1. KEY MANAGEMENT; OTHER PUBLIC-KEY CRYPTOSYSTEMS - Chapter 10 KEY MANAGEMENT; OTHER PUBLIC-KEY CRYPTOSYSTEMS - Chapter 10 KEY MANAGEMENT DIFFIE-HELLMAN KEY EXCHANGE ELLIPTIC CURVE ARITHMETIC ELLIPTIC CURVE CRYPTOGRAPHY

2. KEY MANAGEMENT KEY MANAGEMENT Two Aspects: Distribution of, Public Keys Secret Keys using PKC encryption

3. DISTRIBUTION OF PUBLIC KEYS DISTRIBUTION OF PUBLIC KEYS PUBLIC ANNOUNCEMENT - easy to forge (e.g. append public key to email) PUBLICLY AVAILABLE DIRECTORY - [name,public-key], secure registration/access PUBLIC-KEY AUTHORITY - shared public/private key pair with each user PUBLIC-KEY CERTIFICATES - exchange authentic keys without contacting authority

4. UNCONTROLLED PUBLIC-KEY DISTRIBUTION

5. PUBLIC-KEY PUBLICATION

6. PUBLIC-KEY DISTRIBUTION SCENARIO

7. 7 EXCHANGE OF PUBLIC-KEY CERTIFICATES

8. 8  Any participant can read certificate to determine name and public key of cert. owner determine name and public key of cert. owner  Any participant can verify that cert. is not counterfeit. counterfeit.  Only the certificate authority can create and update certs. and update certs.  Any participant can verify currency of certificate. certificate.

9. 9 EXCHANGE OF PUBLIC-KEY CERTIFICATES To read and verify: D KU auth [C A ] = D KU auth [E KR auth [T,ID A,K U a ]] = (T,ID A,K U a ) Timestamp counteracts: A’s private key learned by opponent A’s private key learned by opponent A updates private/public key pair A updates private/public key pair Opponent replays old cert. to B Opponent replays old cert. to B B encrypts using old public key B encrypts using old public key

10. 10 PKC TO ESTABLISH SESSION KEY

11. 11 PKC TO ESTABLISH SESSION KEY KU a and KR a discarded afterwards Advantage: No keys before or after protocol But, A  [KU a,ID a ] E  [KU e,ID e ] B B  E KU e [K s ] E  E KU a [K s ] A E learns K s A and B unaware

12. 12 PUBLIC-KEY DISTRIBUTION OF SECRET KEYS

13. 13 PUBLIC-KEY DISTRIBUTION OF SECRET KEYS N1 || N2 prevent eavesdropping Scheme ensures confidentiality and authentication

14. 14 DIFFIE-HELLMAN KEY EXCHANGE

15. 15 DIFFIE-HELLMAN KEY EXCHANGE

16. 16 ELLIPTIC CURVES INSTEAD OF RSA ELLIPTIC CURVES INSTEAD OF RSA  Replace multiplication with ’addition’ (a x a x a ….x a) mod n (a x a x a ….x a) mod n replaced by replaced by (a + a + a … + a) mod {elliptic curve} (a + a + a … + a) mod {elliptic curve} Multiplicative order (size of ’circle’)Multiplicative order (size of ’circle’) replaced by replaced by #points on elliptic curve #points on elliptic curve Elliptic curve defined by cubic equation:Elliptic curve defined by cubic equation: y 2 + xy = x 3 + ax 2 + b y 2 + xy = x 3 + ax 2 + b

17. 17 EXAMPLE OF ELLIPTIC CURVES

18. 18 ELLIPTIC CURVE E 23 (1,1)

19. 19 ECC KEY EXCHANGE

20. 20 ELLIPTIC CURVE vs RSA TABLE 10.2