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| author | Bogdan Penkovsky <bogdan@powx.org> | 2021-05-17 21:32:08 +0200 |
|---|---|---|
| committer | bitcoindev <bitcoindev@gnusha.org> | 2021-05-17 19:23:15 +0000 |
| commit | 5fb160c6ecbfff8292785931d0ab5785f75471df (patch) | |
| tree | 21ee01b8c45a943d2bdc0149b1124fd172f9fa7b | |
| parent | 1e4c35b77c0f84132952328fe109d378e51fb74e (diff) | |
| download | pi-bitcoindev-5fb160c6ecbfff8292785931d0ab5785f75471df.tar.gz pi-bitcoindev-5fb160c6ecbfff8292785931d0ab5785f75471df.zip | |
[bitcoin-dev] Proposal: Low Energy Bitcoin PoW
| -rw-r--r-- | c6/e55c480e02738860dbdb8d64860c6ca5416afc | 607 |
1 files changed, 607 insertions, 0 deletions
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+ Title: Durable, Low Energy Bitcoin PoW + Author: Michael Dubrovsky <mike+bip[at]powx.org>, Bogdan Penkovsky +<bogdan+bip[at]powx.org> + Discussions-To: <mike+bip[at]powx.org> + Comments-Summary: No comments yet. + Comments-URI: https://github.com/PoWx-Org/obtc/wiki/BIP + Status: Draft + Type: Standards Track + Created: 2021-05-13 + License: BSD-2-Clause + OPL +</pre> + + +=3D=3D Simple Summary =3D=3D + +Bitcoin's energy consumption is growing with its value (see Figure below). +Although scaling PoW is necessary to maintain the security of the network, +reliance on massive energy consumption has scaling drawbacks and leads to m= +ining +centralization. A major consequence of the central role of local electricit= +y +cost in mining is that today, most existing and potential participants in t= +he +Bitcoin network cannot profitably mine Bitcoin even if they have the capita= +l to +invest in mining hardware. From a practical perspective, Bitcoin adoption b= +y +companies like Tesla (which recently rescinded its acceptance of Bitcoin as +payment) has been hampered by its massive energy consumption and perceived +environmental impact. + +[[https://github.com/PoWx-Org/obtc/raw/main/img/btc_energy-small.png]] + +Figure. Bitcoin price and estimated Bitcoin energy consumption. +Data sources: [https://cbeci.org Cambridge Bitcoin Electricity +Consumption Index], [https://www.coindesk.com CoinDesk]. + +We propose a novel proof-of-work paradigm for Bitcoin--Optical proof-of-wor= +k. It +is designed to decouple Bitcoin mining from energy and make it feasible out= +side +of regions with low electricity costs. ''Optical proof-of-work'' (oPoW) is = +a +modification of Hashcash that is most efficiently computed using a new clas= +s of +photonic processors. Without compromising the cryptographic or game-theoret= +ical +security of Hashcash, oPoW shifts the operating expenses of mining (OPEX), = +to +capital expenses (CAPEX)--i.e. electricity to hardware. oPoW makes it possi= +ble +for billions of new miners to enter the market simply by investing in a +low-energy photonic miner. Shifting to a high-CAPEX PoW has the added benef= +it of +making the hashrate resilient to Bitcoin's price fluctuations - once low-OP= +EX +hardware is operating there is no reason to shut it down even if the value = +of +mining rewards diminishes. oPoW is backward compatible with GPUs, FPGAs, an= +d +ASICs meaning that a transitional period of optical and traditional hardwar= +e +mining in parallel on the network is feasible + +More information is available here: [https://www.powx.org/opow]. + +=3D=3D Abstract =3D=3D + +As Bitcoin gained utility and value over the preceding decade, the +network incentivized the purchase of billions of dollars in mining +equipment and electricity. With the growth of competition, home mining +became unprofitable. Even the most sophisticated special-purpose +hardware (ASIC miners) doesn=E2=80=99t cover its energy costs unless the mi= +ner +also has direct access to very cheap electricity. This heavy reliance +on energy makes it difficult for new miners to enter the market and +leads to hashrate instability as miners shut off their machines when +the price of Bitcoin falls. Additionally as the network stores ever +more value, the percentage of world energy consumption that is +associated with Bitcoin continues to grow, creating the potential for +scaling failure and a general backlash. To ensure that Bitcoin can +continue scaling and reach its full potential as a world currency and +store of value, we propose a low-energy proof-of-work paradigm for +Bitcoin. ''Optical proof of work (oPoW)'' is designed to decouple +Bitcoin=E2=80=99s security from massive energy use and make bitcoin mining +feasible outside of regions with low electricity costs. ''Optical +proof-of-work'' is a modification of Hashcash that is most efficiently +computed using a new class of photonic processors that has emerged as +a leading solution for ultra-low energy computing over the last 5 +years. oPoW shifts the operating expenses of mining (OPEX), to capital +expenses (CAPEX)=E2=80=93i.e. electricity to hardware, without compromising +the cryptographic or game-theoretical security of Hashcash. We provide +an example implementation of oPoW, briefly discuss its cryptographic +construction as well as the working principle of photonic processors. +Additionally, we outline the potential benefits of oPoW to the bitcoin +network, including geographic decentralization and democratization of +mining as well as hashrate resilience to price fluctuations. + +=3D=3D Copyright =3D=3D + +This BIP is dual-licensed under the Open Publication License and BSD +2-clause license. + +=3D=3D Motivation =3D=3D + +As Bitcoin has grown over the past decade from a small network run by +hobbyists to a global currency, the underlying Proof of Work protocol +has not been updated. Initially pitched as a global decentralized +network (=E2=80=9Cone CPU-one vote=E2=80=9D), Bitcoin transactions today ar= +e secured +by a small group of corporate entities. In practice, it is only +feasible for [http://archive.is/YeDwh entities that can secure access +to abundant, inexpensive energy]. The economics of mining limit +profitability to places like Iceland, Texas, or Western China. Besides +the negative environmental externalities, which may be significant, +mining today is performed primarily with the consent (and in many +cases, partnership) of large public utilities and the governments that +control them. Although this may not be a problem in the short term, in +the long term it stands to erode the censorship resistance and +security of Bitcoin and other public blockchains through potential +regulation or [https://arxiv.org/pdf/1605.07524.pdf partitioning +attacks]. + +Recent events, such as the +[https://twitter.com/MustafaYilham/status/1384278267067203590 ~25% +hashrate crash due to coal-powered grid failure in china] and Tesla=E2=80= +=99s +rescinding of its acceptance of Bitcoin as a form of payment, show +that there are practical real-world downsides to Proof of Works=E2=80=99s +massive reliance on energy. + +[[https://github.com/PoWx-Org/obtc/raw/main/img/emusk_tweet.png]] + +Whether on not the Bitcoin community accepts this common criticism as +entirely valid, it has real-world effects which will only get worse +over time. Eliminating the exponentially growing energy use currently +built into Bitcoin without eliminating the security of PoW would be +ideal and should not be a partisan issue. + +New consensus mechanisms have been proposed as a means of securing +cryptocurrencies whilst reducing energy cost, such as various forms of +Proof of Stake and Proof of Space-Time. While many of these +alternative mechanisms offer compelling guarantees, they generally +require new security assumptions, which have not been stress-tested by +live deployments at any adequate scale. Consequently, we still have +relatively little empirical understanding of their safety. Completely +changing the Bitcoin paradigm is likely to introduce new unforeseen +problems. We believe that the major issues discussed above can be +resolved by improving rather than eliminating Bitcoin=E2=80=99s fundamental +security layer=E2=80=94Proof of Work. Instead of devising a new consensus +architecture to fix these issues, it is sufficient to shift the +economics of PoW. The financial cost imposed on miners need not be +primarily composed of electricity. The situation can be significantly +improved by reducing the operating expense (OPEX)=E2=80=94energy=E2=80=94as= + a major +mining component. Then, by shifting the cost towards capital expense +(CAPEX)=E2=80=94mining hardware=E2=80=94the dynamics of the mining ecosyste= +m becomes +much less dependent on electricity prices, and much less electricity +is consumed as a whole. + +Moreover, a reduction in energy consumption automatically leads to +geographically distributed mining, as mining becomes profitable even +in regions with expensive electricity. Additionally, lower energy +consumption will eliminate heating issues experienced by today=E2=80=99s +mining operations, which will further decrease operating cost as well +as noise associated with fans and cooling systems. All of this means +that individuals and smaller entities would be able to enter the +mining ecosystem simply for the cost of a miner, without first gaining +access to cheap energy or a dedicated, temperature-controlled data +center. To a degree, memory-hard