IZMXFSJXLIKEGAEWHEPSWYSWIWIEVXLISXLIVXLIRGEPIRQIVIIBGIIHMWYPFLEVHEWHYPSRRFQMXLE GSTVRIEYVIEXCVMUIMWERGMIWXMJMGCSMWXSJOMIQXLIVIQIVIXQSVSTWHKPEGARCSXRWIEVSWIIBXV
WQLMGLMXQERIWGPSRIHMXQEREKIETXMJTPRGEVEKEITREWHEXXLEXXMZITWAWSQWXSWEXTVEPMRXRSJ LIVITCSWPIYVEWHEVSRIQMXLEYVEOIEWHRXEXIPFEMVEWHKVSTYLXZIXLIKIIXPIJVSZEYPERRGERIM Suppose Eve has intercepted the cryptogram below, and it is known to be encrypted using a simple substitution cipher as follows: 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. More complex use of statistics can be conceived, such as considering counts of pairs of letters ( bigrams), triplets ( trigrams), and so on. Thus the cryptanalyst may need to try several combinations of mappings between ciphertext and plaintext letters. It is unlikely to be a plaintext z or q which are less common. More Xs 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. The basic use of frequency analysis is to first count the frequency of ciphertext letters and then associate guessed plaintext letters with them. 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. 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. 1 Frequency analysis for simple substitution ciphersįrequency analysis for simple substitution ciphers.In some ciphers, such properties of the natural language plaintext are preserved in the ciphertext, and these patterns have the potential to be exploited in a ciphertext-only attack. The nonsense phrase " ETAOIN SHRDLU" represents the 12 most frequent letters in typical English language text. Likewise, TH, ER, ON, and AN are the most common pairs of letters (termed bigrams or digraphs), and SS, EE, TT, and FF are the most common repeats. For instance, given a section of English language, E, T, A and O are the most common, while Z, Q, X and J are rare. Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language. The method is used as an aid to breaking classical ciphers.įrequency analysis is based on the fact that, in any given stretch of written language, certain letters and combinations of letters occur with varying frequencies. In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. Weak ciphers do not sufficiently mask the distribution, and this might be exploited by a cryptanalyst to read the message. A typical distribution of letters in English language text.