In Diffie-Hellman key agreement, can the attacker who captures the keying information compute the symmetric session key?

• A. Yes
• B. No
• C. Only if they know the private keys
• D. Only with a trivial key

Answer: (B)

The concept being tested is the security of Diffie-Hellman against passive observers. In Diffie-Hellman, each party uses a private exponent and computes a public value, and the shared session key is the exponentiation of the other party’s public value by their own private exponent (g^{ab}). An attacker who only sees the two public values g^a and g^b cannot derive the shared secret without solving the discrete logarithm problem to recover a or b. With proper parameters, solving that problem is computationally infeasible, so the captured keying information does not let the attacker compute the symmetric session key. The attacker would only succeed if they somehow obtain one of the private keys or manage to break the discrete logarithm problem.