PoW schemes like +[https://github.com/tromp/cuckoo Cuckoo Cycle], which increase the use +of SRAM in lieu of pure computation, push the CAPEX/OPEX ratio in the +right direction by occupying ASIC chip area with memory. To maximize +the CAPEX to OPEX ratio of the Optical Proof of Work algorithm, we +developed [https://assets.pubpub.org/xi9h9rps/01581688887859.pdf +''HeavyHash''] [1]. HeavyHash is a cryptographic construction that +takes the place of SHA256 in Hashcash. Our algorithm is compatible +with ultra-energy-efficient photonic co-processors that have been +developed for machine learning hardware accelerators. + +HeavyHash uses a proven digital hash (SHA3) packaged with a large +amount of MAC (Multiply-and-Accumulate) computation into a Proof of +Work puzzle. Although HeavyHash can be computed on any standard +digital hardware, it becomes hardware efficient only when a small +digital core is combined with a low-power photonic co-processor for +performing MAC operations. oPoW mining machines will have a small +digital core flip-chipped onto a large, low-power photonic chip. This +core will be bottlenecked by the throughput of the digital to analog +and analog to digital converters. A prototype of such analogue optical +matrix multiplier can be seen in the figure below. + +[[https://github.com/PoWx-Org/obtc/raw/main/img/optical_chip.png]] + +Figure. TOP: Photonic Circuit Diagram, A. Laser input (1550nm, common +telecom wavelength) B. Metal pads for controlling modulators to +transduce electrical data to optical C. Metal pads for tuning mesh of +directional couplers D. Optical signal exits here containing the +results of the computation and is output to fibers via a grating +coupler the terminus of each waveguide. E. Alignment circuit for +aligning fiber coupling stage. Bottom: a photograph of a bare oPoW +miner prototype chip before wire and fiber bonding. On the right side +of the die are test structures (F). + +The ''HeavyHash'' derives its name from the fact that it is bloated or +weighted with additional computation. This means that a cost +comparable oPoW miner will have a much lower nominal hashrate compared +to a Bitcoin ASIC (HeavyHashes/second vs. SHA256 Hashes/second in +equivalent ASIC). We provide the cryptographic security argument of +the HeavyHash function in Section 3 in +[https://assets.pubpub.org/xi9h9rps/01581688887859.pdf Towards Optical +Proof of Work] [1]. In the article, we also provide a game-theoretic +security argument for CAPEX-heavy PoW. For additional information, we +recommend reading +[https://uncommoncore.co/wp-content/uploads/2019/10/A-model-for-Bitcoins-se= +curity-and-the-declining-block-subsidy-v1.02.pdf +this article]. + +While traditional digital hardware relies on electrical currents, +optical computing uses light as the basis for some of or all of its +operations. Building on the development and commercialization of +silicon photonic chips for telecom and datacom applications, modern +photonic co-processors are silicon chips made using well-established +and highly scalable silicon CMOS processes. However, unlike cutting +edge electronics which require ever-smaller features (e.g. 5 nm), +fabricated by exponentially more complex and expensive machinery, +silicon photonics uses old fabrication nodes (90 nm). Due to the large +de Broglie wavelength of photons, as compared to electrons, there is +no benefit to using the small feature sizes. The result is that access +to silicon photonic wafer fabrication is readily available, in +contrast to the notoriously difficult process of accessing advanced +nodes. Moreover, the overall cost of entry is lower as lithography +masks for silicon photonics processes are an order of magnitude +cheaper ($500k vs. $5M). Examples of companies developing optical +processors for AI, which will be compatible with oPoW include +[https://lightmatter.co/ Lightmatter], [https://www.lightelligence.ai/ +Lightelligence], [https://luminous.co/ Luminous], +[https://www.intel.com/content/www/us/en/architecture-and-technology/silico= +n-photonics/silicon-photonics-overview.html +Intel], and other more recent entrants. + +=3D=3D Specification =3D=3D + +=3D=3D=3D HeavyHash =3D=3D=3D + +The HeavyHash is performed in three stages: + +# Keccak hash +# Matrix-vector multiplication +# Keccak of the result xorred with the hashed input + +Note that the most efficiently matrix-vector multiplication is +performed on a photonic miner. However, this linear algebra operation +can be performed on any conventional computing hardware (CPU, GPU, +etc.), therefore making the HeavyHash compatible with any digital +device. + +The algorithm=E2=80=99s pseudo-code: + +<pre>// M is a Matrix 64 x 64 of Unsigned 4 values + +// 256-bitVector +x1 <- keccak(input) + +// Reshape the obtained bitvector +// into a 64-vector of unsigned 4-bit values +x2 <- reshape(x1, 64) + +// Perform a matrix-vector multiplication. +// The result is 64-vector of 14-bit unsigned. +x3 <- vector_matrix_mult(x2, M) + +// Truncate all values to 4 most significant bits. +// This is due to the specifics of analog +// computing by the photonic accelerator. +// Obtain a 64-vector of 4-bit unsigned. +x4 <- truncate_to_msb(x3, 4) + +// Interpret as a 256-bitvector +x5 <- flatten(x4) + +// 256-bitVector +result <- keccak(xor(x5, x1))</pre> + +Which in C can be implemented as: + +<pre> +static void heavyhash(const uint16_t matrix[64][64], void* pdata, +size_t pdata_len, void* output) +{ + uint8_t hash_first[32] __attribute__((aligned(32))); + uint8_t hash_second[32] __attribute__((aligned(32))); + uint8_t hash_xored[32] __attribute__((aligned(32))); + + uint16_t vector[64] __attribute__((aligned(64))); + uint16_t product[64] __attribute__((aligned(64))); + + sha3_256((uint8_t*) hash_first, 32, (const uint8_t*)pdata, pdata_len); + + for (int i =3D 0; i < 32; ++i) { + vector[2*i] =3D (hash_first[i] >> 4); + vector[2*i+1] =3D hash_first[i] & 0xF; + } + + for (int i =3D 0; i < 64; ++i) { + uint16_t sum =3D 0; + for (int j =3D 0; j < 64; ++j) { + sum +=3D matrix[i][j] * vector[j]; + } + product[i] =3D (sum >> 10); + } + + for (int i =3D 0; i < 32; ++i) { + hash_second[i] =3D (product[2*i] << 4) | (product[2*i+1]); + } + + for (int i =3D 0; i < 32; ++i) { + hash_xored[i] =3D hash_first[i] ^ hash_second[i]; + } + sha3_256((uint8_t*)output, 32, (const uint8_t*)hash_xored, 32); +} +</pre> + +=3D=3D=3D Random matrix generation =3D=3D=3D + +The random matrix M (which is a HeavyHash parameter) is obtained in a +deterministic way and is changed every block. Matrix M coefficients +are generated using a pseudo-random number generation algorithm +(xoshiro) from the previous block header. If the matrix is not full +rank, it is repeatedly generated again. + +An example code to obtain the matrix M: + +<pre> +void generate_matrix(uint16_t matrix[64][64], struct xoshiro_state *state) = +{ + do { + for (int i =3D 0; i < 64; ++i) { + for (int j =3D 0; j < 64; j +=3D 16) { + uint64_t value =3D xoshiro_gen(state); + for (int shift =3D 0; shift < 16; ++shift) { + matrix[i][j + shift] =3D (value >> (4*shift)) & 0xF; + } + } + } + } while (!is_full_rank(matrix)); +} + +static inline uint64_t xoshiro_gen(struct xoshiro_state *state) { + const uint64_t result =3D rotl64(state->s[0] + state->s[3], 23) + state= +->s[0]; + + const uint64_t t =3D state->s[1] << 17; + + state->s[2] ^=3D state->s[0]; + state->s[3] ^=3D state->s[1]; + state->s[1] ^=3D state->s[2]; + state->s[0] ^=3D state->s[3]; + + state->s[2] ^=3D t; + + state->s[3] =3D rotl64(state->s[3], 45); + + return result; +} +</pre> + +=3D=3D Discussion =3D=3D + +=3D=3D=3D Geographic Distribution of Mining Relative to CAPEX-OPEX Ratio of +Mining Costs =3D=3D=3D + +Below is a simple model showing several scenarios for the geographic +distribution of mining activity relative to the CAPEX/OPEX ratio of +the cost of operating a single piece of mining hardware. As the ratio +of energy consumption to hardware cost decreases, geographic +variations in energy cost cease to be a determining factor in miner +distribution. + +Underlying assumptions: 1. Electricity price y is fixed in time but +varies geographically. 2. Every miner has access to the same hardware. +3. Each miner=E2=80=99s budget is limited by both the cost of mining equipm= +ent +as well as the local cost of the electricity they consume + +budget =3D a(p+ey), + +where a is the number of mining machines, p is the machine price, e is +the total energy consumption over machine lifetime, and y is +electricity price. + +Note that in locations where mining is not profitable, hashrate is zero. + +[[https://github.com/PoWx-Org/obtc/raw/main/img/sim1.png]] + +[[https://github.com/PoWx-Org/obtc/raw/main/img/sim2.png]] + +[[https://github.com/PoWx-Org/obtc/raw/main/img/sim3.png]] + + +An interactive version of this diagram can be found +[https://www.powx.org/opow here]. + +=3D=3D=3D Why does CAPEX to OPEX shift lead to lower energy consumption? = +=3D=3D=3D + +A common misconception about oPoW is that it makes mining =E2=80=9Ccheaper= +=E2=80=9D by +enabling energy-efficient hardware. There is no impact on the dollar +cost of mining a block, rather the mix of energy vs. hardware +investment changes from about 50/50 to 10/90 or better. We