i just need help with the last two question. im not sure on how to get the first number in the encryted message nor the last question 5. [11.1/16.7 Points]DETAILSMY NOTESEPPDISCMATH5 8.4.037.PREVIOUS ANSWERSASK YOUR TEACHERPRACTICE ANOTHERUse the RSA cipher with public key (n, e) = (713, 43) to encrypt the word "SIS." Start by encoding the letters of the word "SIS" into their numeric equivalents. Assume the letters of the alphabet are encoded asfollows: A =01, B = 02, C = 03, Z = 26.Since the code for S is 19 and since e = 43 = 32 + 8 + 2 + 1, the first letter of the encrypted message is found by computing 19°43mod 713.191a (mod 713)192 b (mod 713)194 c (mod 713)198d (mod 713)1916e (mod 713)1932 = f (mod 713)The result is that a = 19b = 361, C = 555d = 9e=81Thus, 1943mod 713 = (abd f) mod 713 = 570. So the first number in the encrypted message isand f=144Repeat 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 tripleis written using a fixed number of digits: 001 for 1, 002 for 2, 099 for 99.)Need Help?Read ItWatch It

To encrypt the word "SIS" using the RSA cipher with the given public key (n, e) = (713, 43), we…

Answered: 5. [11.1/16.7 Points] DETAILS MY NOTES…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 92E

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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 .
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:
Encrypt the message KILLTHEBEAST using shift cipher with K=18.
Encrypt the word "WATER" by using the cipher function f(p) = (3p+7)mod 26.
Suppose the RSA system that is used for sending secret messages has private key (15, 3) and the cipher text "4" is received. What was the plain text sent? 12 0 8 6 4
5. Find the plaintext message if the ciphertext produced by exponential encryption (§8.3) with key (e, p) (7,3001) is: = 2059 2010 1027 1524 1511 1717 1378 1713 0668 0937 1734
Alice received the following ciphertext from Bob, "08 01 08 05". Bob had encrypted it using the RSA cypher with Alice's public key (pq, e) = (55, 3), where p = 5 and q = 11. Note that (p − 1)(q − 1) = 40. The value for d in Alice's private key, (pq, d) is a positive inverse for 3 modulo (p − 1)(q − 1). It was found to be 27 in Examples 8.4.8(b) and 8.4.10. What is Bob's message after Alice decrypts it? (Assume Bob encoded one letter at a time using the encoding A = 01, 8 = 02, C = 03, ..., Z = 26.) To decrypt Bob's message, Alice uses the decryption formula M = C mod where M is the code for a letter of the message, C is the encrypted version of the letter, (pq, e) = (55, 3) is the public key, and (pq, d) = (55, 27) is the private key. (a) To begin, Alice computes the values of a, b, c, d and e that are indicated below. 084 c (mod 55) 08¹ = a (mod 55) 088 d (mod 55) She finds that a = 082 b (mod 55) 0816e (mod 55) b = , C = d= and e = Because 27 = 16 + 8 + 2 + 1, 0827= 0816 +8+2+1 =…

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