Question

Discrete Mathematics.

Question 2:
(a) Use modular arithmetic to find 1040 mod 210. Show your working.
(b) An RSA cryptosystem uses public key pq = 65 and e = 7. Decrypt the ciphertext 57 9 and translate the result into letters of the alphabet to discover the message.

Answer 1

we have to find loto mod 210 105 10 (mod 21. ) 10²= 100 (mod 210 ) 103 1000 = 160 (mod 2 10 ) 1600 130 (mod 210) > (mod 2 lo ) PI 105 = 1300 = 40 lo 400 190 (mod 210) 1906: 10 (Mod 210) ) 102 10 (mod 210) (107) 106 (mod 210) 키 A Dolgot mode) ) 89COMB) 8 lot ) lof (mod 210 ) By the Rule of congurence equation Now 10².1040 106 (mod 210) > 1040 4 (mod 210) (By the setep ®) 7 > 130 (mod 210) 2 10 to 13. (mod 2.10) Auswer ) cipher text 57 9 In RSA cryptosystem & given piq=65 e-7 þ.2= 65 = 5X13 >> P = 5,4=13 Now we have to Decrypt 57,9 do k[(4-1)(2-1)] +1 whene KEN- set of natural numbers

put K=1 » da 1x (6-1)(13-1) + 4.*12+1 49 7 7 → 10=7 Now MIE 8 (57)" (mod 65) M2 = 91? (mod65) - 9 & > Mi=8 - H 1- In English Alphabates & M2= 9 - I So the HI is → Answor Message
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