A Verifiable Delay Function (VDF) is a function that requires substantial time to evaluate (even with a polynomial number of parallel processors) but can be very quickly verified as correct. VDFs can be used to construct randomness beacons with multiple applications in a distributed network environment. By introducing a time delay during evaluation, VDFs prevent malicious actors from influencing output. The output cannot be differentiated from a random number until the final result is computed. See https://eprint.iacr.org/2018/712.pdf for more details.
This VDF implementation is written in Rust. The GMP library is used for arithmetic and greatest common divisor (GCD) calculations. We use class groups to implement the approaches described in the following papers:
The chosen generator is (2, 1, c), where c is calculated from the provided discriminant. A form is represented internally (a, b, c), with the discriminant not being used in most omputations. This implementation performs reduction is performed after every multiplication and squaring, as not doing so did not give any gains in our benchmarks.
This repo includes three crates:
classgroup: a class group implementation, as well as a trait for class
groups.vdf: a Verifyable Delay Function (VDF) trait, as well as an
implementation of that trait.vdf-cli: a command-line interface to the vdf crate. It also includes
additional commands, which are deprecated and will be replaced by a CLI to
the classgroup crate.sh
$ sudo apt-get install -y libgmp-dev
sh
$ sudo dnf -y install gmp-devel
Download and prepare the repository
sh
$ git clone https://github.com/poanetwork/vdf.git
$ cargo install --path=vdf-cli
$ # or for the competition binary
$ cargo install --path=vdf-competition
To initiate, use the vdf-cli command followed by 2 arguments:
This generates the Weslowski proof of time. To generate the Pietrzak proof of
time, pass -tpietrzak. For detailed usage information, run vdf-cli --help.
Once complete you will see the output, returned as a Vec<u8>. The CLI tool
hex-encodes its output.
Example
sh
$ vdf-cli aa 100
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
To verify, use the vdi-cli command with the same arguments and include the
output.
Example
sh
$ vdf-cli aa 100 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
Proof is valid
```rust extern crate vdf; use vdf::{InvalidProof, PietrzakVDFParams, VDFParams, WesolowskiVDFParams, VDF};
/// The correct solution. const CORRECTSOLUTION: &[u8] = b"\x00\x52\x71\xe8\xf9\xab\x2e\xb8\xa2\x90\x6e\x85\x1d\xfc\xb5\x54\x2e\x41\x73\xf0\x16\ \xb8\x5e\x29\xd4\x81\xa1\x08\xdc\x82\xed\x3b\x3f\x97\x93\x7b\x7a\xa8\x24\x80\x11\x38\ \xd1\x77\x1d\xea\x8d\xae\x2f\x63\x97\xe7\x6a\x80\x61\x3a\xfd\xa3\x0f\x2c\x30\xa3\x4b\ \x04\x0b\xaa\xaf\xe7\x6d\x57\x07\xd6\x86\x89\x19\x3e\x5d\x21\x18\x33\xb3\x72\xa6\xa4\ \x59\x1a\xbb\x88\xe2\xe7\xf2\xf5\xa5\xec\x81\x8b\x57\x07\xb8\x6b\x8b\x2c\x49\x5c\xa1\ \x58\x1c\x17\x91\x68\x50\x9e\x35\x93\xf9\xa1\x68\x79\x62\x0a\x4d\xc4\xe9\x07\xdf\x45\ \x2e\x8d\xd0\xff\xc4\xf1\x99\x82\x5f\x54\xec\x70\x47\x2c\xc0\x61\xf2\x2e\xb5\x4c\x48\ \xd6\xaa\x5a\xf3\xea\x37\x5a\x39\x2a\xc7\x72\x94\xe2\xd9\x55\xdd\xe1\xd1\x02\xae\x2a\ \xce\x49\x42\x93\x49\x2d\x31\xcf\xf2\x19\x44\xa8\xbc\xb4\x60\x89\x93\x06\x5c\x9a\x00\ \x29\x2e\x8d\x3f\x46\x04\xe7\x46\x5b\x4e\xee\xfb\x49\x4f\x5b\xea\x10\x2d\xb3\x43\xbb\ \x61\xc5\xa1\x5c\x7b\xdf\x28\x82\x06\x88\x5c\x13\x0f\xa1\xf2\xd8\x6b\xf5\xe4\x63\x4f\ \xdc\x42\x16\xbc\x16\xef\x7d\xac\x97\x0b\x0e\xe4\x6d\x69\x41\x6f\x9a\x9a\xce\xe6\x51\ \xd1\x58\xac\x64\x91\x5b"; fn main() { // The length of the prime numbers generated, in bits. let numbits: u16 = 2048;
// An instance of the VDF. Instances can be used arbitrarily many times.
