Skip to main content

Catalyst: Prime numbers and unbreakable codes

Posted 
Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume.
Man and woman look at electrical gadgets
Catalyst: Prime numbers and unbreakable codes

SUBJECTS:  MathsTechnologies

YEARS:  5–6, 7–8


Imagine if anyone was able to read all our secret, encrypted messages and information.

Watch and find out how scientists at the Australian National University are developing a new encryption system using quantum physics and quantum computing.


Things to think about

  1. 1.Encryption 'keys' are currently based on prime numbers. A prime number is a number that can only be divided evenly by 1 and itself. What about the numbers 17 and 12? The prime number is 17, 12 can be divided evenly by 1, 2, 3, 4, 6 and 12. Mentally think of prime numbers between 0 and 30. Can you find 10?
  2. 2.How are prime numbers used in encryption? Listen for the explanation of a 'public' key and a 'private' key. Look for multiplications written on the whiteboard 3 x 5, 71 x 113 and 947 x 2131 and their answers. Which of part of these are 'public' keys and which part are 'private' keys? Dr Tim Ralph explains that public keys are harder to crack as the number used as a 'public' key gets larger. Why is this the case?
  3. 3.Find or create a list of all the prime numbers less than 100. How many 'public' keys could you create? Why might one 'public' key be better than another? If you were given a 'public' key that had 4 digits (1537), what strategies would you use to find the 'private' key (two prime numbers multiplied to give the 'public' key)?
  4. 4.Here's an application of encryption. If a 'public' key is 33 then the 'private' key is 3 and 11 which can be written as 311. This can be used to code words, for example, 'HELLO' would be written as KFMOP. H has been shifted forward 3 spaces to K. E is shifted 1 space to F. L is shifted 1 space to M (we have now completed one cycle of 311 so we start again). The second L is shifted 3 spaces to O and the O is shifted 1 space to P. Write a short phrase and choose two prime numbers as a 'private' key. Use the key, as shown above, to write your phrase in code. Swap your message with a friend, giving them only the 'public' key to decipher it.



Date of broadcast: 24 Aug 2006


Copyright

Metadata © Australian Broadcasting Corporation and Education Services Australia Ltd 2012 (except where otherwise indicated). Digital content © Australian Broadcasting Corporation (except where otherwise indicated). Video © Australian Broadcasting Corporation (except where otherwise indicated). All images copyright their respective owners. Text © Australian Broadcasting Corporation and Education Services Australia is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).

Posted