In which I celebrate the life of Edgar Allen Poe
A monoalphabetic substitution is one where a letter ofplaintext always produces the same letter of ciphertext.
These are special cases, of the more general substitution, so you may like to read the description of these first.
In general, an example of a monoalphabetic substitution is shown below.
PLAINTEXT a b c d e f g h i j k l m CIPHERTEXT Q R S K O W E I P L T U Y PLAINTEXT n o p q r s t u v w x y z CIPHERTEXT A C Z M N V D H F G X J B
You may naïvely think that this cipher is secure, after all there are 26! different cipher alphabets ( 4 x 1026 ) to choose from, however the letter frequencies and underlying patterns will be unchanged - and as such the cipher can be solved by pen and paper techniques. The best way to see how the cryptanalysis is performed is by doing some analysis.
Let us try to solve a monoalphabetic cipher. In solving this I will not use any of the more advanced techniques available.
These more advanced techniques include looking systematically at the position of letters in words in order to identify vowels, pattern words, and looking at the letter frequencies, though common pairings (TH, HE etc.) may come up. For more detail, see books such as cryptanalysis by Helen Fouche Gaines
Note, this cipher was NOT constructed specially for this page, it was generated automatically by a program and I solved it as I wrote the page. (I no longer have a copy of the program)
Here is the ciphertext:
Ftt bdv bfhvq efno ukvj f tnmvbnxv ic bdv fkvjfyv Fxvjnlfz fjv qevzb ic bdv yukvjzxvzb nz tvqq bdfz f qvluzo. Pnx Mnviny
Let's count some letters. The most common letter is V, followed by F, N, B, Z. The most common English letters are ETAIN... it is highly likely that we have some matches here - though it is not a certainty. Also 'F' probably stands for I or A as 'F' appears alone more than once.
It should also be noted that where V ends a three letter word, that word is 'BDV'. The most common trigraph (three letter sequence) in English is 'THE' - so let us guess that 'BDV' is 'THE'.
the t e e et e the Ftt bdv bfhvq efno ukvj f tnmvbnxv ic bdv e e e e e t the e e t fkvjfyv Fxvjnlfz fjv qevzb ic bdv yukvjzxvzb e th e nz tvqq bdfz f qvluzo. e Pnx Mnviny
The sequence 'BDFZ' gives a little hope, as f is likely to be 'A' or 'I' then 'BDFZ' could be 'THIS' or 'THAN' (not 'THAT'!).
What else can we establish? Either N or Z is likely to be a vowel ('NZ') - and so is I or C ('IC').
Looking at the first word, Ftt - F is likely to be A or I, so what could this be?
I think that the only reasonable answer is 'ALL'. This, in turn, implies that 'BDFZ' is 'THAN'. Filling in these assumptions give us the following:
All the ta e a e a l et e the Ftt bdv bfhvq efno ukvj f tnmvbnxv ic bdv a e a e A e an a e ent the e n ent fkvjfyv Fxvjnlfz fjv qevzb ic bdv yukvjzxvzb n le than a e n nz tvqq bdfz f qvluzo. e Pnx Mnviny
It's at this stage where, if all is correct, words will appear. I spent a few moments looking, and I thought I recognised a word in 'yukvjzxvzb' - '***e*n*ent'.
To my mind, this looks like 'govErNmENT'. Trying these letters, 'Fxvjnlfz' reveals itself to be 'Amer**an'. This is looking promising, let us assume further that 'nl' represents 'ic'.
All the ta e ai over a li etime the Ftt bdv bfhvq efno ukvj f tnmvbnxv ic bdv average American are ent the government fkvjfyv Fxvjnlfz fjv qevzb ic bdv yukvjzxvzb in le than a secon nz tvqq bdfz f qvluzo. im ie ig Pnx Mnviny
We immediately recognise the words 'taxes' and 'lifetime', and can guess therefore that 'E' represents 'P', 'O' represents 'D', and 'IC' represents 'BY'.
We therefore have:
All the taxes paid over a lifetime by the average American are spent by the government in less than a second *im *iebig Pnx Mnviny
Now, all we have are the last two letters to account for. These are a bit of a shot in the dark as we have no way of checking the letters elsewhere in the text, and the name might be something unusual, like Fim Qiebig.
Unaccounted for letters are: F, J, K, Q, U, W, Z.
The name could be Kim or Jim, Fiebig, Wiebig or Ziebig.
I would have to try and look this up as I don't know of any person by any of these names. Fortunately, I do have the facility to cheat on my monoalphabet generator, and this quote was by someone called Jim Fiebig.
Try this one for yourself... please don't email me for a solution - I won't give it to you! A solution may be found by viewing the HTML comments on this page
Yxdy pq yjc xzpvpyw ya icqdepzc ayjceq xq yjcw qcc yjcuqcvrcq. Xzexjxu Vpsdavs
When cryptanalysing more complex ciphers, such as Vigenère, one of the first steps could be to try and reduce the cipher into a series of monoalphabetic ciphers.
Of course the analysis may be done automatically by a computer program which observes letter positions and frequencies etc.
26! is a shorthand way of writing the number given by
26 x 25 x 24 x 23 x 22 x 21 ..... 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4 x 1026 is an example of scientific notation. It is a shorthand way of wring very large, or very small numbers. e.g. an atomic nucleus is about 10-15 metres across.
4 x 1026, is an approximation to 26! and corresponds to the following number.
400 000 000 000 000 000 000 000 000
I am sure you'll agree that this is a lot of possible combinations!
Atbash is a simple substitution very similar in nature to the Caesar Substitution. Whereas the Caesar substitution was Roman in origin, atbash is Jewish in origin.
In atbash, the last letter represents the first, the second to last represents the second and so on.
Atbash is even simpler to solve than the Caesar Substitution as there is only one solution to try!
You may start to wonder how we could start to solve a monoalphabetic substitution if we do not know whether the cipher alphabet is atbash, caesar, some combination of the two or just random! This will be addressed later when I discuss monoalphabetic substitution. In the meantime, can you decode the following atbash? I've provided a key to save some legwork.
PLAINTEXT a b c d e f g h i j k l m CIPHERTEXT Z Y X W V U T S R Q P O N PLAINTEXT n o p q r s t u v w x y z CIPHERTEXT M L K J I H G F E D C B A
Blf ziv mlg z Qvwr bvg (Wzigs Ezwvi gl Ofpv Hpbdzopvi)
You shouldn't have had a problem with this, it's fairly easy!
Atbash can also be combined with a caesar shift, to produce a Reversed Caesar substitution.
An example is shown below.
PLAINTEXT a b c d e f g h i j k l m CIPHERTEXT W V U T S R Q P O N M L K PLAINTEXT n o p q r s t u v w x y z CIPHERTEXT J I H G F E D C B A Z Y X
A look at the Caesar Cipher, one of the simplest ciphers.