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Determine the value of x, where y = 7, e = 12 and n = 566 using modular exponentiation method (x ≡ y^e (mod n)).

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Determine the value of x, where y = 7, e = 12 and n = 566 using modular exponentiation method (x ≡ y^e (mod n)).

(a) 735

(b) 321

(c) 872

(d) 487

The question was posed to me in an interview.

My question is based upon Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

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Correct option is (d) 487

Explanation: Given y = 5, e = 12, and n = 566 and so x ≡ 512 (mod 566). Now 512 comes out to 244140625 and taking this value modulo 566, x is determined to be 487.

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