For all who did not see the confrontation which took place , the interesting trigger for this confrontation was when Vitalik challenged the technical opinion put forth by Craig Wright. The claim Vitalik says is that Craig Wright argued that making the Lightning Network work is as hard as solving a discrete logarithm problem. This kind of problem is known as an NP hard problem.
What is a discrete logarithm problem and what does polynomial time mean?
An NP Hard problem is a non-deterministic polynomial-time problem. To understand how this works just take a look at this video:
As you can see from the video, it's not practical due to time limitations to solve the discrete logarithm problem if the prime mod is large enough. This is the kind of encryption which PGP/GNUPG uses and is the kind of algorithm behind for example public key cryptography. The security of these forms of cryptography is based on the fact that mathematics proves them to be NP Hard. The security is based on statistics, on the probability that an adversary could randomly guess by trial and error to find the right number.
Now if we look at the Lightning Network then in my opinion there are challenges in implementing it. But I do not think "as hard as" applies to this unless there is a proof (math) which shows that the Lightning Network cannot work based on the same probability statistics that back the security of discrete logarithm problem hardness. Hardness is hard because there is some practical constraint which makes it hard, such as the amount of time before the universe is expected to die. If we have an infinite universe where you have infinite time then any cryptography based on the discrete logarithm problem can be solved, along with most forms of cryptography, but because the universe as we know it is based on the laws of physics, and is indeed finite (unlike the infinite tape of a Turing machine), it means the practical security of these hard problems are based on the correct math in terms of probability.
Summary:
- Done correctly, an NP hard problem is secure based on the fact that it costs more time to solve than the universe offers (practically unsolvable).
- Public key cryptography is secure if the keysize is large enough. For example integer factorization is not solvable efficient by any known mathematics.
- Discrete logarithm problems are known as being hard and are probably unsolvable efficiently.
- Is Lightning Network proven to be so hard to implement correctly that it would take more time than the universe offers to do it right? If yes then Craig Wright is correct, if no then his statement is wrong. Of course this depends on what we mean by implementing it correctly. If it is merely according to the specification then of course on the face of it then it's wrong but if we are talking about doing it in a way which upholds some principles or goals outside of the specification? Who knows. Craig Wright also claims Lightning Network can by Sybil attacked based on the topology. My question is just because it can be attacked doesn't mean that it can be shut down or that it's not resilient enough to survive the attack so does the math show it can be attacked in a way in which something is lost or it cannot recover? Btw Craig Wright is a Bitcoin Maximalist.