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### T101 Networks

12 – Key Exchange

Updated Notes

- the original notes from last week contained an error in the transposition cipher
- new notes are on moodle

Practical Demo

- Competency-based assessment
- tick list is on moodle
- take the pressure off the final week
- optional…
- …but you have to do it sometime
- no penalty if you don’t succeed, you’ll get another go if there is time
- exam conditions apply

Lesson Objectives

- explain problems with key exchange
- describe a solution to the key exchange problem
- explain problems with asymmetric ciphers

But first…

- Zodiac killer and his first cipher
- was a substitution cipher
- used multiple symbols to represent the same letter
- awkward to crack because the frequency analysis fails, and he also made spelling mistakes and cipher errors
- cracked by hand by guessing that:
- the first letter would be ‘I’
- the message would contain “kill’ or ‘killing’ or ‘killed’ etc…

Cryptography Basics

- Cryptography is…
- protecting privacy
- authentication of identities
- preservation of integrity

- …in an environment of mistrust

Symmetric Ciphers

- same key to encrypt as to decrypt
- on a network, both parties must have the same key
- the key is called a shared key
- big problem is key exchange
- how big was this problem?

Asymmetric Ciphers

- … but asymmetric ciphers can solve the big problem that symmetric ciphers have
- this week, solving the big problem
- but first…

Lab Results

- old substitution ciphers are very easy to crack
- the strength of modern symmetric ciphers is entirely based on the length of the key
- 128 bits (16 bytes) is a good strength key because:

How long is that?

- 3e26 years is 3 followed by 26 zeroes
- 300,000,000,000,000,000,000,000,000
- so if we had 10,000,000 computers that were all running 1,000 times faster the lab computers, you would crack the code in about…
- …30,000,000,000,000,000 years
- the universe is 13,700,000,000 years old

Key Choice

- so symmetric ciphers are secure provided that
- the key length is long enough not to be brute forced
- 128 bits looks good, shorter keys are problematic

- the key is chosen randomly
- but humans are not very good at remembering random numbers

- the key length is long enough not to be brute forced

Short Keys Example 1

- WEP initially used a 40 bit key
- giving at most 240 different keys
- some keys are weaker than others, so fewer keys are available

- there are other problems with WEP
- hence WEP can be cracked in a few minutes if you have enough ciphertext

Short Keys Example 2

- DVDs are protected using CSS which uses 40 bit keys
- there are problems with the way CSS uses the key, reducing the effective key length to 32 bits
- the key can be recovered in less than 1 minute even on slow hardware
- hence DVDs can be copied easily

Why 40 bits?

- the US considered strong security as “munitions” and therefore came under the export of arms legislation
- 40 bit encryption was considered weak, and therefore not munitions
- restrictions were lifted in 1996

Shared Key ProblemsHow many keys are needed?

Key Exchange

- as the number of people gets big, the problems get worse
- how to exchange keys securely with all these people?
- how to keep a (secure) record of all those keys?
- how to (securely) change a key if one gets lost?

Idea 1 – A KDC

- Key Distribution Centre (KDC)
- if everybody exchanges a key securely with the KDC, we can communicate with it securely
- to communicate with a third party, we ask the KDC for a key
- the KDC gives you and the third party the same key

KDC Problems

- who do you trust to be the KDC?
- who does everybody trust to be the KDC?
- the KDC knows all your secrets
- how do you exchange initial keys with the KDC?
- …and other problems

KDC today

- KDCs are a good option for LANs
- computers on a LAN, generally trust other computers on a LAN inside the same organisation
- Microsoft’s Active Directory is an example of a KDC
- how does AD get your initial password?

Key Exchange Problem

- originally solved by Whitfield Diffie and Martin Hellman, called Diffie-Hellman key exchange
- still used but currently the most common method is to use asymmetric encryption
- mostly RSA encryption
- elliptic curves getting to be popular because they use smaller numbers than RSA so the arithmetic is easier

Asymmetric Encryption

- key used to encrypt is called the public key
- key used to decrypt is called the private key
- the two keys are related to each other
- the private key cannot be easily discovered from the public key
- how does this help?

Shared Key Exchange using Asymmetric ciphers

- Alice wants to talk to Bob
- Alice asks for Bob’s public key
- Bob sends his public key

Send me your public key

Here is my public key

Shared Key Exchange with using Asymmetric ciphers

- Alice creates a shared key and encrypts it with Bob’s public key

Bob’s Public key

Asymmetric

Encryption

Ciphertext = Encrypted key

Cleartext = Shared key

Send the encrypted shared key to Bob

Shared Key Exchange with using Asymmetric ciphers

- Bob gets encrypted shared key
- Bob uses his private key to decrypt the shared key

Bob’s Private key

Asymmetric

Encryption

Cleartext = Shared key

Ciphertext = Encrypted Shared key

Shared Key Exchange with using Asymmetric ciphers

- all messages between Alice and Bob can now be encrypted with symmetric ciphers using the shared key

Encrypted Message = “Hello”

Key Exchange

- using asymmetric encryption to exchange a shared key is a good solution because
- the asymmetric encryption and decryption tasks only happen once, and at the start of the communication
- so it takes a little longer to set the communication channel up but…
- …fast symmetric encryption is used for the rest of the communication

Exercise

- see page 4 of this week’s notes

Eve the Eavesdropper

- what does an eavesdropper see?
- request for Bob’s public key
- Bob’s public key
- a message encrypted with Bob’s public key
- messages encrypted with a shared key

- in order to read the messages, Eve would need to either
- get Bob’s private key or
- brute force the private key or the shared key

Are we there yet?

- we have now got
- privacy using symmetric encryption
- key exchange using asymmetric encryption

- we still have a big problem
- before next week, work out how Alice can be duped by Eve!

Asymmetric Cipher Uses

- why not just use asymmetric ciphers, then everybody just needs one private/public key pair?
- we don’t need to use symmetric ciphers???
- but…

Problems with Asymmetric Ciphers

- all current asymmetric systems rely on some awkward arithmetic
- coding errors in the arithmetic have been known
- about 1,000 times slower than symmetric (although Elliptic Curves are better)
- produce big chunks of ciphertext (because of those big numbers that are used)
- so not suitable for encrypting lots of small packets, especially if speed is important

More problems…

- an advance in mathematics may break asymmetric encryption
- remember that RSA relies on the notion that it is easy to multiply two large numbers together, but there is no known quick way to factor very large numbers

- perhaps someone has already made this breakthrough
- it is hoped that the promise of instant fame and a Nobel prize will be enough to ensure publication

and another one…

- imagine using asymmetric encryption to encrypt votes in a poll
- poll site sends you their public key
- you encrypt the message “NATIONAL” or “LABOUR” or “GREEN” etc… using the public key, and send your vote
- Eve intercepts the encrypted message
- Eve can work out who you voted for!!!
- how does she do it?

Summary

- key exchange is a problem when there are many users
- a KDC can help on the LAN
- asymmetric encryption solves the key exchange problem…
- …almost

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