it's more like math hasn't got to the stage where it can describe complex systems, i.e. chaotic systems, e.g. weather, turbulence, market behaviour. That's not a 'human element', it's a 'chaotic element'. Cryptography's purpose is to obscure information for the purpose of un-obscuring it later. Which is essential for underpinnings of mechanics of crypto currency. But when you want to start to lose information like you do with anonymity, (in my opinion) it's not the best suited way. Because it's essentially reversible with the right tools (because the information is confined in one place, it security relies on your ability to decode it). Trying to lose information in a complex system, i don't think that approach is a good idea. You need to abstract the problem and use the system itself, in DRK's case, disparate location of the information, combining information to create ambiguity, across a chaotic network, is used to help 'lose' it - a cryptographic function can't do that; it's an alternative method. So just because there is not a mathematical proof to describe it doesn't matter, current math fails to describe most complex systems, forward brances are trying to like chaos theory. it's the application that counts and the efficacy of it's application which distils down to a statistic result, same as cryptography does IMO.
Hi BlockaFett,
I'm not sure what you mean by "math hasn't got to the stage where it can describe complex systems". I have a math degree and several published papers in mathematics and I can't for the life of me square this claim with actual work in the field. Mathematics, though the power of clever abstractions, is able to describe extremely complex systems with inhuman precision and correctness. The breakdown in modeling real systems comes from the fact that real systems have many independent moving parts which we are unable to measure precisely and which are infeasible to compute with anyway. So the problem is not complexity per se, nor is it somehow a failure of mathematics that things are this way. The breakdown in modeling software is that there often is no much-simpler description of a software program than the program itself (which can span many millions of bits). Oh -- and we can define "simpler description" precisely and actually prove that this is true for almost all programs.
"Chaotic systems" can be modeled as stochastic processes, and this field is much better developed than I think you realize. And anyway this is about situations where there is no physical way to obtain complete information, not about systems which are humanly defined and whose components are purely mathematical in nature anyway. It sounds like you're trying to justify the standard altcoin practice of responding to criticism by piling on so much complexity that experts won't bother looking at it anymore. But there is no mathematical or scientific result or practice that justifies this. It's just charlatanism.
Next, cryptography's purpose is not "to obscure information for the purpose of un-obscuring it later". If you define "obscure" as "computationally indistinguishable from the encryption of a random element" I suppose it might be the purpose of encryption, but that is a much stronger definition of obscure than is usually meant by the word. Lots of cryptography is designed specifically to remove information: zero-knowledge proofs, ring signatures, preimage-resistant hash functions and pseudorandom functions are some examples (and there are many others ... this is just the longest list I could form without slowing typing to think). So this notion that cryptography is inappropriate for these kind of applications is just not true. In fact the only way to do these things without cryptography is to physically control the flow of information, which is at odds with trust-minimization and public verifiability, not to mention really difficult in a world where people routinely communicate over long distances.
I hope this helps clarify some things.
Andrew
Hi
Surely Cryptography to 'lose' information is only required when the information is confined in a shared space, if you can move the information out of the space, you don't need cryptography. For example you don't need to encode text on a piece of paper if you can lock it in a box that no one can access and that is more secure than leaving it on a table with an encoded cypher that anyone can access. Saying that you need cryptographic functions to 'lose' information in a cryptocurrency seems to assume that the encoded information is still accessible in the system (which is true with XMR) but in DRK it isn't. This seems like a weaker solution to me than moving the information permanently out of the reach for anyone to access and try to decode it later?
About "the fact that real systems have many independent moving parts which we are unable to measure precisely and which are infeasible to compute with anyway" seems like another way of saying "we don't have a method yet" and hypothetical. Modeling complex systems today involves taking math and building that into a complex system with many parts as you say. But how do we know that there aren't new mathematical methods that can model complex systems more elegantly than the current way of thinking, and itsn't this what fields like Chaos theory are trying to do and having some success at?
Not sure I agree on the definition of cryptography (just my opinion) as I agree it seeks to 'confine and constrain' information but isn't that missing the last part you need to explain the purpose - confine and constrain information for the purpose of deconfining it and un-constraining it later? What else it is needed for (unless 'losing' information in a shared space)?
All I am saying is, looking at complex systems like p2p networks, brain neural network models, there are properties and behaviour that are clearly following rules but we don't understand yet (can't quantify mathematically at a macro level without having to model each 'moving part' at a micro level within a macro simulation). So to say that the math is already as far as it an go and it just requires modelling, i dont see that, and applied to cryptocurrencies, to say that all jobs have to use cryptography, i don't see that either, in fact it seems like permanent anonymity in a cryptocurrency is the one area that needs to not use cryptography unless you want the information sitting there in the shared space (blockchain) to be potentially decoded later. Secondly, (as some people here have said) that because then the anonymity 'system' can't be trusted because it's not following a mathematical proof, my response is that that does not mean that a proof can't be found or is even required, the mathematics needs to be developed to model what the system is achieving statistically not the other way around, because in the real world most of the 'systems' in people's lives don't have mathematical proofs for but we depend on them. but thats my opinion
thanks for your comments