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Gate2017 cs Q40

40In a RSA cryptosystem a participant A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. If the public key of A is 35. Then the private key of A is ______.

Note – Numerical Type question
  • Option : C
  • Explanation :
     Given DataAs per RSA Algorithm
     P = 13Step1: Calculate n = pxq = 13x 17 = 221
     Q = 17Step2: Calculate ϕ(n) = (p-1)(q-1) = (12)(16) = 192
     E = 35Step3: de mod ϕ(n) = 1 (or) de = 1modϕ(n)
     ⇒ d x 35 mod 192 = 1  ⇒ d = 11
    D = ?
    So, D is 11
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