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224 lines
10 KiB
Markdown
224 lines
10 KiB
Markdown
# Verifiable Delay Function (VDF) Implementation in Rust
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## What is a VDF?
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A Verifiable Delay Function (VDF) is a function that requires substantial time
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to evaluate (even with a polynomial number of parallel processors) but can be
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very quickly verified as correct. VDFs can be used to construct randomness
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beacons with multiple applications in a distributed network environment. By
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introducing a time delay during evaluation, VDFs prevent malicious actors from
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influencing output. The output cannot be differentiated from a random number
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until the final result is computed. See <https://eprint.iacr.org/2018/712.pdf>
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for more details.
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## Description
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This VDF implementation is written in Rust. The GMP library is used for
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arithmetic and greatest common divisor (GCD) calculations. We use class groups
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to implement the approaches described in the following papers:
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1. [Simple Verifiable Delay Functions](https://eprint.iacr.org/2018/627.pdf). Pietrzak, 2018
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2. [Efficient Verifiable Delay Functions](https://eprint.iacr.org/2018/623.pdf). Wesolowski, 2018
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The chosen generator is (2, 1, c), where c is calculated from the provided
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discriminant. A form is represented internally (a, b, c), with the
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discriminant not being used in most omputations. This implementation performs
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reduction is performed after every multiplication and squaring, as not doing so
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did not give any gains in our benchmarks.
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This repo includes three crates:
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* `classgroup`: a class group implementation, as well as a trait for class
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groups.
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* `vdf`: a Verifyable Delay Function (VDF) trait, as well as an
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implementation of that trait.
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* `vdf-cli`: a command-line interface to the vdf crate. It also includes
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additional commands, which are deprecated and will be replaced by a CLI to
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the classgroup crate.
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## Usage
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- Install [Rust]. We (POA Networks) have tested the code with the latest
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stable, beta, and nightly versions of Rust. It may work with older
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versions, but this is not guaranteed.
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- Install the [GNU Multiple Precision Library](https://gmplib.org/)
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* On Debian and derivatives (including Ubuntu):
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```sh
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$ sudo apt-get install -y libgmp-dev
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```
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* On Red Hat and derivatives (Fedora, CentOS)
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```sh
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$ sudo dnf -y install gmp-devel
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```
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- Download and prepare the repository
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```sh
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$ git clone https://github.com/poanetwork/vdf.git
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$ cargo install --path=vdf-cli
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$ # or for the competition binary
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$ cargo install --path=vdf-competition
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```
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### Command Line Interface
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To initiate, use the `vdf-cli` command followed by 2 arguments:
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- _challenge_: byte string of arbitrary length
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- _difficulty_: number of iterations, each iteration requires more time to evaluate
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This generates the Weslowski proof of time. To generate the Pietrzak proof of
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time, pass `-tpietrzak`. For detailed usage information, run `vdf-cli --help`.
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Once complete you will see the output, returned as a `Vec<u8>`. The CLI tool
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hex-encodes its output.
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**Example**
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```sh
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$ vdf-cli aa 100
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```
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To verify, use the `vdi-cli` command with the same arguments and include the
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output.
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**Example**
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```sh
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$ vdf-cli aa 100 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Proof is valid
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```
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### VDF Library
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<!--
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Keep as is, and possibly include argument explanations as well (for byte_length for example). May not be needed though is CLI is main user interaction tool.
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-->
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```rust
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extern crate vdf;
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use vdf::{InvalidProof, PietrzakVDFParams, VDFParams, WesolowskiVDFParams, VDF};
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/// The correct solution.
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const CORRECT_SOLUTION: &[u8] =
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b"\x00\x52\x71\xe8\xf9\xab\x2e\xb8\xa2\x90\x6e\x85\x1d\xfc\xb5\x54\x2e\x41\x73\xf0\x16\
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\xb8\x5e\x29\xd4\x81\xa1\x08\xdc\x82\xed\x3b\x3f\x97\x93\x7b\x7a\xa8\x24\x80\x11\x38\
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\xd1\x77\x1d\xea\x8d\xae\x2f\x63\x97\xe7\x6a\x80\x61\x3a\xfd\xa3\x0f\x2c\x30\xa3\x4b\
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\x04\x0b\xaa\xaf\xe7\x6d\x57\x07\xd6\x86\x89\x19\x3e\x5d\x21\x18\x33\xb3\x72\xa6\xa4\
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\x59\x1a\xbb\x88\xe2\xe7\xf2\xf5\xa5\xec\x81\x8b\x57\x07\xb8\x6b\x8b\x2c\x49\x5c\xa1\
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\x58\x1c\x17\x91\x68\x50\x9e\x35\x93\xf9\xa1\x68\x79\x62\x0a\x4d\xc4\xe9\x07\xdf\x45\
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\x2e\x8d\xd0\xff\xc4\xf1\x99\x82\x5f\x54\xec\x70\x47\x2c\xc0\x61\xf2\x2e\xb5\x4c\x48\
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\xd6\xaa\x5a\xf3\xea\x37\x5a\x39\x2a\xc7\x72\x94\xe2\xd9\x55\xdd\xe1\xd1\x02\xae\x2a\
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\xce\x49\x42\x93\x49\x2d\x31\xcf\xf2\x19\x44\xa8\xbc\xb4\x60\x89\x93\x06\x5c\x9a\x00\
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\x29\x2e\x8d\x3f\x46\x04\xe7\x46\x5b\x4e\xee\xfb\x49\x4f\x5b\xea\x10\x2d\xb3\x43\xbb\
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\x61\xc5\xa1\x5c\x7b\xdf\x28\x82\x06\x88\x5c\x13\x0f\xa1\xf2\xd8\x6b\xf5\xe4\x63\x4f\
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\xdc\x42\x16\xbc\x16\xef\x7d\xac\x97\x0b\x0e\xe4\x6d\x69\x41\x6f\x9a\x9a\xce\xe6\x51\
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\xd1\x58\xac\x64\x91\x5b";
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fn main() {
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// The length of the prime numbers generated, in bits.
