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One of the benefits mentioned of SCP in comparison to POW is 'asymptotic security' https://www.stellar.org/blog/stellar-consensus-protocol-proof-code/. What does this form of security mean in practice and why is it a vulnerability in POW?

For pure terminology sake, POW security guarantees are probabilistic since each additional block confirmation strengthens the probability of the chain being the longest and correct chain. Logically I would consider probabilistic and asymptotic to be relatively synonymous in this context.

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As a practical matter, SCP's asymptotic security follows from the fact that it depends only on digital signatures (and hash functions) for security, and that these can be tuned to resist arbitrarily powerful attackers.

For example, you consider an attack in which every grain of sand on earth is a supercomputer attempting to break SCP a billion times per second, and you decide you'd like the expected time required for such an attack to succeed to be over 100 years. Then that means you need roughly 128-bit security, so you choose cryptographic key lengths and hash function sizes accordingly. (Note that for public key algorithms you generally need longer than 128-bit keys for 128-bit security.)

The more powerful an attacker you want to resist, the longer your cryptographic keys and the slower your operations. But the important point is that the cost of running the protocol increases far more slowly than the cost of attacking it, so you can basically adapt to an arbitrarily powerful attacker.

In Proof-of-Work, the cost of running the protocol is the same as the cost of attacking the protocol, so you cannot resist an arbitrarily powerful attacker. Instead PoW generally adds an additional incentive structure (mining fees) and then assumes a rational attacker. In Stellar's case, those incentives are not good enough because Stellar allows tokens other than XLM to be traded, so even if Stellar did provide some kind of mining reward denominated in XLM, the reward might not be valuable enough to deter attacks on other assets. (Financial networks send around trillions of dollars a day, which is more than even the Bitcoin market cap.)

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You're mixing up two completely different concepts here. One is about transaction finality, and the other is about resistance to sybil attacks.

POW has probabilistic finality, since there's always the potential of a longer chain reverting your transaction. SCP has deterministic finality -- when a transaction is included in a ledger update, that's it. No need to wait for confirmations.

'asymptotic security' is about sybil attacks.

POW has its famous 51% attacks. SCP doesn't. You can flood the network with bad actors, and it doesn't matter, as long as no-one includes them in their quorum sets.

As to what asymptotic security actually means, check https://crypto.stackexchange.com/a/47073

  • I don't see any reference to sybil attacks in the link you referenced. The link it mostly is concerned with 'computational effort' required to sabotage the network, which would fall in the boat of probabilistic finality rather than sybil attacks. Which form of sybil attack were you referring to? – Brutus123 Jun 13 '18 at 1:47

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