Frequency Analysis For Simple Substitution Ciphers
In a simple substitution cipher, each letter of the plaintext is replaced with another, and any particular letter in the plaintext will always be transformed into the same letter in the ciphertext. For instance, if all occurrences of the letter e turn into the letter X, a ciphertext message containing numerous instances of the letter X would suggest to a cryptanalyst that X represents e.
The basic use of frequency analysis is to first count the frequency of ciphertext letters and then associate guessed plaintext letters with them. More X's in the ciphertext than anything else suggests that X corresponds to e in the plaintext, but this is not certain; t and a are also very common in English, so X might be either of them also. It is unlikely to be a plaintext z or q which are less common. Thus the cryptanalyst may need to try several combinations of mappings between ciphertext and plaintext letters.
More complex use of statistics can be conceived, such as considering counts of pairs of letters (digrams), triplets (trigrams), and so on. This is done to provide more information to the cryptanalyst, for instance, Q and U nearly always occur together in that order in English, even though Q itself is rare.
Read more about this topic: Frequency Analysis
Famous quotes containing the words frequency, analysis, simple and/or substitution:
“The frequency of personal questions grows in direct proportion to your increasing girth. . . . No one would ask a man such a personally invasive question as “Is your wife having natural childbirth or is she planning to be knocked out?” But someone might ask that of you. No matter how much you wish for privacy, your pregnancy is a public event to which everyone feels invited.”
—Jean Marzollo (20th century)
“A commodity appears at first sight an extremely obvious, trivial thing. But its analysis brings out that it is a very strange thing, abounding in metaphysical subtleties and theological niceties.”
—Karl Marx (1818–1883)
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)
“To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty space with sequences of form.”
—Max J. Friedländer (1867–1958)