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
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 = 3007Β β¦ β¦ (1)
And,
Ο(n) = (p β 1) * (q β 1) = 2880 β¦ β¦ (2)
β pq β p β q + 1 = 2880
β 3007 β p β q + 1 = 2880
β p + q = 128 β¦β¦(2)
Using equation (1) and (2),
β (3007 / q) + q = 128
β q2 β (128*q) + 3007 = 0
On solving the above equation:
q = 31, 97Β
97 is greater than 50.