# Difference between revisions of "Equihash"

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The puzzle for Equihash-n/k/d is to find i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>2<sup>k</sup></sub> such that | The puzzle for Equihash-n/k/d is to find i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>2<sup>k</sup></sub> such that | ||

− | < | + | H(i<sub>1</sub>) xor H(i<sub>2</sub) xor ...xor H( i<sub>2<sup>k</sup>) = 0 and H(i<sub>1</sub>|| i<sub>2</sub|| ...|| i<sub>2<sup>k</sup>) has d leading zeros, where H is the Blake2b hash function. There are also certain restrictions on the length and order of i<sub>j</sub>. |

== Properties == | == Properties == |

## Revision as of 21:37, 16 October 2016

Equihash is a memory-hard proof-of-work scheme. It solves a computational puzzle, best algorithms for which require certain computational and memory resources.

## High Level View

- Article:
*"Equihash: asymmetric proof-of-work based on the Generalized Birthday problem*^{[1]} - Authors: Alex Biryukov and Dmitry Khovratovich

Equihash is a family of proof-of-work schemes with three parameters n, k, and d, which determine the scheme Equihash-n/k/d and the time and memory complexity of the puzzle solver for it, and seed S, which makes every puzzle unique and solutions incompatible.
The best algorithms for Equihash-n/k/d require O(2^{n/(k+1)+d}) time and O(2^{n/(k+1)}) memory, though implementations of this algorithms differ in both metrics, see below.

The puzzle for Equihash-n/k/d is to find i_{1}, i_{2}, ..., i_{2k} such that
H(i_{1}) xor H(i_{2</sub) xor ...xor H( i2k) = 0 and H(i1|| i2</sub|| ...|| i2k) has d leading zeros, where H is the Blake2b hash function. There are also certain restrictions on the length and order of ij.
}

## Properties

## Instances

Here, we list several Equihash instances with d=0, and provide time and memory requirements of our reference implementation. We also provide lower bounds on the memory requirements such that any ASIC implementation using less memory should incur a significant penalty

n,k | Time | Memory | Minimum memory |
---|---|---|---|

144,5 | 15 sec | 2 GB | 500 MB |

200,9 | 5 sec | ||

| |

## Resources

- NDSS'16 paper: To appear
- Eprint version: To appear
- Bibtex entry: To appear
- Presentation slides:
- Reference implementation:
- Optimized implementations: .

## References

- ↑ Biryukov, A. and Khovratovich, D. (2016).
*Equihash: asymmetric proof-of-work based on the Generalized Birthday problem*. In Network and Distributed System Security Symposium (NDSS) 2016.