Suppose that in a long ciphertext message the letter
Example 2 Translation Cipher Associate the
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Elements Of Modern Algebra
- 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 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_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
- Use 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_forward6. Prove that if is a permutation on , then is a permutation on .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
- Show that the transformation T(x1, x2) = (2x1 − 2x2, 9x1 − 8x2) is invertible, and find a formula for T^−1arrow_forwardSuppose an additional binary-valued variable k bears the following relationship: i) Pr(X1,X6|X5, X7)=Pr(X1|X5, X7)Pr(X6|X5,X7) ii) Pr(X2,X3|X7)≠Pr(X2|X7)Pr(X3|X7) Incorporate the variable k into the Bayesian network in figure 1. Hint: you need to add into figure 1 by drawing the directional link(s) to/from the variable X7 from/to the relevant variable(s), and add the appropriate joint/conditional probability terms. However, you do not need to specify the exact value for the probability termsarrow_forwardLet f and g be any permutations. Show that the order of h=fgf^(-1) is the same as the order of g.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning