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Decrypt the message EABW EFRO ATMAR ASIN, which is the ciphertext produced by encrypting a plaintext message using the transposition cipher with blocks of four letters and the permutation o of {1,2,3,4} define by
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Chapter 4 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- 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 .arrow_forwardSuppose that in an RSA Public Key Cryptosystem, the public key is e=13,m=77. Encrypt the message "go for it" using two-digit blocks and the 27-letter alphabet A from Example 2. What is the secret key d? Example 2 Translation Cipher Associate the n letters of the "alphabet" with the integers 0,1,2,3.....n1. Let A={ 0,1,2,3.....n-1 } and define the mapping f:AA by f(x)=x+kmodn where k is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of a through z, in natural order, followed by a blank, then we have 27 "letters" that we associate with the integers 0,1,2,...,26 as follows: Alphabet:abcdef...vwxyzblankA:012345212223242526arrow_forwardSuppose that in an RSA Public Key Cryptosystem, the public key is. Encrypt the message "pay me later” using two-digit blocks and the -letter alphabet from Example 2. What is the secret key? 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:arrow_forward
- Suppose the alphabet consists of a through z, in natural order, followed by a blank and then the digits 0 through 9, in natural order. Associate these "letters" with the numbers 0,1,2,...,36, respectively, thus forming a 37-letter alphabet, D. Use the affine cipher to decipher the message X01916R916546M9CN1L6B1LL6X0RZ6UII if you know that the plaintext message begins with "t" followed by "h". Write out the affine mapping f and its inverse.arrow_forwardSuppose that in an RSA Public Key Cryptosystem. Encrypt the message "algebra" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forwardIn the -letter alphabet described in Example, use the affine cipher with keyto encipher the following message. all systems go What is the inverse mapping that will decipher the ciphertext? 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:arrow_forward
- 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:arrow_forwardUse the alphabet C from the preceding problem and the affine cipher with key a=11andb=7 to decipher the message RRROAWFPHPWSUHIFOAQXZC:Q.ZIFLW/O:NXM and state the inverse mapping that deciphers this ciphertext. Exercise 7: Suppose the alphabet consists of a through z, in natural order, followed by a colon, a period, and then a forward slash. Associate these "letters" with the numbers 0,1,2,...,28, respectively, thus forming a 29-letter alphabet, C. Use the affine cipher with key a=3andb=22 to decipher the message OVVJNTTBBBQ/FDLWLFQ/GATYST and state the inverse mapping that deciphers this ciphertext.arrow_forwardIn the -letter alphabet A described in Example, use the translation cipher with key to encipher the following message. the check is in the mail What is the inverse mapping that will decipher the ciphertext? 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:arrow_forward
- Suppose an RSA cryptosystem is used to send the plaintext 4" with public key (n, e) = : (33, 3) What is the ciphertext that corresponds to the message "4?" 4 15 28 31arrow_forwardDecrypt the message ORWWPGDII which was encrypted using the affine cipher: f(p) = (11p+ 5) mod 26 Alphabet: A = 0, B = 1, ... , Z = 25 Message:arrow_forwardUse the RSA cipher with public key (n, e) = (713, 43) to encrypt the word "TEE." Start by encoding the letters of the word "TEE" into their numeric equivalents. Assume the letters of the alphabet are encoded as follows: A = 01, 8 = 02, C = 03, ..., Z = 26. Since the code for T is 20 and since e = 43 = 32 + 8 + 2 + 1, the first letter of the encrypted message is found by computing 2043 mod 713. 20¹a (mod 713) 20² Eb (mod 713) 204 c (mod 713) 208 d (mod 713) 2032 = f (mod 713) 2016 e (mod 713) b = The result is that a = C = d = e = and f = Thus, 2043 mod 713 = (a · b. d. f) mod 713 = So the first number in the encrypted message is Repeat these computations for each letter to find the complete encrypted message and enter your answer below. (Enter the message as a sequence of integer triples separated by a single space, where each triple is written using a fixed number of digits: 001 for 1, 002 for 2, ..., 099 for 99.)arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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