@guildofweavers/genstark

genSTARK

This library is intended to help you quickly and easily generate STARK-based proofs of computation using JavaScript. The goal is to take care of as much boilerplate code as possible, and let you focus on the specific "business logic" of your computations.

Background

A STARK is a novel proof-of-computation scheme that allows you to create an efficiently verifiable proof that a computation was executed correctly. The scheme was developed by Eli-Ben Sasson and team at Technion-Israel Institute of Technology. STARKs do not require an initial trusted setup, and rely on very few cryptographic assumptions. See references for more info.

Disclaimer

DO NOT USE THIS LIBRARY IN PRODUCTION. At this point, this is a research-grade library. It has known and unknown bugs and security flaws.

Install

$ npm install @guildofweavers/genstark --save

Usage

Here is a trivial example of how to use this library. In this example, the computation is just adding 2 to the current value at each step. That is: x_n+1 = x_n + 2.

import { Stark } from '@guildofweavers/genstark';

// define a STARK for this computation
const fooStark = new Stark(`
define Foo over prime field (2^32 - 3 * 2^25 + 1) {

    // define transition function
    transition 1 register in 64 steps {
        out: $r0 + 2;
    }

    // define transition constraints
    enforce 1 constraint {
        out: $n0 - ($r0 + 2);
    }
}`);

// create a proof that if we start computation at 1, we end up at 127 after 64 steps
const assertions = [
    { register: 0, step: 0, value: 1n },    // value at first step is 1
    { register: 0, step: 63, value: 127n }  // value at last step is 127
];
const proof = fooStark.prove(assertions, [1n]);

// verify that if we start at 1 and run the computation for 64 steps, we get 127
const result = fooStark.verify(assertions, proof);
console.log(result); // true

There are a few more sophisticated examples in this repository:

• Demo STARKs - demonstration of how to use various features of this library.
• MiMC STARK - basically the same as Vitalik Buterin's MiMC tutorial.
• Rescue STARKs - various STARKs based on Rescue hash function (e.g. proof of hash preimage, Merkle proof).

When you run the examples, you should get a nice log documenting each step. Here is an example output of running MiMC STARK for 2¹³ steps:

Starting STARK computation
Set up evaluation context in 86 ms
Generated execution trace in 33 ms
Converted execution trace into polynomials and low-degree extended them in 826 ms
Computed Q(x) polynomials in 337 ms
Computed Z(x) polynomial in 24 ms
Inverted Z(x) numerators in 148 ms
Computed D(x) polynomials in 85 ms
Computed B(x) polynomials in 478 ms
Serialized evaluations of P(x), B(x), and D(x) polynomials in 451 ms
Built evaluation merkle tree in 233 ms
Computed 80 evaluation spot checks in 2 ms
Computed random linear combination of evaluations in 468 ms
Computed low-degree proof in 1358 ms
STARK computed in 4530 ms
--------------------
Proof serialized in 3 ms; size: 214.19 KB
--------------------
Proof parsed in 8 ms
--------------------
Starting STARK verification
Set up evaluation context in 22 ms
Computed positions for evaluation spot checks in 1 ms
Decoded evaluation spot checks in 2 ms
Verified evaluation merkle proof in 6 ms
Verified liner combination proof in 3 ms
Verified low-degree proof in 70 ms
Verified transition and boundary constraints in 29 ms
STARK verified in 137 ms
-------------------

API

You can find complete API definitions in genstark.d.ts. Here is a quick overview of the provided functionality:

Defining a STARK

To create a STARK for a computation you need to create a Stark object like so:

const myStark = new Stark(source, options, logger);

The meaning of the constructor parameters is as follows:

Parameter	Description
source	AirScript source defining transition function, transition constraints, and other properties of the STARK.
options?	An optional property specifying security parameters for the STARK.
logger?	An optional logger. The default logger prints output to the console, but it can be replaced with anything that complies with the Logger interface.

Security options

Security options parameter should have the following form:

Property	Description
extensionFactor?	Number by which the execution trace is "stretched." Must be a power of 2 at least 2x of the constraint degree, but cannot exceed 32. This property is optional, the default is smallest power of 2 that is greater than 2 * constraint degree.
exeQueryCount?	Number of queries of the execution trace to include into the proof. This property is optional; the default is 80; the max is 128.
friQueryCount?	Number of queries of the columns of low degree proof to include into the proof. This property is optional; the default is 40; the max is 64.
hashAlgorithm?	Hash algorithm to use when building Merkle trees for the proof. Currently, can be one of two values: sha256 or blake2s256. This property is optional; the default is sha256.

