Explanation Given information: (i) k = 11 (ii) The 31-letter alphabet A - If alphabet consist of a to z , in natural order followed by a blank, a comma, a period, an apostrophe, and a question mark, in that order, then have 31 “letters” that associates with the integer 0 , 1 , 2 , 3 , . . . , 30 as follows: Alphabet: a b c d e f . . . v w x y z " b l a n k " , . ' ? B: 0 1 2 3 4 5 . . . 21 22 23 24 25 26 27 28 29 30 Formula used: 1) Translation cypher: Associated with n letters “alphabet” with the integer 0 , 1 , 2 , 3 , . . . , n − 1 . Let A = { 0 , 1 , 2 , 3 , . . . , n − 1 } and define the mapping f : A → A by f ( x ) = x + k mod n . Where k is the key, the number of positions from the plaintext to the cipher text. 2) One-One function: If f : X → Y , f is one-one if ∀ x , y ∈ X , x ≠ y ⇒ f ( x ) ≠ f ( y ) . 3) Onto: For all y ∈ Y there exist x such that, y = f ( x ) Calculation: If key, k = 11 , To decipher the cipher text need to find the inverse. Define a mapping, f : B → B such that, f ( x ) = x + 11 mod 31 , where B = { 0 , 1 , 2 , 3 , . . . , 30 } One-one: Let x , y ∈ B such that x ≠ y mod 31 x + 11 ≠ y + 11 mod 31 f ( x ) ≠ f ( y ) mod 31 Thus, x ≠ y ⇒ f ( x ) ≠ f ( y ) Therefore, f is one-one. Onto: For all y ∈ B , there is x ∈ B , such that f ( y ) = x . Thus, f is onto. A function has an inverse if and only if it is one-one and onto. Thus, the inverse mapping exist and it is defined as, f − 1 ( x ) = x + ( − 11 ) mod 31 Which is equivalent to f − 1 ( x ) = x + 20 mod 31 . Therefore, the mapping f − 1 : B → B such that, f − 1 ( x ) = x + 20 mod 31 , where B = { 0 , 1 , 2 , 3 , . . . , 30 } exist that will decipher the cipher text. Translate the statement ‘?TRP.HGOZGEZAG

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Chapter 2.8, Problem 3E

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In 31− letter alphabet B, use the translation cipher with key k = 11 to decipher the message, “?TRP.HGOZGEZAG.PLOGXPK” and find the inverse mapping that will decipher the cipher text.

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Chapter 2.8, Problem 2E

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Use 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.)

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In 31 − letter alphabet B , use the translation cipher with key k = 11 to decipher the message, “?TRP.HGOZGEZAG.PLOGXPK” and find the inverse mapping that will decipher the cipher text.

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In 31− letter alphabet B, use the translation cipher with key k = 11 to decipher the message, “?TRP.HGOZGEZAG.PLOGXPK” and find the inverse mapping that will decipher the cipher text.

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