Question

QUESTION 4 137 and 151 are assigned to p and q respectively to generate a pair of public and private keys. What is the modulus n? What is the value of the totient function ? If 11 is assigned to public key e, what is the value of the private key d? Choose from 1854, 1880, 16691, 16699

Answer 1

p       = 137

q       = 151

n       = p * q

          = 137 * 151

          = 20687

modulus n = 20687

phi ($\phi$)        = (p – 1) * (q – 1)

                   = (137 – 1) * (151 – 1)

                   = 136 * 150

                   = 20400

totient function phi ($\phi$) = 20400

ed = 1 mod $\phi$

where e = 11 and $\phi$ = 20400

11 * d                        = 1 mod 20400

i.e, (11 * d) % 20400 = 1 (if we divide (11 * d) by 20400, remainder will be 1)

i.e, 11 * d                  = 20400 + 1

i.e, 11 * d                  = 20401

i.e, d                        = 20401 / 11

                                = 1854

Value of d = 1854