Generating proofs

Once you have a Stark object, you can start generating proofs using Stark.prove() method like so:

const proof = myStark.prove(assertions, initValues, publicInputs?, secretInputs?);

The meaning of the parameters is as follows:

Parameter	Description
assertions	An array of Assertion objects (also called boundary constraints). These assertions specify register values at specific steps of a valid computation. At least 1 assertion must be provided.
initValues	An array of BigInt's containing initial values for all mutable registers.
publicInputs?	An array containing values for all specified public registers. This parameter is optional and can be skipped if no public input registers have been defined.
secretInputs?	An array containing values for all specified secret registers. This parameter is optional and can be skipped if no secret input registers have been defined.

Initial values and inputs

Handling of initial values and inputs deserves a bit more explanation. As described above, there are 3 ways to supply inputs to STARK.prove() method:

• initValues parameter is always required. It is basically used to define step 0 or the execution trace. Thus, the number of values provided must match the number of mutable registers in the STARK.
• The other two parameters provide values for the input registers defined in the STARK. To learn more about these, refer to Readonly registers section of AirScript documentation. These parameters are required only if STARK's definition includes input registers.

For example, the fragment below specifies that a STARK must have 3 readonly registers, but that the values for these registers are not available at the STARK's definition time (the [...] indicate that the values will be provided later):

using 3 readonly registers {
    $p0: repeat [...];
    $p1: spread [...];
    $s0: spread [...];
}

Moreover, by using prefixes $p and $s it also specifies that 2 of the registers are public (the values will be known to the prover and the verified), and 1 of the registers is secret (the values will be known only to the prover).

So, based on this definition, the parameters for STARK.prove() method should be supplied like so:

// let's say we have 2 mutable registers
let initValues = [1n, 2n];

// define values for public input registers
let pValues1 = [1n, 2n, 3n, 4n];
let pValues2 = [1n, 2n, 3n, 4n, 5n, 6n, 7n, 7n];

// define values for secret input registers
let sValues = [10n, 11n, 12n, 13n];

// generate the proof
let proof = fooStark.prove(assertions, initValues, [pValues1, pValues2], [sValues]);

When the proof is generated, the provided values will "appear" in registers $p0, $p1, and $s0 to be used in transition function and transition constraints. The rules for how this happens are also described in the Readonly registers section of AirScript documentation.

Verifying proofs

Once you've generated a proof, you can verify it using Stark.verify() method like so:

const result = myStark.verify(assertions, proof, publicInputs?);

The meaning of the parameters is as follows:

Parameter	Description
assertions	The same array of Assertion objects that was passed to the prove() method.
proof	The proof object that was generated by the prove() method.
publicInputs?	An array containing values for all specified public registers. This parameter is optional and can be skipped if no public input registers have been defined.

Verifying a proof basically attests to something like this:

If you start with some set of initial values (known to the prover), and run the computation for the specified number of steps, the execution trace generated by the computation will satisfy the specified assertions.

Assertions

Assertions (or boundary constraints) are objects that specify the exact value of a given mutable register at a given step. An assertion object has the following form:

interface Assertion {
    register: number;   // index of a mutable register
    step    : number;   // step in the execution trace
    value   : bigint;   // value that the register should have at the specified step
}

Performance

Some very informal benchmarks run on Intel Core i5-7300U @ 2.60GHz (single thread):

STARK	Field Size	Degree	Registers	Steps	Proof Time	Proof Size
Fibonacci	32 bits	1	2	26	50 ms	9 KB
Fibonacci	32 bits	1	2	213	1 sec	140 KB
Fibonacci	32 bits	1	2	217	13 sec	280 KB
MiMC	256 bits	3	1	26	100 ms	36 KB
MiMC	256 bits	3	1	213	4.5 sec	214 KB
MiMC	256 bits	3	1	217	72 sec	381 KB
Merkle Proof (d=8)	128 bits	4	8	28	800 ms	88 KB
Merkle Proof (d=16)	128 bits	4	8	29	1.6 sec	109 KB

Merkle proofs are based on a modified version of Rescue hash function, and in addition to 8 state registers require 1 public input register and 1 secret input register.

The potential to improve proof time is at least 10x (by moving hashing and math functions out of JavaScript), and potentially much higher (by using SIMD and parallelism).

References

This library is largely based on Vitalik Buterin's zk-STARK/MiMC tutorial. Other super useful resources:

• STARKs whitepaper: Scalable, transparent, and post-quantum secure computational integrity

Vitalik Buterin's blog series on zk-STARKs:

• STARKs, part 1: Proofs with Polynomials
• STARKs, part 2: Thank Goodness it's FRI-day
• STARKs, part 3: Into the Weeds

StarkWare's STARK Math blog series:

• STARK Math: The Journey Begins
• Arithmetization I
• Arithmetization II
• Low Degree Testing
• A Framework for Efficient STARKs

License

MIT © 2019 Guild of Weavers