Scenario:Two servers need to agree on a shared secret key over an insecure network without transmitting the key directly. Question: Which method should be used?

Question

BlackTom AI · Accepted Answer

Diffie-Hellman key exchange enables two parties to establish a shared secret over an insecure channel without ever transmitting the secret directly.

1) Relevant knowledge points and concepts
- Diffie-Hellman (DH) is a key-agreement protocol based on the discrete logarithm problem: each side sends a public value derived from a private exponent; combining the other side’s public value with your private exponent yields the same shared secret.
- Security relies on the hardness of computing discrete logarithms (recovering private exponents from public values).
- ElGamal is an encryption scheme built on the same math but is not the canonical key-agreement procedure.
- RSA is an asymmetric encryption/signature algorithm; it can be used to encrypt a key (i.e., send it encrypted) but that transmits a key material (encrypted) rather than mutually deriving one via agreement.
- SHA-256 is a hash function, not a key-exchange protocol.

2) Step-by-step reasoning (protocol outline)
- Parties agree on public parameters: a large prime p and generator g.
- Alice picks private a, computes A = g^a mod p and sends A.
- Bob picks private b, computes B = g^b mod p and sends B.
- Alice computes s = B^a mod p. Bob computes s = A^b mod p. Both s values are equal: s = g^(ab) mod p.
- An eavesdropper observing A and B cannot feasibly recover a or b (discrete log), so cannot compute s.

3) Example calculations (all intermediate steps)
Take small example p = 23, g = 5, Alice a = 6, Bob b = 15:
- A = 5^6 mod 23. Compute: 5^2 = 25 ≡ 2; 5^4 = 2^2 = 4; 5^6 = 5^4 * 5^2 = 4 * 2 = 8 → A = 8.
- B = 5^15 mod 23. Compute: 5^8 = 16, 5^4 = 4, 5^2 = 2, 5^1 = 5 ⇒ 5^15 = 5^8 *5^4 *5^2 *5 = 16*4*2*5 = 19 → B = 19.
- Shared secret s (Alice): s = B^a = 19^6 mod 23. 19^2 = 16, 19^4 = 16^2 = 3, 19^6 = 19^4 *19^2 = 3*16 = 48 ≡ 2 mod 23.
- Shared secret s (Bob): s = A^b = 8^15 mod 23 also equals 2. Both obtain same secret 2 without sending it.

4) Why the correct answer is correct
Diffie-Hellman is explicitly designed for establishing a shared secret over an insecure channel without transmitting the secret itself. The example shows both parties compute the identical secret while only exchanging public values.

5) Why other options are incorrect
- a. ElGamal: an encryption scheme (can be used for secure messages) but not the standard key-agreement primitive asked for.
- b. RSA: can encrypt a key to a recipient (sending encrypted key material), but that transmits the key (encrypted) rather than mutually deriving a secret; also has different trust/operation assumptions.
- d. SHA-256: a hash function, not a protocol for establishing shared secrets.

6) Conclusion
The correct choice is c. Diffie-Hellman, which matches the provided answer.

Scenario:Two servers need to agree on a shared secret key over an insecure network without transmitting the key directly. Question: Which method should be used?单项选择题

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