1package plonky2_verifier
  2
  3import (
  4	. "gnark-ed25519/field"
  5
  6	"github.com/consensys/gnark/frontend"
  7)
  8
  9type PlonkOracle struct {
 10	index    uint64
 11	blinding bool
 12}
 13
 14var CONSTANTS_SIGMAS = PlonkOracle{
 15	index:    0,
 16	blinding: false,
 17}
 18
 19var WIRES = PlonkOracle{
 20	index:    1,
 21	blinding: true,
 22}
 23
 24var ZS_PARTIAL_PRODUCTS = PlonkOracle{
 25	index:    2,
 26	blinding: true,
 27}
 28
 29var QUOTIENT = PlonkOracle{
 30	index:    3,
 31	blinding: true,
 32}
 33
 34type PlonkChip struct {
 35	api   frontend.API           `gnark:"-"`
 36	qeAPI *QuadraticExtensionAPI `gnark:"-"`
 37
 38	commonData CommonCircuitData `gnark:"-"`
 39
 40	DEGREE        F                  `gnark:"-"`
 41	DEGREE_BITS_F F                  `gnark:"-"`
 42	DEGREE_QE     QuadraticExtension `gnark:"-"`
 43}
 44
 45func NewPlonkChip(api frontend.API, qeAPI *QuadraticExtensionAPI, commonData CommonCircuitData) *PlonkChip {
 46	// TODO:  Should degreeBits be verified that it fits within the field and that degree is within uint64?
 47
 48	return &PlonkChip{
 49		api:   api,
 50		qeAPI: qeAPI,
 51
 52		commonData: commonData,
 53
 54		DEGREE:        NewFieldElement(1 << commonData.DegreeBits),
 55		DEGREE_BITS_F: NewFieldElement(commonData.DegreeBits),
 56		DEGREE_QE:     QuadraticExtension{NewFieldElement(1 << commonData.DegreeBits), ZERO_F},
 57	}
 58}
 59
 60func (p *PlonkChip) expPowerOf2Extension(x QuadraticExtension) QuadraticExtension {
 61	for i := uint64(0); i < p.commonData.DegreeBits; i++ {
 62		x = p.qeAPI.SquareExtension(x)
 63	}
 64
 65	return x
 66}
 67
 68func (p *PlonkChip) evalL0(x QuadraticExtension, xPowN QuadraticExtension) QuadraticExtension {
 69	// L_0(x) = (x^n - 1) / (n * (x - 1))
 70	evalZeroPoly := p.qeAPI.SubExtension(
 71		xPowN,
 72		p.qeAPI.ONE_QE,
 73	)
 74	denominator := p.qeAPI.SubExtension(
 75		p.qeAPI.ScalarMulExtension(x, p.DEGREE),
 76		p.DEGREE_QE,
 77	)
 78	return p.qeAPI.DivExtension(
 79		evalZeroPoly,
 80		denominator,
 81	)
 82}
 83
 84func (p *PlonkChip) checkPartialProducts(
 85	numerators []QuadraticExtension,
 86	denominators []QuadraticExtension,
 87	challengeNum uint64,
 88	openings OpeningSet,
 89) []QuadraticExtension {
 90	numPartProds := p.commonData.NumPartialProducts
 91	quotDegreeFactor := p.commonData.QuotientDegreeFactor
 92
 93	productAccs := make([]QuadraticExtension, 0, numPartProds+2)
 94	productAccs = append(productAccs, openings.PlonkZs[challengeNum])
 95	productAccs = append(productAccs, openings.PartialProducts[challengeNum*numPartProds:(challengeNum+1)*numPartProds]...)
 96	productAccs = append(productAccs, openings.PlonkZsNext[challengeNum])
 97
 98	partialProductChecks := make([]QuadraticExtension, 0, numPartProds)
 99
100	for i := uint64(0); i <= numPartProds; i += 1 {
101		ppStartIdx := i * quotDegreeFactor
102		numeProduct := numerators[ppStartIdx]
103		denoProduct := denominators[ppStartIdx]
104		for j := uint64(1); j < quotDegreeFactor; j++ {
105			numeProduct = p.qeAPI.MulExtension(numeProduct, numerators[ppStartIdx+j])
106			denoProduct = p.qeAPI.MulExtension(denoProduct, denominators[ppStartIdx+j])
107		}
108
109		partialProductCheck := p.qeAPI.SubExtension(
110			p.qeAPI.MulExtension(productAccs[i], numeProduct),
111			p.qeAPI.MulExtension(productAccs[i+1], denoProduct),
112		)
113
114		partialProductChecks = append(partialProductChecks, partialProductCheck)
115	}
116	return partialProductChecks
117}
118
119func (p *PlonkChip) evalVanishingPoly(proofChallenges ProofChallenges, openings OpeningSet, zetaPowN QuadraticExtension) []QuadraticExtension {
120	// Calculate the k[i] * x
121	sIDs := make([]QuadraticExtension, p.commonData.Config.NumRoutedWires)
122
123	for i := uint64(0); i < p.commonData.Config.NumRoutedWires; i++ {
124		sIDs[i] = p.qeAPI.ScalarMulExtension(proofChallenges.PlonkZeta, p.commonData.KIs[i])
125	}
126
127	// Calculate L_0(zeta)
128	l0Zeta := p.evalL0(proofChallenges.PlonkZeta, zetaPowN)
129
130	vanishingZ1Terms := make([]QuadraticExtension, 0, p.commonData.Config.NumChallenges)
131	vanishingPartialProductsTerms := make([]QuadraticExtension, 0, p.commonData.Config.NumChallenges*p.commonData.NumPartialProducts)
132	for i := uint64(0); i < p.commonData.Config.NumChallenges; i++ {
133		// L_0(zeta) (Z(zeta) - 1) = 0
134		z1_term := p.qeAPI.MulExtension(
135			l0Zeta,
136			p.qeAPI.SubExtension(openings.PlonkZs[i], p.qeAPI.ONE_QE))
137		vanishingZ1Terms = append(vanishingZ1Terms, z1_term)
138
139		numeratorValues := make([]QuadraticExtension, 0, p.commonData.Config.NumRoutedWires)
140		denominatorValues := make([]QuadraticExtension, 0, p.commonData.Config.NumRoutedWires)
141		for j := uint64(0); j < p.commonData.Config.NumRoutedWires; j++ {
142			// The numerator is `beta * s_id + wire_value + gamma`, and the denominator is
143			// `beta * s_sigma + wire_value + gamma`.
