How would you decrypt the Vigen`ere cipher used to encrypt "pineapple"? In general, if your friend said they encrypted a Vingen`ere cipher using the key (5,11,1, 2), how would you decrypt their ciphertext?
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- a. Excluding the identity cipher, how many different translation ciphers are there using an alphabet of n "letters"? b. Excluding the identity cipher, how many different affine ciphers are there using an alphabet of n "letters," where n is a prime?Suppose that in a long ciphertext message the letter occurred most frequently, followed in frequency by. Using the fact that in the -letter alphabet, described in Example, "blank" occurs most frequently, followed in frequency by, read the portion of the message enciphered using an affine mapping on. Write out the affine mapping and its inverse. Example 2 Translation Cipher Associate the letters of the "alphabet" with the integers. Let and define the mapping by where is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of through, in natural order, followed by a blank, then we have "letters" that we associate with the integers as follows:Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .
- The ciphertext OIKYWVHBX was produced by encrypting a plaintext message using the Vigen`ere cipher with key HOT. What is the plaintext message?Use the Caesar cipher (shift of 3 places) to encryptBRAVEOnce the length of the key string of a Vig`enere cipher is known, explain how to determine each of its characters. Assume that the plaintext is long enough so that the frequency of its letters is reasonably close to the frequency of letters in typical English text.
- Express the Vigen`ere cipher as a cryptosystem.a) What is the difference between a public key and a private key cryptosystem? b) Explain why using shift ciphers is a private key system. c) Explain why the RSA cryptosystem is a public key system.A department store wants to send codes for $15 off a $75 purchase to the subscribers of its e-mail list. The coupon code will have three letters, followed by one digit, followed by one letter. The letters P , Q , and R will not be used. So, there are 23 letters and 10 digits that will be used. Assume that the letters can be repeated. How many such coupon codes can be generated?
- Suppose that the most common letter and the second most common letter in a long ciphertext produced by encrypting a plaintext using an affine cipher f (p) = (ap + b) mod 26 are Z and J, respectively. What are the most likely values of a and b?Consider the affine cipher with key k = (k1, k2) whose encryption and decryption functions are given by (1.11) on page 43. Alice and Bob decide to use the prime p = 601 for their affine cipher. The value of p is public knowledge, and Eve intercepts the ciphertexts c1 = 324 and c2 = 381 and also manages to find out that the corresponding plaintexts are m1 = 387 and m2 = 491. Determine the private key and then use it to encrypt the message m3 = 173.A burger chain wants to send codes for a free small drink to the members of its kids club. The coupon code will have one letter, followed by two digits, followed by two letters. The letters R , S , T , and U and the digit 3 will not be used. So, there are 22 letters and 9 digits that will be used. Assume that the letters and digits can be repeated. How many such coupon codes can be generated?