Equihash is a mining algorithm proposed by Alex Biryukov and Dmitry Khovratovich as part of the University of Luxembourg research group CryptoLUX. It proposed a fast, memory-asymmetric and optimization/amortization-free PoW, based on the generalized birthday problem. In plain English, the problem states that: “Given a year with d days, what is the n amount of randomly chosen people to have a birthday coincidence of at least 50%?” Which can be generalized into k-types of people, finding common birthdays between them. The generalization states that: “Given k lists of n-bit values, find some way to choose one element from each list so that the resulting k values XOR to zero.”
Zcash Foundation implemented Equihash PoW, specified with parameters of n=200, k=9, which dictate how much memory space/bandwidth will be needed to find a solution. In June 2018, Bitmain released the ASIC Antminer Z9 mini, which managed to mine Equihash much more efficiently than commodity CPUs and GPUs by interfacing with SRAM chips at relatively low cost. Zcash founder Zooko Wilcox wrote in a forum post that he never committed to ASIC-resistance since it would be impossible in the long-term.
Equihash, however, allows for an initial widespread distribution of the coins and mining. Beam will set the parameters giving CPU and GPU miners significant head start over ASICs. Thus we will achieve a balance between the tradeoffs of a widespread, democratic coin distribution and the inevitable but synergic attack-resistance from ASIC miners.