Kasiski Method Reference

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Presentation transcript:

Kasiski Method Reference Matt Bishop, Computer Security, Addison Wesley, 2003.

Kasiski Method The Cesar Cipher is a monoalphabetic-key cipher and is susceptable to statistical analysis of ciphertext. Consider plaintext using the English language. The frequency of occurrence of the letters a through z is well documented. When the Cesar Cipher is used, the plaintext becomes ciphertext, but the ciphertext still retains the frequency of occurrence of the plaintext and the code can be broken.

Kasiski Method (p.2) In the Vigenère Cipher, the longer key might obscure the statistics. Kasiski, however, noticed that repetitions occur when characters of the key appear over the same characters in the ciphertext. The number of characters between repetitions must be a multiple of the length of the key.

Kasiski Method (p.3) The index of coincidence (IC)measures the difference in the frequencies of letters in the ciphertext. A frequency analysis of the ciphertext could provide estimates of Fi, where Fi is the relative frequency of the ith ciphertext characters. Then IC = {1/N(N-1)}i=0,25 Fi(Fi-1).

Kasiski Method (p.4) Now the index of coincidence (IC) will decrease as the length of the key (or period) increases. This means by estimating the IC, we have an estimate of the period. This can be used to check the observed repetitions.

Kasiski Method (p.5) How does knowledge of the key length help break the code? The ciphertext can be separated into groups, with each group being ciphertext from using the jth element of the key. If the key length is L, then the L groups are analyzed as simple Cesar ciphers. Thus the Vigenère cipher, like the Cesar cipher can be broken using ciphertext only.