let pietrzak_vdf = PietrzakVDFParams(num_bits).new();
// Solve for the correct answer. This will take a minute or two.
assert_eq!(
&pietrzak_vdf.solve(b"\xaa", 10000).unwrap()[..],
CORRECT_SOLUTION
);
// Verify the answer. This should be far faster (less than a second).
assert!(pietrzak_vdf.verify(b"\xaa", 10000, CORRECT_SOLUTION).is_ok());
} ```
Benchmarks are provided for the classgroup operations. To run benchmarks:
sh
$ ./bench.sh <your challenge here>
Additional benchmarks are under development.
These were generated by ./bench.sh aadf. Outliers could be due to preemption
by the OS and/or hypervisor. Changes are relative to the previous test run
done on the same machine. Since the previous run was done with different
settings and/or code than reported here, these changes are not meaningful.
```text Benchmarking square with seed aadf: 512: Collecting 100 samples in estimated 5.0439 s (374k iteratio square with seed aadf: 512 time: [13.301 us 13.333 us 13.372 us] change: [-22.286% -21.745% -21.225%] (p = 0.00 < 0.05) Performance has improved. Found 22 outliers among 100 measurements (22.00%) 5 (5.00%) high mild 17 (17.00%) high severe
Benchmarking multiply with seed aadf: 512: Collecting 100 samples in estimated 5.0452 s (293k iterat multiply with seed aadf: 512 time: [17.219 us 17.251 us 17.287 us] change: [-24.323% -23.739% -23.149%] (p = 0.00 < 0.05) Performance has improved. Found 10 outliers among 100 measurements (10.00%) 4 (4.00%) high mild 6 (6.00%) high severe
Benchmarking square with seed aadf: 1024: Collecting 100 samples in estimated 5.0822 s (177k iterati square with seed aadf: 1024 time: [28.672 us 28.716 us 28.767 us] change: [-29.947% -29.339% -28.708%] (p = 0.00 < 0.05) Performance has improved. Found 8 outliers among 100 measurements (8.00%) 1 (1.00%) low mild 1 (1.00%) high mild 6 (6.00%) high severe
Benchmarking multiply with seed aadf: 1024: Collecting 100 samples in estimated 5.0886 s (136k itera multiply with seed aadf: 1024 time: [37.163 us 37.207 us 37.254 us] change: [-21.403% -20.750% -20.170%] (p = 0.00 < 0.05) Performance has improved. Found 8 outliers among 100 measurements (8.00%) 1 (1.00%) low mild 1 (1.00%) high mild 6 (6.00%) high severe
Benchmarking square with seed aadf: 2048: Collecting 100 samples in estimated 5.2519 s (76k iteratio square with seed aadf: 2048 time: [69.115 us 69.254 us 69.430 us] change: [-28.091% -27.738% -27.341%] (p = 0.00 < 0.05) Performance has improved. Found 8 outliers among 100 measurements (8.00%) 1 (1.00%) low mild 1 (1.00%) high mild 6 (6.00%) high severe
Benchmarking multiply with seed aadf: 2048: Collecting 100 samples in estimated 5.0554 s (56k iterat multiply with seed aadf: 2048 time: [90.922 us 91.057 us 91.201 us] change: [-25.236% -24.794% -24.336%] (p = 0.00 < 0.05) Performance has improved. Found 13 outliers among 100 measurements (13.00%) 2 (2.00%) low mild 5 (5.00%) high mild 6 (6.00%) high severe ```
Copyright 2018 Chia Network Inc and POA Networks Ltd.
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
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