7. The Bedrock of Cybersecurity: Cryptography 151 The twenty-six letters of the English alphabet all have a unique personality—some are more “shy” than others and some groups of letters tend to “hang out” together! For example, the letters E T A O I N S H R D L U are the most popular letters, in order, in English text (approximately). The letter E is by far the most frequently occurring, and for texts a paragraph or more of length, it will easily stand out, even if it is “wearing the disguise” of a different letter or a dancing stick man. Also, some pairs (bigrams) and triplets (trigrams) of letters appear much more frequently than others. For example, the trigram THE is the most frequently occurring three letter combination in English text. The more ciphertext characters, the more the pattern emerges. In our short attack at dawn example, the second and third ciphertext letters are the same, and this narrows down the plaintext letter possibilities for this character because some English letters do not occur back-to-back. Taking this paragraph (not counting this sentence) as a representative sample of typical letter frequencies, E appears the most (115 occurrences) followed by T (93 occurrences). Claude Shannon, one of the founding fathers of computing, studied the theoretical underpinnings of cryptography in the 1940s as part of the United States World War II effort, and he published a paper that was declassified in 2013. In this paper, Shannon showed that for the English language, it takes about thirty letters of a monoalphabetic substitution ciphertext to uniquely determine a message. The longer the message, the more fodder for the cryptanalysts, and the easier it is to crack the ciphertext. Because it does not sufficiently conceal the pattern of the underlying language, the monoalphabetic substitution cipher is not secure and should never be used to protect valuable information. The next evolution in classical cryptography was the polyalphabetic substitution cipher. In this scheme, multiple ciphertext alphabets are mapped to the plaintext alphabet (poly means many in Greek). The Vigenère cipher is a polyalphabetic substitution cipher that uses a cleverly-designed table to aid in encrypting and decrypting (see Table 7.4). The key in this cipher is the number of ciphertext alphabets used and their order, and it can be remembered with a simple codeword or phrase. For example, the codeword SECRET. This key uses six ciphertext alphabets. To encrypt a plaintext message, the S ciphertext alphabet encrypts the first letter, E the second letter, C the third letter, and so on. When the key runs out, it circles back to the beginning, so the seventh letter of ciphertext is also encrypted with the S ciphertext alphabet, the eighth with E, and so on. In the Vigenère table, the key is used to index the column and the plaintext letter to index the row, and the letter at the intersection is the ciphertext letter. Using the Vigenère cipher to encrypt the message attack at dawn with the key SECRET produces the ciphertext SXVRGDSXFRAG. To check this, note that the second ciphertext letter, X, is at the intersection of the E column (the second letter in the key) and the t row (the second letter in the plaintext) in the table. Also note that the third letter of the plaintext is also a t, but the ciphertext for it is the letter V, not the letter X. This demonstrates that polyalphabetic substitution ciphers do a better job of concealing patterns in the plaintext
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