Question Bank - Computer Networks

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Let P = 17 and Q = 11 is taken in RSA algorithm, what are possible values of E( (public key), N and D (Private key) respectively?

A.
5, 187, 37
B.
7, 160, 23
C.
7, 187, 23
D.
9, 160, 37

Solution:

Compute the value of N and ?It is given as,N = P × Q and ? = (P-1) × (Q-1)Here in the example,N = 17 × 11 = 187? = (17-1) × (11-1) = 16 × 10 = 160Find the value of E (public key)Choose E, such that e should be co-prime. Co-prime means it should not multiply by factors of ? and also not divide by ?Gcd(E, ? (N) ) =1Gcd(E, 160 ) =1Gcd(7,160) =1 // taken from optionCompute the value of D (private key)The condition is given as,E × D ? 1 mod ? (7 × 23) ? 1 mod 160 //taking from OptionsBecause 161mod160 ? 1

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