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MATH221-2021-S3-A3-Q Sample-Answer with Notes on Marking.pdf

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Math221 – Mathematics for Computer ScienceS3-2021 Assignment 3 Sample Answer(Each question worth 10 marks)General Marking NotesFeedbackMeaningWithnomarksdeductedSome mistakes and/or weaknesses in the answers,improvement neededWithnomarksdeductedSome mistakes-20% of the marks is deductedfrom the question or subquestionSignificant mistakes-50% of the marks is deductedfrom the question or subquestionThere are very major mistakes made. The answer isactually wrong.-80% of the marks is deductedfrom the question or subquestionThe answer is actually fully wrong.-100%ofthemarksisdeducted from the question orsub questionNo attempt madePlease also read the marking notes for some questions.1.Find the inverse s of -1959 modulo 979 such that 0s < 979. You must show allthe detailed steps.
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Hence, gcd(1959, 979) =1From the result obtained by Euclidian Algo earlier, we have:(1)1 = 1959 - 979x2----(2)Work backwards, we get1= 1959 - 979x2---from (2)Hence,1= -1959x(-1) - 979x2Therefore -1 is the inverse of -1959 modulo 979-1978 (mod 979)Therefore, 978 is the inverse of -1959 modulo 9792.In the use of RSA Cryptography, if the public key and private key are (11, 65)and (35, 65), find the original message of ciphertext 50. You must show all thedetailed steps.)(1)65)65)65)65)
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