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The symmetric difference of A and B, denoted by
Show hos’ bitwise operations on bit strings can be used to find these combinations of
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Suppose that in an RSA Public Key Cryptosystem. Encrypt the message "pascal" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forwardSuppose a codding scheme is devised that maps -bit words onto -bit code words. The efficiency of the code is the ratio . Compute the efficiency of the coding scheme described in each of the following examples. Example 1 Example 2 Example 3 Example 4 Example 1: Parity check – Consider -bit words of the form . One coding scheme maps onto , where is called the parity check digit. Example 2: Repetition Codes – Multiple errors can be detected (but not corrected) in a scheme in which a -bit word is mapped onto a -bit code word according to the following scheme: Example 3: Maximum Likelihood Decoding- Multiple errors can be detected and corrected if each -bit word is mapped onto a - bit code word according to the following scheme (called a triple repetition code): Example 4: Error Detection and Correction – Suppose -bit words are mapped onto -bit code words using the scheme , Where is the parity check digit .arrow_forwardSuppose the alphabet consists of a through, in natural order, followed by a blank, a comma, and a period, in that order. Associate these "letters" with the numbers, respectively, thus forming a -letter alphabet,. Use the affine cipher to decipher the message if you know that the plaintext message begins with "" and ends with ".". Write out the affine mapping and its inverse.arrow_forward
- Suppose 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 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. 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
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,