144
145			wireValuePlusGamma := p.qeAPI.AddExtension(
146				openings.Wires[j],
147				p.qeAPI.FieldToQE(proofChallenges.PlonkGammas[i]),
148			)
149
150			numerator := p.qeAPI.AddExtension(
151				p.qeAPI.MulExtension(
152					p.qeAPI.FieldToQE(proofChallenges.PlonkBetas[i]),
153					sIDs[j],
154				),
155				wireValuePlusGamma,
156			)
157
158			denominator := p.qeAPI.AddExtension(
159				p.qeAPI.MulExtension(
160					p.qeAPI.FieldToQE(proofChallenges.PlonkBetas[i]),
161					openings.PlonkSigmas[j],
162				),
163				wireValuePlusGamma,
164			)
165
166			numeratorValues = append(numeratorValues, numerator)
167			denominatorValues = append(denominatorValues, denominator)
168		}
169
170		vanishingPartialProductsTerms = append(
171			vanishingPartialProductsTerms,
172			p.checkPartialProducts(numeratorValues, denominatorValues, i, openings)...,
173		)
174	}
175
176	vanishingTerms := append(vanishingZ1Terms, vanishingPartialProductsTerms...)
177	vanishingTerms = append(vanishingTerms, []QuadraticExtension{p.qeAPI.ZERO_QE, p.qeAPI.ZERO_QE, p.qeAPI.ZERO_QE, p.qeAPI.ZERO_QE}...)
178
179	reducedValues := make([]QuadraticExtension, p.commonData.Config.NumChallenges)
180	for i := uint64(0); i < p.commonData.Config.NumChallenges; i++ {
181		reducedValues[i] = p.qeAPI.ZERO_QE
182	}
183
184	// reverse iterate the vanishingPartialProductsTerms array
185	for i := len(vanishingTerms) - 1; i >= 0; i-- {
186		for j := uint64(0); j < p.commonData.Config.NumChallenges; j++ {
187			reducedValues[j] = p.qeAPI.AddExtension(
188				vanishingTerms[i],
189				p.qeAPI.ScalarMulExtension(
190					reducedValues[j],
191					proofChallenges.PlonkAlphas[j],
192				),
193			)
194		}
195	}
196
197	return reducedValues
198}
199
200func (p *PlonkChip) Verify(proofChallenges ProofChallenges, openings OpeningSet) {
201	// Calculate zeta^n
202	zetaPowN := p.expPowerOf2Extension(proofChallenges.PlonkZeta)
203
204	vanishingPolysZeta := p.evalVanishingPoly(proofChallenges, openings, zetaPowN)
205
206	// Calculate Z(H)
207	zHZeta := p.qeAPI.SubExtension(zetaPowN, p.qeAPI.ONE_QE)
208
209	// `quotient_polys_zeta` holds `num_challenges * quotient_degree_factor` evaluations.
210	// Each chunk of `quotient_degree_factor` holds the evaluations of `t_0(zeta),...,t_{quotient_degree_factor-1}(zeta)`
211	// where the "real" quotient polynomial is `t(X) = t_0(X) + t_1(X)*X^n + t_2(X)*X^{2n} + ...`.
212	// So to reconstruct `t(zeta)` we can compute `reduce_with_powers(chunk, zeta^n)` for each
213	// `quotient_degree_factor`-sized chunk of the original evaluations.
214	for i := 0; i < len(vanishingPolysZeta); i++ {
215		quotientPolysStartIdx := i * int(p.commonData.QuotientDegreeFactor)
216		quotientPolysEndIdx := quotientPolysStartIdx + int(p.commonData.QuotientDegreeFactor)
217		prod := p.qeAPI.MulExtension(
218			zHZeta,
219			p.qeAPI.ReduceWithPowers(
220				openings.QuotientPolys[quotientPolysStartIdx:quotientPolysEndIdx],
221				zetaPowN,
222			),
223		)
224
225		p.qeAPI.AssertIsEqual(vanishingPolysZeta[i], prod)
226	}
227}