Adolfcoin will in future use Cuckoo Cycles, however the CryptoNight hash function is currently being used.

Cryptonight Hash Function

First, some initial 128 bit values are determined by hashing the block state using a Keccak (sha3) variant – call them A and B. The big lookup table is also populated using that same state, mixed around using AES. Then, executed 500,000 times, are rounds of mixing as shown at the right: Use A to determine a pseudorandom location in the scratchpad, take that, mix it in, AES encrypt it (one round), use the result to determine a second location, use that in a 64 bit multiply, store it back, and repeat. Elegantly simple.
cryptonight

Adapted from David Andersen‘s post.

Full paper

 

Cuckoo Cycles

In Cuckoo Cycle, proofs take the form of a length 42 cycle (loop) in a large random graph defined by some nonce. Imagine two countries, each with a billion cities, and imagine picking a billion border crossing roads that connect a random city in one country to a random city in the other country (the PoW actually uses a cheaply computed hash function to map the nonce, road number, and country to a city). We are asked if there is cycle of 42 roads visiting 42 different cities. If someone hands you a nonce and 42 road numbers, it is indeed easy to verify, requiring negligible time and memory.

But finding such a cycle is no easy task. Note however, that a city that connects to one road only cannot be part of the solution, nor can that road. David Andersen pointed out that such dead-end roads can be repeatedly eliminated, using one bit of memory per road to remember if that road is useful, and two bits per city to count if there are zero, one, or multiple useful roads to that city.

This process of computing counts for cities, and marking roads that lead to a city with count one as not useful, is the essence of Cuckoo Cycle mining and accounts for about 98% of the effort. It results in billions of random global memory accesses for reading and writing the counters. Consequently, about 2/3 of the runtime is memory latency, making this a low-power algorithm that keeps computers running cool.

From Tromp’s blog