---
title: 'Lecture 09 Key Distribution'
disqus: hackmd
---

:::info
ST2504 Applied Cryptography
:::

Lecture 09 Key Distribution
===

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## Table of Contents

[TOC]

Distribution of Public Keys
---
### Public Announcement
- users distribute pub keys to recipients/boradcast to community
- append PGP keys to emails & send across network
- post PGP keys on news grps/email list
- various site that support PGP keys as part of user profile
- Eg. facebook
- convenient & works well for small scale distro
- weakness - forgery
- anyone can create key claiming to be someone else & broadcast
- adversary can masquerade as claimed user

### Publicly Available Directory
- dir must be trusted with properties
- contains {name, public-key} entries
- participants register securely with dir
- participants can replace key anytime
- dir periodically published
- can publish entire/just changes of dir
- dir can be accessed electronically
- dir must be trusted
- greater security compared to public announce but still vulnerable to tampering/forgery
- pretend to be authorised dir
- change records in dir

### Public-key Authority
- improved security - tighten control over distro of keys from dir
- central authority maintains dynamic dir of pub keys of everyone
- requirements
- authority secured
- all users know pub key of dir/authority
- only authority know corr private key
- real-time access to dir/authority when keys needed
- AKA always on server
- issues
- authority can be bottleneck
- records maintained can be tampered

__E: Encryption/signing msg (if from authority)
N: Some random val that's hard to predict__

- A & B know their key pair
- pub/priv keys & so is authority
- A & B published their pub key to authority
- authority verify all pub keys correct
- A & B know pub key of authority
- msg 3, 6 & 7 are for A & B to cfm they talking to right pt

### Public-key Certificate
- to overcome bottleneck, can use pub key certs
- allow key exchange w/o real-time access to pub-key authority
- binds identity to pub key
- with other info like period of validity, rights of use etc.
- pub key signed by trusted Certificate Authority (CA) can be verified by anyone
- pub key of CA is publicly available


- when A & B want to comm, only msg sent is (1) and (2)
- M1 & M4 happen in advance way before msg (1) and (2)
- this why performance improved greatly
- only (1) and (2) needed for A & B to exchange msg
- no msg goes to authority during comm
- certs exchnage between A & B issued by CA
- CA not involved in comm
- certs received verified using CA's pub key

#### Certificate

### Key Exchange
- sharing secret keys securely with aid of pub key
- pub key encryption
- need long key to be effective
- AKA hard to break
- hence slow/CPU intensive
- use secure way to exchange secret/session key
- encrypt msg based on secret/session key

Diffie-Hellman Key Exchange
---
- 1st pub-key scheme proposed
- by diffie & hellman 1976
- note
- Williamson (UK CESG) secretly proposed the concept in 1970
- DH not for data secrecy/auth
- DH key exchange is practical method for public exchange of secret key/shared value


- DH features
- establish common key known only to the 2
- val of key depends on participants & their priv & pub key info
- properties
- cannot be used to exchange arbitrary msg
- shld be
- computationally easy - forward processing
- exponentials modulo a prime/polynomial
- computationally hard - reverse processing
- discrete logarithms

### DH Setup
- all agree on global params
- p is large prime int
- g is primitive root modulo of p
- ea user generates his/her key
- chooses secret key
- 
- ea user makes pub key
- alice's pub key
- 
- bob's pub key
- 
- shared session key for users


- K(ab) is session key in priv key encryption scheme between Alice & Bob
- subsequent comms between Alice & Bob will have same key as before
- unless they change their pub keys
- atker must solve discrete log to get Xa r Xb

#### Example

### Key Exchange Protocols
- if pub key properly secured in central dir AKA with PKI
- other users can query pub key, compute secret key, communicate
- auth of user possible because of PKI
- DH key exchange atks
- replay atks with/without PKI
- MITM atks (w/o PKI)

###### tags: `ACG` `DISM` `School` `Notes`