KEY MANAGEMENT OTHER PUBLICKEY CRYPTOSYSTEMS Chapter 10 KEY

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

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

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

UNCONTROLLED PUBLIC-KEY DISTRIBUTION 4

PUBLIC-KEY PUBLICATION 5

PUBLIC-KEY DISTRIBUTION SCENARIO 6

EXCHANGE OF PUBLIC-KEY CERTIFICATES 7

EXCHANGE OF PUBLIC-KEY CERTIFICATES § Any participant can read certificate to determine name and public key of cert. owner § Any participant can verify that cert. is not counterfeit. § Only the certificate authority can create and update certs. § Any participant can verify currency of certificate. 8

EXCHANGE OF PUBLIC-KEY CERTIFICATES To read and verify: DKUauth[CA] = DKUauth[EKRauth[T, IDA, KUa]] = (T, IDA, KUa) Timestamp counteracts: A’s private key learned by opponent A updates private/public key pair Opponent replays old cert. to B B encrypts using old public key 9

PKC TO ESTABLISH SESSION KEY 10

PKC TO ESTABLISH SESSION KEY KUa and KRa discarded afterwards Advantage: No keys before or after protocol But, A [KUa, IDa] E [KUe, IDe] B B EKUe[Ks] E EKUa[Ks] A E learns Ks A and B unaware 11

PUBLIC-KEY DISTRIBUTION OF SECRET KEYS 12

PUBLIC-KEY DISTRIBUTION OF SECRET KEYS • N 1 || N 2 prevent eavesdropping • Scheme ensures confidentiality and authentication 13

DIFFIE-HELLMAN KEY EXCHANGE 14

DIFFIE-HELLMAN KEY EXCHANGE 15

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

EXAMPLE OF ELLIPTIC CURVES 17

ELLIPTIC CURVE E 23(1, 1) 18

ECC KEY EXCHANGE 19

ELLIPTIC CURVE vs RSA TABLE 10. 2 20