discuss +this at length and rigorously in our paper[1]. + +=3D=3D=3D Working Principles of Photonic Processors =3D=3D=3D + +Photonics accelerators are made by fabricating waveguides in silicon +using standard lithography processes. Silicon is transparent to +infrared light and can act as a tiny on-chip fiber optical cable. +Silicon photonics found its first use during the 2000s in transceivers +for sending and receiving optical signals via fiber and has advanced +tremendously over the last decade. + +By encoding a vector into optical intensities passing through a series +of parallel waveguides, interfering these signals in a mesh of tunable +interferometers (acting as matrix coefficients), and then detecting +the output using on-chip Germanium photodetectors, a matrix-vector +multiplication is achieved. A generalized discussion of matrix +multiplication setups using photonics/interference can be found in +[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.73.58 Reck +et al.] and [https://arxiv.org/abs/1506.06220 Russell et al.] A +detailed discussion of several integrated photonic architectures for +matrix multiplication and corresponding tuning algorithms can be found +in [https://arxiv.org/pdf/1909.06179.pdf Pai et al.] + +Below is a conceptual representation of a 3D-packaged oPoW mining +chip. Note that the majority of the real estate and cost comes from +the photonic die and the laser, with only a small digital SHA3 die +needed (as opposed to a conventional miner of the same cost, which +would have many copies of this die running in parallel). + +[[https://github.com/PoWx-Org/obtc/raw/main/img/optminer.png]] + +=3D=3D=3D Block Reward Considerations =3D=3D=3D + +Although it is out of the scope of this proposal, the authors strongly +recommend the consideration of a change in the block reward schedule +currently implemented in Bitcoin. There is no clear way to incentivize +miners with transaction fees only, as has been successfully shown in +[https://www.cs.princeton.edu/~smattw/CKWN-CCS16.pdf On the +Instability of Bitcoin Without the Block Reward] and other +publications, therefore looking a decade or two ahead it will be +important to implement a fixed block reward or to slow the decay of +the block reward to maintain the security of the network. Given that +oPoW miners have low operating costs, once a large number of machines +are running the reward level sufficient to keep them in operation and +providing robust security can potentially be significantly smaller +than in the case of the current SHA256 ASICs securing Bitcoin. + +=3D=3D=3D Implementation on the Bitcoin Network =3D=3D=3D + +A hard fork is not necessarily required for the Bitcoin network to +test and eventually implement oPoW. It=E2=80=99s possible to add oPoW as a +dual PoW to Bitcoin as a soft fork. Tuning the parameters to ensure +that, for example, 99.9% of the security budget would be earned by +miners via the SHA256 Hashcash PoW and 0.1% via oPoW would create +sufficient incentive for oPoW to be stress-tested and to incentivize +the manufacture of dedicated oPoW miners. If this test is successful, +the parameters can be tuned continuously over time, e.g. oPoW share +doubling at every halving, such that oPoW accounts for some target +percentage (up to 100% in a complete SHA256 phase-out). + +=3D=3D Endnotes =3D=3D + +With significant progress in optical and analog +matrix-vector-multiplication chipsets over the last year, we hope to +demonstrate commercial low-energy mining on our network in the next 6 +months. The current generation of optical matrix processors under +development is expected to have 10x better energy consumption per MAC +operation than digital implementations, and we expect this to improve +by another order of magnitude in future generations. + +PoWx will also be publishing the designs of the current optical miner +prototypes in the near term under an open-source hardware license. + +=3D=3D Acknowledgments =3D=3D + +We thank all the members of the Bitcoin community who have already +given us feedback over the last several years as well as others in the +optical computing community and beyond that have given their input. + + + + +[1] M. Dubrovsky et al. Towards Optical Proof of Work, CES conference +(2020) https://assets.pubpub.org/xi9h9rps/01581688887859.pdf + +[2] https://sciencex.com/news/2020-05-powering-bitcoin-silicon-photonics-po= +wer.html + +[3] KISS random number generator http://www.cse.yorku.ca/~oz/marsaglia-rng.= +html + + + + +---- +We have taken into account the moderator's comments we received previously. + + + +Bogdan and Mike, + +PoWx + |