Asymmetric proof-of-work based on the Generalized Birthday problem

The proof-of-work is a central concept in modern cryptocurrencies, but the requirement for fast verification so far made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW) based on a computationally hard problem, which requires a lot of memory to generate a proof (called ”memory-hardness” feature) but is instant to verify. Our primary proposal is a PoW based on the generalized birthday problem and enhanced Wagner’s algorithm for it. We introduce the new technique of algorithm binding to prevent cost amortization and demonstrate that possible parallel implementations are constrained by memory bandwidth. Our scheme has tunable and steep time-space tradeoffs, which impose large computational penalties if less memory is used. Our solution is practical and ready to deploy: a reference implementation of a proof-of-work requiring 700 MB of RAM runs in 30 seconds on a 1.8 GHz CPU, increases the computations by the factor of 1000 if memory is halved, and presents a proof of just 148 bytes long.