Ciphers

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Mehran Sahami CS 106A

Handout #26 October 22, 2007

Strings and Ciphers
Based on a handout by Eric Roberts.

Cryptography, derived from the Greek word κρυπτοσ meaning hidden, is the science of creating and decoding secret messages whose meaning cannot be understood by others who might intercept the message. In the language of cryptography, the message you are trying to send is called the plaintext; the message that you actually send is called the ciphertext. Unless your adversaries know the secret of the encoding system, which is usually embodied in some privileged piece of information called a key, intercepting the ciphertext should not enable them to discover the original plaintext version of the message. On the other hand, the intended recipient, who is in possession of the key, can easily translate the ciphertext back into its plaintext counterpart. Caesar ciphers One of the earliest documented uses of ciphers is by Julius Caesar. In his De Vita Caesarum, the Roman historian Suetonius describes Caesar’s encryption system like this: If he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others.

Even today, the technique of encoding a message by shifting letters a certain distance in the alphabet is called a Caesar cipher. According to the passage from Suetonius, each letter is shifted three letters ahead in the alphabet. For example, if Caesar had had time to translate the final words Shakespeare gives him, ET TU BRUTE would have come out as HW WX EUXWH, because E gets moved three letters ahead to H, T gets moved three to W, and so on. Letters that get advanced past the end of the alphabet wrap around back to the beginning, so that X would become A, Y would become B, and Z would become C. Caesar ciphers have been used in modern times as well. The “secret decoder rings” that used to be given away as premiums in cereal boxes were typically based on the Caesar cipher principle. In early electronic bulletin board systems, users often disguised the content of postings by employing a mode called ROT13, in which all letters were cycled forward 13 positions in the alphabet. And the fact that the name of the HAL computer in Arthur C. Clarke’s 2001 is a one-step Caesar cipher of IBM has caused a certain amount of speculation over the years. Let's consider writing a simple program that encodes or decodes a message using a Caesar cipher. The program needs to read a numeric key and a plaintext message from the user and then display the ciphertext message that results when each of the original letters is shifted the number of letter positions given by the key. A sample run of the program might look like the example on the following page.

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For the Caesar cipher, decryption does not require a separate program as long as the implementation is able to accept a negative key, as follows:

Letter-substitution ciphers Although they are certainly simple, Caesar ciphers are also extremely easy to break. There are, after all, only 25 nontrivial Caesar ciphers for English text. If you want to break a Caesar cipher, all you have to do is try each of the 25 possibilities and see which one translates the ciphertext message into something readable. A somewhat better scheme is to allow each letter in the plaintext message to be represented by an arbitrary letter instead of one a fixed distance from the original. In this case, the key for the encoding operation is a translation table that shows what each of the 26 plaintext letters becomes in the ciphertext. Such a coding scheme is called a letter-substitution cipher. The key in such a cipher can be represented as a 26-character string, which shows the mapping for each character, as shown in the following example: A B C D E F...
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