GATE CS 2019 Set 1 — Question 64
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Computer Networks → Application Layer → Symmetric & Asymmetric Encryption
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Question
In an RSA cryptosystem, the value of the public modulus parameter is 3007. If it is also known that , where denotes Euler's Totient Function, then the prime factor of which is greater than 50 is ___________.
Correct answer
97 to 97
Solution
In an RSA cryptosystem, the public modulus is the product of two distinct prime numbers and .Euler's Totient Function for a product of two primes is given by:Expanding the expression for :Substituting the value of :Now we have a system of two equations:
1)
2)
These values and are the roots of the quadratic equation:Using the quadratic formula :Since and , and the last digit is 6, .The prime factors of are 31 and 97. The factor greater than 50 is 97.
1)
2)
These values and are the roots of the quadratic equation:Using the quadratic formula :Since and , and the last digit is 6, .The prime factors of are 31 and 97. The factor greater than 50 is 97.
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