Bitcoin Security Budget: ASIC Edition

Jordan McKinney
Oct 1, 2018 · 9 min read
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Approximate bounding inequality for attack cost (with ASICs)

Initial Hardware

So you want to 51% attack Bitcoin (or any ASIC-mined PoW system). First you need to buy the hardware. How much will that cost?

Present Value of Income Stream

Miners are funded by the income stream that the protocol provides (block rewards + tx fees). They care about the dollar amount of this stream. This is the security budget that I talked about in the previous posts.

Present Value Equation

The present value of some income stream can be determined with the… present value equation:

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Summed Across all Miners

Each miner does this calculation individually — they claim a fraction of the overall income stream (security budget) by spending less than the present value of the stream fraction.

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What if ASICs Stop Advancing?

If ASIC advancement plateaus then miners only need to buy hardware once, then can mine forever. tH is then infinite. Does H get huge? Does this break the bound?

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Operational & Upgrade Costs

So we’ve got a cap on the hardware cost.

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Final Expression

Combining the initial hardware investment cost (the first integral) with the operational and upgrade cost (second integral) we get:

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Conclusion

So the equation has S, S*, P, r, and the bounds t0, tH, tA:

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Appendix

More Precise Description of Upgrade Cost

The network upgrades in discrete chunks. A miner does a calculation and determines they can capture some slice of the overall income stream, S(t) for less than PV of that stream slice.

Discounting Income Streams

Assuming hardware advances, the total hash power produced by a network will tend to increase even if security budget (total miner revenue) is constant. So the percentage of total hash power produced by any given piece of hardware will decline over time.

Hardware Over-Allocation Smooth Out

Hardware spend is based on the present value (PV) of a projection of some income stream. If things are booming the projected income stream might justify the miners buying lots of hardware.

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Jordan McKinney

Written by

jordanmmck.com

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

Jordan McKinney

Written by

jordanmmck.com

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

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