Recap: Part 6 Public key cryptosystem: a pair of keys Public-key: - - PowerPoint PPT Presentation

Recap: Part 6

• Public key cryptosystem: a pair of keys

– Public-key: meant for public, should be given out – Private-key: remains always secret – An operation performed by one key in the pair can be inversed only by the other key

Encryption: e(M, kB) = X Decryption: d(X, KB) = M

Recap: Part 6

• One-way function: usage in achieving integrity

H(M, k) = x and H(M, k) ≠ y Given x, k; it is impossible to find M

Recap: Part 6

• Digital Signature: A sequence of operations

performed by a sender, such that the receiver

• f the message can be ensured with the

following 3 security properties:

– Message authentication – Message integrity – Message non-repudiation

Recap: Part 6

• Digital Signature:

H(M) = x E(x, KA) = MA Alice sends M and MA to Bob over insecure network Bob performs the following (Bob knows kA): H(M) = x D(MA, kA) = x

Exercise

• We just saw composition of a digital signature

that Alice performed on message M. The composition provided authentication, integrity, non-repudiation

• What needs to be done in order to provide

confidentiality to message M?

• http://crypto.stackexchange.com/questions/5782

/why-is-asymmetric-cryptography-bad-for-huge- data

Sam acting as Trusted Third Party (TTP)

Sam Alice Bob

KPS KSS KPA KSA KPB KSB (KPA KPB … )

Certification Authority

Sam Alice Bob

KPS KSS KPA KSA KPB KSB (KPA KPB … )

Digital Certificate from a CA

Sam acting as TTP in NSSK Protocol

Sam Alice Bob

KAS KBS (KAS KBS … )

{NA}KAB {NA - 1}KAB

Diffie Hellman Key Exchange

Alice Bob

KAS KBS

{NA}KAB {NA - 1}KAB

DHKE Protocol

• 1. Bob: comes up with 2 prime numbers g, p
• 2. Alice: pick a secret number a and compute

ga mod p = A

• 3. Bob: pic a secret number b and compute

gb mod p = B

• 4. Alice: Ba mod p = (gb mod p)a mod p

gba mod p = KAB

• 5. Bob: Ab mod p = (ga mod p)b mod p

gab mod p = KAB

Diffie Hellman Key Exchange

Alice Bob

g, p, b

{NA}KAB {NA - 1}KAB

g, p, a

Exercise

Sam Alice Bob

KPS KSS KPA, KSA, KPS, g, p, a KPB, KSB, KPS, g, p, b (KPA KPB … )

Alice wants to send a huge message M to Bob with the following properties: Authentication, integrity, non-repudiation, confidentiality Alice and Bob trust TTP Sam Symmetric key encryption is multiple orders cheaper than asymmetric key encryption List out the steps involved in transferring M from Alice to Bob