You know that when you log on to a computer system you have to use a password. Passwords are very important in protecting access to personal areas in computer systems and also to files and bank accounts. Credit and debit cards use PINs, which are the same as passwords but they use only digits.
The more characters available the stronger the passwords can be.
Passwords based on binary digits would be weak as there are only 2 of them. We know that in 8 bits there are a possible 2^8 combinations (256) so it wouldn't take long to try them all. Even in 32 bits there are just over 4 billion combinations, which is a small number in modern computing.
Passwords based on denary digits (0-9) can provide 10^4 combinations (10,000) in 4 digits, which is adequate for a PIN as an ATM will keep any card after 4 wrong entries. If a digit can only be used once the number of permutations shrinks considerably to just 210.
Passwords based on the 26 English letters can provide a much greater number of permutations. A password of 6 letters has 26^6 permutations, which you might have thought was a very large number. This is not really 'safe', however, as it turns out to be not very big at all in modern computing; what's more, many people use real words or names that can be found by checking a dictionary.
Passwords based on the 52 upper and lower case letters plus the 10 digits plus symbols such as £ and $ provide a more reassuring number of passwords. Passwords should have at least 8 characters and include at least 1 capital, 1 lower case letter and 1 digit, giving a range of 62^8 permutations. The password should be made up of random letters and digits and should not be based on a real word. These are known as 'strong' passwords.
How long would it take to discover a password like this of 8 characters? What about 12 characters?
What effect does the fact that password length is generally unknown have on the number of possible permutations?
Create a spreadsheet to investigate these features of passwords. Find the number of permutations in passwords of 6 and 8 characters in 26 and 62 character sets and then find the number of hours/days/years it would take to crack them at different speeds of execution. Of course, you might hit lucky and get it on the first go but the chances of this are small.
Biometric methods: face, fingerprint, iris scan, DNA, brain-response. Are they fool-proof?
Cards and keys: used in combination with passwords or PINs?