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let num_bits: u16 = 2048;
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// An instance of the VDF. Instances can be used arbitrarily many times.
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let pietrzak_vdf = PietrzakVDFParams(num_bits).new();
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// Solve for the correct answer. This will take a minute or two.
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assert_eq!(
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&pietrzak_vdf.solve(b"\xaa", 10000).unwrap()[..],
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CORRECT_SOLUTION
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);
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// Verify the answer. This should be far faster (less than a second).
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assert!(pietrzak_vdf.verify(b"\xaa", 10000, CORRECT_SOLUTION).is_ok());
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}
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```
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## Benchmarks
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Benchmarks are provided for the classgroup operations. To run benchmarks:
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```sh
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$ ./bench.sh <your challenge here>
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```
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Additional benchmarks are under development.
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### Current Benchmarks
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These were generated by `./bench.sh aadf`. Outliers could be due to preemption
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by the OS and/or hypervisor. Changes are relative to the previous test run
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done on the same machine. Since the previous run was done with different
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settings and/or code than reported here, these changes are not meaningful.
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```text
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Benchmarking square with seed aadf: 512: Collecting 100 samples in estimated 5.0439 s (374k iteratio square with seed aadf: 512
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time: [13.301 us 13.333 us 13.372 us]
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change: [-22.286% -21.745% -21.225%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 22 outliers among 100 measurements (22.00%)
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5 (5.00%) high mild
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17 (17.00%) high severe
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Benchmarking multiply with seed aadf: 512: Collecting 100 samples in estimated 5.0452 s (293k iterat multiply with seed aadf: 512
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time: [17.219 us 17.251 us 17.287 us]
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change: [-24.323% -23.739% -23.149%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 10 outliers among 100 measurements (10.00%)
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4 (4.00%) high mild
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6 (6.00%) high severe
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Benchmarking square with seed aadf: 1024: Collecting 100 samples in estimated 5.0822 s (177k iterati square with seed aadf: 1024
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time: [28.672 us 28.716 us 28.767 us]
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change: [-29.947% -29.339% -28.708%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 8 outliers among 100 measurements (8.00%)
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1 (1.00%) low mild
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1 (1.00%) high mild
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6 (6.00%) high severe
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Benchmarking multiply with seed aadf: 1024: Collecting 100 samples in estimated 5.0886 s (136k itera multiply with seed aadf: 1024
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time: [37.163 us 37.207 us 37.254 us]
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change: [-21.403% -20.750% -20.170%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 8 outliers among 100 measurements (8.00%)
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1 (1.00%) low mild
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1 (1.00%) high mild
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6 (6.00%) high severe
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Benchmarking square with seed aadf: 2048: Collecting 100 samples in estimated 5.2519 s (76k iteratio square with seed aadf: 2048
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time: [69.115 us 69.254 us 69.430 us]
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change: [-28.091% -27.738% -27.341%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 8 outliers among 100 measurements (8.00%)
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1 (1.00%) low mild
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1 (1.00%) high mild
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6 (6.00%) high severe
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Benchmarking multiply with seed aadf: 2048: Collecting 100 samples in estimated 5.0554 s (56k iterat multiply with seed aadf: 2048
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time: [90.922 us 91.057 us 91.201 us]
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change: [-25.236% -24.794% -24.336%] (p = 0.00 < 0.05)
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Performance has improved.
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Found 13 outliers among 100 measurements (13.00%)
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2 (2.00%) low mild
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5 (5.00%) high mild
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6 (6.00%) high severe
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```
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[Rust]: <https://doc.rust-lang.org/cargo/getting-started/installation.html>
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## License
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Copyright 2018 Chia Network Inc and POA Networks Ltd.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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<http://www.apache.org/licenses/LICENSE-2.0>
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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