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1. (a) Use Fermat's Little Theorem to calculate: (i) 123578946 (mod 47) (ii) 58¹17 (mod 59) (iii) 56 +5060 +500600 + 50006000 (mod 7) (b) Messages are to be encoded using the RSA method, and the primes chosen are p = 11 and q = 13, so that n = pq = 143. The encryption exponent is e = 17. Thus, the public key is (143, 17). (i) Show that the decryption exponent d (the private key) is 113. (ii) Use the repeated squaring algorithm to find the encrypted form c of the message m = 44.

1. (a) Use Fermat's Little Theorem to calculate: (i) 123578946 (mod 47) (ii) 58¹17 (mod 59) (iii) 56 +5060 +500600 + 50006000 (mod 7) (b) Messages are to be encoded using the RSA method, and the primes chosen are p = 11 and q = 13, so that n = pq = 143. The encryption exponent is e = 17. Thus, the public key is (143, 17). (i) Show that the decryption exponent d (the private key) is 113. (ii) Use the repeated squaring algorithm to find the encrypted form c of the message m = 44.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. (a) Use Fermat's Little Theorem to calculate: (i) 123578946 (mod 47) (ii) 58¹17 (mod 59) (iii) 56 +5060 +500600 + 50006000 (mod 7) (b) Messages are to be encoded using the RSA method, and the primes chosen are p = 11 and q = 13, so that n = pq = 143. The encryption exponent is e = 17. Thus, the public key is (143, 17). (i) Show that the decryption exponent d (the private key) is 113. (ii) Use the repeated squaring algorithm to find the encrypted form c of the message m = 44.
Transcribed Image Text:1. (a) Use Fermat's Little Theorem to calculate: (i) 123578946 (mod 47) (ii) 58¹17 (mod 59) (iii) 56 +5060 +500600 + 50006000 (mod 7) (b) Messages are to be encoded using the RSA method, and the primes chosen are p = 11 and q = 13, so that n = pq = 143. The encryption exponent is e = 17. Thus, the public key is (143, 17). (i) Show that the decryption exponent d (the private key) is 113. (ii) Use the repeated squaring algorithm to find the encrypted form c of the message m = 44.
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