Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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in that ollowed ph ciphe INTRODUCTION TO CRYPTOGRAPHY 60 I1. Encrypt the message GOOD CHOICE using an exponential cipher with modulus , 2609 and exponent k = 7. 12. The ciphertext obtained from an exponential cipher with modulus p = 2551 and enci- phering exponent k = 43 is = d 1518 2175 1249 0823 2407 Determine the plaintext message. 13. Encrypt the plaintext message GOLD MEDAL using the RSA algorithm with key (2561,3). 14. The ciphertext message produced by the RSA algorithm with key (n, k) = (2573, 1013) is 046414720636 1262 2111 Determine the original message. [Hint: The Euclidean algorithm yields 1013 · 17 = 1 (mod 2573).] 15. Decrypt the ciphertext 1030 1511 0744 1237 1719 that was encrypted using the RSA algorithm with key (n, k) = (2623, 869). [Hint: The recovery exponent is j = 29.] %3D 10.2 THE KNAPSACK CRYPTOSYSTEM A public-key cryptosystem also can be based on the classic problem in combinatorics known as the knapsack problem, or the subset sum problem. This problem may be stated as follows: Given a knapsack of volume V and n items of various volumes 42, ..., an, can a subset of these items be found that will completely fill the knapsack? There is an alternative formulation: For positive integers a1, a2, . .., An and a sum V , solve the equation Uxup +...+ + D = / Where xị = 0 or 1 for i = 1, 2, . . . , n. the onght be no solution, or more than one solution, to the problem, dependng knapsack problem is not solvable; but 3D%3= has two distinct solutions
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Transcribed Image Text:in that ollowed ph ciphe INTRODUCTION TO CRYPTOGRAPHY 60 I1. Encrypt the message GOOD CHOICE using an exponential cipher with modulus , 2609 and exponent k = 7. 12. The ciphertext obtained from an exponential cipher with modulus p = 2551 and enci- phering exponent k = 43 is = d 1518 2175 1249 0823 2407 Determine the plaintext message. 13. Encrypt the plaintext message GOLD MEDAL using the RSA algorithm with key (2561,3). 14. The ciphertext message produced by the RSA algorithm with key (n, k) = (2573, 1013) is 046414720636 1262 2111 Determine the original message. [Hint: The Euclidean algorithm yields 1013 · 17 = 1 (mod 2573).] 15. Decrypt the ciphertext 1030 1511 0744 1237 1719 that was encrypted using the RSA algorithm with key (n, k) = (2623, 869). [Hint: The recovery exponent is j = 29.] %3D 10.2 THE KNAPSACK CRYPTOSYSTEM A public-key cryptosystem also can be based on the classic problem in combinatorics known as the knapsack problem, or the subset sum problem. This problem may be stated as follows: Given a knapsack of volume V and n items of various volumes 42, ..., an, can a subset of these items be found that will completely fill the knapsack? There is an alternative formulation: For positive integers a1, a2, . .., An and a sum V , solve the equation Uxup +...+ + D = / Where xị = 0 or 1 for i = 1, 2, . . . , n. the onght be no solution, or more than one solution, to the problem, dependng knapsack problem is not solvable; but 3D%3= has two distinct solutions
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