Advanced Discrete Mathematics & Math
Q99 / 100

Why is the discrete logarithm problem considered hard, and how does it underpin Diffie-Hellman key exchange?

Correct! Well done.

Incorrect.

The correct answer is B) Because no known classical polynomial-time algorithm computes x given gˣ ≡ h (mod p) in a large cyclic group, while computing gˣ itself is efficient via fast exponentiation — this asymmetry lets two parties derive a shared secret from public exchanges

B

Correct Answer

Because no known classical polynomial-time algorithm computes x given gˣ ≡ h (mod p) in a large cyclic group, while computing gˣ itself is efficient via fast exponentiation — this asymmetry lets two parties derive a shared secret from public exchanges

Explanation

Diffie-Hellman relies on a one-way function: computing gˣ mod p is fast (repeated squaring), but recovering x from gˣ mod p — the discrete logarithm — has no known efficient classical algorithm for well-chosen groups. Both parties compute g^(ab) mod p from exchanged values g^a and g^b without ever transmitting a or b.

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