![In an RSA cryptosystem, the value of the public modulus parameter π is 3007. If it is also known that Ο(π) = 2880, where Ο() denotes Eulerβs Totient Function](https://www.gkseries.com/blog/wp-content/uploads/2023/08/In-an-RSA-cryptosystem-the-value-of-the-public-modulus-parameter-π-is-3007.-If-it-is-also-known-that-Οπ-2880-where-Ο-denotes-Eulers-Totient-Function.jpg)
Q. In an RSA cryptosystem, the value of the public modulus parameter π is 3007. If it is also known that Ο(π) = 2880, where Ο() denotes Eulerβs Totient Function, then the prime factor of π which is greater than 50 is
Ans:
Given,
n = p * q = 3007 … … (1)
And,
Ο(n) = (p – 1) * (q – 1) = 2880 … … (2)
β pq – p – q + 1 = 2880
β 3007 – p – q + 1 = 2880
β p + q = 128 ……(2)
Using equation (1) and (2),
β (3007 / q) + q = 128
β q2 – (128*q) + 3007 = 0
On solving the above equation:
q = 31, 97
97 is greater than 50.