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:
“One is apt to be discouraged by the frequency with which Mr. Hardy has persuaded himself that a macabre subject is a poem in itself; that, if there be enough of death and the tomb in one’s theme, it needs no translation into art, the bold statement of it being sufficient.”
—Rebecca West (1892–1983)
“The spider-mind acquires a faculty of memory, and, with it, a singular skill of analysis and synthesis, taking apart and putting together in different relations the meshes of its trap. Man had in the beginning no power of analysis or synthesis approaching that of the spider, or even of the honey-bee; but he had acute sensibility to the higher forces.”
—Henry Brooks Adams (1838–1918)
“No author, without a trial, can conceive of the difficulty of writing a romance about a country where there is no shadow, no antiquity, no mystery, no picturesque and gloomy wrong, nor anything but a commonplace prosperity, in broad and simple daylight, as is happily the case with my dear native land.”
—Nathaniel Hawthorne (1804–1864)
“Virtue is the adherence in action to the nature of things, and the nature of things makes it prevalent. It consists in a perpetual substitution of being for seeming, and with sublime propriety God is described as saying, I A—.”
—Ralph Waldo Emerson (1803–1882)