Determinación de la plata en concentrados de minerales por Absorción

We introduced an abstract notion for proof-of-work puzzles and thereby worked out the minimum set of puzzle properties, that are necessary for implementing proof-of-work based blockchain protocols. This enables further research on replacements for the standard hash inversion based puzzles. New puzzles might be useful or cause more pleasant economies-of-scale.

Most existing publications present puzzle solving and hash linking of blocks as a tightly integrated mechanism. Our bottom-up construction comes with a disassembly of the complex Bitcoin protocol [25] into its different building blocks. This enables targeted research for further improvements.

Our new notion of proof-of-work puzzles is compatible with existing security research. We were able to restate the security properties of the Bitcoin backbone protocol [16] within our framework. Unlike the backbone protocol, we work on the continuous time scale and are able to consider nodes of different solving power. Since that is what we observe in practice, we consider our model to be more more intuitive.

Being based on the well understood exponential distribution, the puzzles allow for straightforward probabilistic analyses, as we have demonstrated in section 4.2. Our framework is also well suited to be used as foundation for existing game-theoretic analyses like the one by Dimitri [9], who models Bitcoin mining as an all-pay contest.

In its current state, our work has a few limitations that might be subject of further research. In previous work on computational task for rate limitation, like the original work on cost functions by Dwork and Naor [12] and the one by Ball et al. [2], who elaborate on useful moderately hard tasks, it was correctly highlighted that tasks should not be amendable to amortization. I. e., the information gained from solving previous tasks should not help on solving upcoming tasks. In our notion of proof-of-work puzzles, this important property is implicitly included. Future work might try to integrate this requirement explicitly.

Our work tries to abstract from the specific puzzle used in the Bitcoin backbone protocol by Garay et al. [16]. Our protocol and the desiderata follow the original work closely, but we miss on reconstructing their proofs. Providing such proofs would confirm our claim, that our notion of proof-of-work puzzles is sufficient for abstract blockchain protocol analyses. Additionally to these proofs, the probabilistic analysis of protocol 1 might be transferred to the one for proceeding consensus. Proposing attack strategies and analysing the adversary’s success probability using these strategies, gives upper bounds on the security of the protocol. Such bounds would complement the results gained from reconstructing the proofs of Garay et al. [16], who consider a worst-case adversary and thereby provide lower bounds.

In section 3, we argue for the exponentially distributed solving time of puzzles. We highlight that the distribution implies a certain fairness of finding solutions first. The exponential distribution is also what we observe on puzzles used in practice. A promising direction of research would be to question this decision, e. g. by picking different distributions, and redo the analysis of section 4.2 for each of them. This might either lead to an argument for the solving time being actually exponential distributed, or to a potential relaxation of our puzzle definition. Ideally, the experiment provides enough insight to formulate a proof that the exponential distribution is the best choice, and to which degree puzzles can deviate from the specification without undermining a protocol’s security.

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