Crypto analysis frequency analysis

Note: Remember that this web site contains a number of potentially useful Java applets, which you may choose to use to help you with the work in this assignment. A MonoAlphabetic Substitution Cipher maps individual plaintext letters to individual ciphertext letters, on a 1-to-1 unique basis.

That is, every instance of a given letter always maps to the same ciphertext letter. The oldest such cipher known is the Caesar cipher, where the mapping involved a simple shift within the alphabet. For example, the following represents a Caesar cipher with a shift of Notice that we are doing a circular shift, by wrapping the end of the alphabet around to the beginning. To encipher a message, we simply take each letter in the plaintext, find that letter in the Plaintext row, and substitute the corresponding letter immediately below it, in the Ciphertext row.

For example, using this substitution table, we can take the message: Once more unto the breach, dear friends and encipher into the following: Lkzb jlob rkql qeb yobxze, abxo cofbkap Of course, to decipher the text, we simply reverse the process -- or equivalently, use the negative of the original shift value. What is the plaintext for this message? This should be really easy! In reality, because case, word spacing and punctuation in the ciphertext give additional clues about the plaintext, they are usually removed, and the ciphertext is often organized into groups of characters.

Removing such clues from the plaintext before enciphering it makes it quite a lot harder to crack the cipher. When attempting to decipher a shift substitution ciphertext, if you don't already know the number of characters to shift, of course, you need to figure it out. There are a couple of ways you might be able to do this:. In this case, we try every possibility, until we find a reasonable looking plaintext. Question 2: Given the approach described above, for a Shift Substitution Cipher, how many possibilities are there for a shift value?

Is this a feasible task? You can try my Java applet that implements this, if you'd like. MonoAlphabetic Substitution Ciphers employ a more complex approach: Instead of using a simple shift to determine the letter mapping, they select an individual mapping for each character, where the relative position of the corresponding characters is, in general, different for all characters.

So, in order to decipher a MonoAlphabetic Substitution cipher, you need to determine the mapping for every character -- a lot more complex than just determining a single fixed shift value. Here's an example of a MonoAlphabetic Substitution Cipher. Here's a letter substitution table for such a cipher:. A bowl of Moose Tracks ice cream.

O eumc uy Duulv Bjoxgl axv xjvod. The top line is the plaintext, and the bottom line is the ciphertext. You can figure out how the translation is done by working through each letter of the plaintext, and matching it with the corresponding letter in the substitution table. Question 3: Given the approach described above, for a MonoAlphabetic Substitution cipher, how many possibilities are there for character mappings?

The brute force approach is pretty self-explanatory, so let's examine the Letter Frequency Analysis approach in more detail. First, we need to recognize that we're making some assumptions about the plaintext: That it consists of characters, not some kind of binary code. That it is written in some known natural language in our case, English That we know the frequency of letters in a typical piece of text in that language.

That the plaintext is typical of English text, and so we expect the same frequencies of letters approximately, within statistical fluctuations. As long as we know that there is a 1-to-1, unique, mapping from plaintext to ciphertext and therefore also from ciphertext to plaintext , we can employ our knowledge of those letter frequencies to help us crack a substitution cipher. Note that we need a large enough piece of text to give us some expectation that we have a large enough statistical sample.

The longer the message, the better statistical sample we are likely to have. The left hand side is in order by the letter position within the alphabet, while the right hand side is in decreasing order by frequency. This is a useful lesson in itself. Notice that the relative frequencies of U and C are 2.

That is, the frequencies of both are already quite low -- certainly when compared with E at Different sets of English texts will produce slightly different frequencies, and the numbers are also subject to statistical fluctuations. So, all we basically do, given a piece of ciphertext, is to count the number of occurrences of each letter, and from that build up a table that shows the relative frequency of letters in that ciphertext. Then we attempt to match it with the known English letter frequencies, and try to figure out corresponding letters -- and thus the substitution table.

Rxmm ksi uyklxtkz rxd ksi Zeuilatrm yvyxd, ksxz niyl? Well, we could actually count the number of each of the letters in this by hand. However, let's do it by computer. Here's what my program gives us:. So, let's make the simple assumption that the letters really do match up, based on the English letter frequencies, and that would give us the following substitution table:. Stnn eha coeitler std eha Rmcaiulsn ofotd, ehtr waoi?

So what's the problem? It is also possible that the plaintext does not exhibit the expected distribution of letter frequencies. Shorter messages are likely to show more variation. It is also possible to construct artificially skewed texts. For example, entire novels have been written that omit the letter " e " altogether — a form of literature known as a lipogram. The first known recorded explanation of frequency analysis indeed, of any kind of cryptanalysis was given in the 9th century by Al-Kindi , an Arab polymath , in A Manuscript on Deciphering Cryptographic Messages.

By , Cicco Simonetta had written a manual on deciphering encryptions of Latin and Italian text. Several schemes were invented by cryptographers to defeat this weakness in simple substitution encryptions. These included:. A disadvantage of all these attempts to defeat frequency counting attacks is that it increases complication of both enciphering and deciphering, leading to mistakes.

The rotor machines of the first half of the 20th century for example, the Enigma machine were essentially immune to straightforward frequency analysis. However, other kinds of analysis "attacks" successfully decoded messages from some of those machines. Frequency analysis requires only a basic understanding of the statistics of the plaintext language and some problem solving skills, and, if performed by hand, tolerance for extensive letter bookkeeping.

During World War II WWII , both the British and the Americans recruited codebreakers by placing crossword puzzles in major newspapers and running contests for who could solve them the fastest. Several of the ciphers used by the Axis powers were breakable using frequency analysis, for example, some of the consular ciphers used by the Japanese.

Today, the hard work of letter counting and analysis has been replaced by computer software , which can carry out such analysis in seconds. With modern computing power, classical ciphers are unlikely to provide any real protection for confidential data.

Frequency analysis has been described in fiction. The cipher in the Poe story is encrusted with several deception measures, but this is more a literary device than anything significant cryptographically. From Wikipedia, the free encyclopedia. Study of the frequency of letters or groups of letters in a ciphertext. For other uses, see Frequency analysis disambiguation. Retrieved 26 October Archived from the original on Retrieved BBC Radio 4. Retrieved 29 April The codebreakers: the story of secret writing.

New York: Scribner. ISBN Classical cryptography. Playfair Two-square Four-square.

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