • i.e. Prob[ random R is a prime ] 1/lnR

  13. Efficiency for all • Exponentiation: Repetitive Squaring • bA mod N takes 1.5 lg A long multiplications • Cost of multiplication • quadratic in length • Optimization: mod N  (mod p) + (mod q) +CRT • Watch out!

  14. Attacks on factoring • (N), N => factoring (quadratic equation) • Trick: • obtain x, s.t. x0 mod p, x mod q0 • gcd(x, N)=p • SQRTmodN => Factoring • vy2mod N; zSQRTmodN(v) • If z  ±y, then x  y-z • Computing (mod p) + (mod q) + CRT • Random error mod p (or mod q) => factoring

  15. Other Crypto Encryption Hashing MACs

  16. Encryption • One time pad • Block cipher • DES • Feistel approach • AES/Rijndael • Modes of operation • EBC, CFB, CBC, etc. • Stream ciphers • RC-4 • Pseudo-random generators

  17. Hashing • Hashing algorithms • MD-5 • SHA • Applications • Digital signatures • MAC

  18. Systems Certificates SSL IPSEC Kerberos

  19. Certificates • X-509 • CA’s • Trust infrastructure • Hierarchical • X.509 • Networks of Trust • PGP

  20. SSL • TCP level secure channel • Establish Shared Secret • DH+Certificates [+signatures] • RSA+Certificates [+signatures] • Kerberos [TLS] • Do not confuse with Kerberos over SSL/TLS • Encrypt & MAC • Usually authenticates only server • Client authentication possible • Typical application: HTTPS

  21. IPSEC • IP level secure channel • Similar tools to SSL • Some traffic confidentiality • Both ends authenticated • Tunneling • Typical application:VPN

  22. Kerberos • Key-Distribution Centers approach • Trusted Third Party – another term • Authentication Server • Ticket Granting Servers • Tickets • Realms

  23. Other topics • Firewalls • Non-repudiation • SET

  24. Final: Tuesday May 10 9-11am See you there! Best of Luck!!!

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