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