> A basic tenet of cryptographic security definitions is that the honest parties should have an advantage over the attackers in the sense that a small increase

> A basic tenet of cryptographic security definitions is that the honest parties should have an advantage over the attackers in the sense that a small increase the work done by the honest parties results in a large increase in the work that must be done to attack the system. I think a more accurate claim would be that cryptography aims to achieve the best security guarantees that can be assured mathematically. In the case of establishing consensus the best guarantees you can achieve are just different from what you can achieve in those other situations. That doesn't mean that Bitcoin is somehow going against some kind of cryptographic standard like you are implying here. It is using cryptographic technologies to achieve the most secure possible solution (as far as we have discovered) to the problem which it aims to solve. It just happens to be a different problem than those other problems and therefore the nature of the solution is different. > Note also that cryptographic security definitions assume ... that the attackers do coordinate with each other That's just one possible scenario which you might consider. Again I think it is misleading to imply this is some kind of "cryptographic litmus test" or something. > You mention incentive structures, but incentive structures are not very reliable. Right, but there's just no stronger guarantees which you can make when it comes to this problem. > One does not follow from the other. Security requirements have nothing to do with popularity and everything to do with the ability of some attacker to succeed in attacking a system. I think you are interpreting what I said backwards. Popularity defines what level of security is required. The level of security defines what attacks can be resisted. The more popular the coin, the bigger need it will have to resist attacks. And this is accommodated in the design: the higher the market price of the coin, the bigger the reward will be for miners (thus funding more mining, increasing the cost of an attack).