from simple addidition and subtraction plus logical thinking, In fact some of the most
famous code breakers in history have been mathematicians who have been able to use
quite simple maths to uncovered plots, to identify traitors and inflience battes.
The Roman Times
Nearly 2000 years ago, Julius Caesar was busy taking over the word, invading countries
to increase the size of the Roman Empire, he needed a way of communicating his
battle plans and tactics to everyone on his side without the enemy finding out, Caesar
would write his messages to his Generals in code, using a simple alphabet.
Instead of writing the letter A he would write the letter that comes three places
further into the alphabet, the letter D, instead of the letter B, hee would use E,
and istead of C, it would be F, and so n, when he got to the end of alphabet he
would have to go right back to the beginnng, so instead of an X, he would write A,
instead of Y, he wrote B, and Z would be a C and soon.
When Caesar`s Generals came to decipher the message they knew that all they
had to do was to go back three places in the alphabet to solve the code.
The maths came into it as Caesar was using an alphabet form of 0-25 as said,
0 being 1, A, 2, B, 3 etc, then encoding, shifting the alphabet forward three
places is the same as adding three to the starting number, for example:
A is 0+3=3which is D, I is 8+3=11 which is L, He would have to be careful again
when getting to the end of the alphabet, as there is no number 26, he would
go back to 0 again, In maths this is called `MOD` 26, instead of writing 26 he
would have to go back to 0.
I think our alphabet nowadays of A-Z and 1-26 would have been easier to use.
With this simple alphabet number code Caesar used, it was a simple code to crack.
It can be easily done just by trial and error, an enemy code breaker would only
have try out 25 different possible shifts before they were able to read the message,
which means that the message wouldn`t be a secret for very long.
There was another code used at this time, instead of using a letter, a symbol or
picture was used, A would be an asterik * and B a plus sign +, etc.
For a long time people thought this code would be very hard to crack,it would
take the enemy ages to uncode it, finding which symbol or picture was for
which letter, there was over 400 milion symbols and pictures possible combinations
to try.
This type of code was used by Mary Queen of Scots when she was plotting
against Elizabeth the First, Mary wanted to kill Elizabeth so that she herself could
be Queen of England,by sending a coded message of this sort to her co-conspirator,
Anthony bablington, she set the plan in action.
Unfortuately for Mary there was a very simple way of cracking the code that
doesn`t involve trial and error, but which did involve maths!
An example of a message sent, try and decode this;
hqhpb dssurdflklqj
Wkluwb ghdg
Uhwuhdw wr iruhvw
What does it say?
letters in the English language are unusual because some get used more often
than others, E and A are more common than Z and Q, the graph shows the
averge frequency of the letters in used, to compile this information people
looked through thousands and thousands of books, magazines and newspapers
and counted the number of times each letter came up.
`frequency analysis` and it was a clever method used with cracking codes
that resulted in Mary getting her head chopped off!