Enigma, Cyphers and Encryption How do computers communicate securely and secretly?

Caesar Cypher h e l o a b c d e f g h i j k l m n o p q r s t u v w x z h e l o   Key a to h

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Caesar Cypher h e l o   https://www.tes.com/teaching-resource/operation-ultra-gchq-codebreaking-project-6340594 Secret key a to h

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Caesar Cypher – plus 1 h e l o o l r u +1 Move inside rotor once clockwise at the beginning of each move h e l o  o l  r  u  +1 Secret key a to h Move 1

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More rotors

The Prinigma machine https://slp.somerset.org.uk/sites/edtech/New%20Wessex/Year%206/Y6%20Programming%20UP%20Prinigma%20Machine.pdf http://wiki.franklinheath.co.uk/index.php/Enigma/Paper_Enigma

Prinigma “ By making our own prinigma machine it was easy to understand something that was so hard to invent in the first place.” Y6 St George’s

Prinigma Three rotors h e l o “It was fun to build my own machine and the videos were interesting, especially seeing the original machines. I wish I had had more time to crack codes.” Y6 St George’s h e l o   Secret key Reflector B Q, E, V, A

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Prinigma Three wheels Move right rotor once each time at the start h e   Three wheels Move right rotor once each time at the start “It was really cool to see how the enigma machine worked and how it was used. It was fun that we could upcycle something to make our own technology.” Y6 St George’s Secret key Q, E, V, A Move 1

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Cypher and Encryption https://www.youtube.com/watch?v=ZghMPWGXexs

Where do we see encryption? Connections with learning

Common letters Do different languages have different frequent letters? English - e t a o i n s h r d l u Polish - https://en.wikipedia.org/wiki/Letter_frequency#Relative_frequencies_of_letters_in_other_languages

Public and Private keys? A tells you where there is place you can safely put your information – PUBLIC KEY B posts his code – PRIVATE KEY Only A can open box and find the PRIVATE KEY for B

In reality – AES (Advanced Encryption Standard) algorithm Bob chooses two very large (distinct) prime numbers p and q; n=pq , m= lcm {p−1 , q−1 } (lcm is the least common multiple ); Bob chooses r , where r>1 and r is coprime with m (i.e. r and m have no factors in common); Bob then finds the unique s such that rs≡1(mod m) Bob now tells everyone what n and r are, but does NOT say what p, q or s are. Alice wants to send the message M (a single number) where M and n are coprime and 0<M<n. Alice finds Mc , where Mc≡Mr(mod n) , and sends the message Mc to Bob. Bob receives the message Mc from Alice and decodes it. Now Bob knows p, q, m, n, r, s , and he uses these to decode the message Mc from Alice so as to find M . To do this Bob uses the theorem that (Mc)s≡M(mod n)

Playing with primes What is the largest prime under 100? What is the largest prime under 1000? What is the largest prime under 10000? What is the largest prime under 1000000000000000000? Can you write an algorithm to find these? Can you program this?

Playing with Factors Think of the factors of: 12 120 1200 12000 120000 1200000 12000000 1200000000000000000000000000000000000000000

Websites https://www.amazon.co.uk/

Wireless connections WPA2 – Wi-Fi Protected Access 2 AES – Advanced Encryption Standard Do your children know how to set up a secure link?

WhatsApp Provides encrypted communication https://www.techadvisor.co.uk/feature/internet/how-secure-is-whatsapp-whatsapp-security-encryption-explained-3637780/

Internet of Things How far are we going to allow the ease of use to question our privacy or state intervention? Smart speakers? Self driving cars?