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Assume the following simplified protocol:

  • seed = curve25519SharedKey(theirPublicKey, myPrivateKey)
  • sharedKey = scrypt(seed, salt, sufficientlyHardWorkFactors...)
  • cipherText = aes256(sharedKey, clearText)

Does using a slow-hash on the output of an asymmetric key-exchange offer any more protection in a quantum-computing era? I know that quantum computing is supposed to make breaking diffie-hellman easy... what I don't know is exactly how easy. Is the algorithm (greatly) diminished, or completely broken?

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Does using a slow-hash on the output of an asymmetric key-exchange
offer any more protection in a quantum-computing era?

No. $\:$ A quantum attacker would simply find seed even if you didn't use "a slow-hash on" it.

Is the algorithm (greatly) diminished, or completely broken?

The algorithm will still be completely broken by quantum attacks. $\:$ Furthermore, your simplified
protocol would just have one more link (scrypt) that could potentially be broken by classical attacks.

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No, as mentioned above.

More importantly, security in cryptography is defined based on the algorithmic complexity of solving a problem. Security protocols that involve solving a difficult problem (with non-polynomial complexity) to find the seed are considered secure. In this case, elliptic curves are problems that can be easily solved (with polynomial complexity) by a quantum computer.

So

seed = curve25519SharedKey(theirPublicKey, myPrivateKey)

is a vulnerability.

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