https://github.com/arnaucube/kzg-commitments-study

Kate-Zaverucha-Goldberg Polynomial Commitments
https://github.com/arnaucube/kzg-commitments-study

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Kate-Zaverucha-Goldberg Polynomial Commitments

• Host: GitHub
• URL: https://github.com/arnaucube/kzg-commitments-study
• Owner: arnaucube
• License: gpl-3.0
• Created: 2021-06-26T16:14:51.000Z (over 3 years ago)
• Default Branch: master
• Last Pushed: 2021-11-20T18:00:33.000Z (about 3 years ago)
• Last Synced: 2024-10-04T09:27:58.048Z (3 months ago)
• Language: Go
• Size: 47.9 KB
• Stars: 28
• Watchers: 2
• Forks: 4
• Open Issues: 1
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# kzg-commitments-study [![GoDoc](https://godoc.org/github.com/arnaucube/kzg-commitments-study?status.svg)](https://godoc.org/github.com/arnaucube/kzg-commitments-study) [![Go Report Card](https://goreportcard.com/badge/github.com/arnaucube/kzg-commitments-study)](https://goreportcard.com/report/github.com/arnaucube/kzg-commitments-study) [![Test](https://github.com/arnaucube/kzg-commitments-study/workflows/Test/badge.svg)](https://github.com/arnaucube/kzg-commitments-study/actions?query=workflow%3ATest)

Doing this to study and learn [KZG commitments](http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf), do not use in production. More details at https://arnaucube.com/blog/kzg-commitments.html .

Thanks to [Dankrad Feist](https://dankradfeist.de/ethereum/2020/06/16/kate-polynomial-commitments.html), [Alin Tomescu](https://alinush.github.io/2020/05/06/kzg-polynomial-commitments.html), [Tom Walton-Pocock](https://hackmd.io/@tompocock/Hk2A7BD6U) for their articles, which helped me understand a bit the KZG Commitments.

It uses the [ethereum bn256](https://github.com/ethereum/go-ethereum/tree/master/crypto/bn256/cloudflare).

### Usage

```go

// p(x) = x^3 + x + 5

p := []*big.Int{

	big.NewInt(5),

	big.NewInt(1), // x^1

	big.NewInt(0), // x^2

	big.NewInt(1), // x^3

}

assert.Equal(t, "1x³ + 1x¹ + 5", PolynomialToString(p))

// TrustedSetup

ts, err := NewTrustedSetup(p)

assert.Nil(t, err)

// Commit

c := Commit(ts, p)

// p(z)=y --> p(3)=35

z := big.NewInt(3)

y := big.NewInt(35)

// z & y: to prove an evaluation p(z)=y

proof, err := EvaluationProof(ts, p, z, y)

assert.Nil(t, err)

// verification

v := Verify(ts, c, proof, z, y)

assert.True(t, v)

```

Batch Proofs:

```go

// zs & ys contain the f(z_i)=y_i values that will be proved inside a batch proof

zs := []*big.Int{z0, z1, z2}

ys := []*big.Int{y0, y1, y2}

// prove an evaluation of the multiple z_i & y_i

proof, err := EvaluationBatchProof(ts, p, zs, ys)

assert.Nil(t, err)

// batch proof verification

v := VerifyBatchProof(ts, c, proof, zs, ys)

assert.True(t, v)

```