gnark-plonky2-verifier/fri/fri.go
fri/fri.goRaw
1package fri
2
3import (
4 "fmt"
5 "math"
6 "math/big"
7 "math/bits"
8
9 "github.com/consensys/gnark-crypto/field/goldilocks"
10 "github.com/consensys/gnark/frontend"
11 gl "github.com/succinctlabs/gnark-plonky2-verifier/goldilocks"
12 "github.com/succinctlabs/gnark-plonky2-verifier/poseidon"
13 "github.com/succinctlabs/gnark-plonky2-verifier/types"
14 "github.com/succinctlabs/gnark-plonky2-verifier/variables"
15)
16
17type Chip struct {
18 api frontend.API `gnark:"-"`
19 gl gl.Chip `gnark:"-"`
20 poseidonBN254Chip *poseidon.BN254Chip `gnark:"-"`
21 commonData *types.CommonCircuitData `gnark:"-"`
22 friParams *types.FriParams `gnark:"-"`
23}
24
25func NewChip(
26 api frontend.API,
27 commonData *types.CommonCircuitData,
28 friParams *types.FriParams,
29) *Chip {
30 poseidonBN254Chip := poseidon.NewBN254Chip(api)
31 return &Chip{
32 api: api,
33 poseidonBN254Chip: poseidonBN254Chip,
34 commonData: commonData,
35 friParams: friParams,
36 gl: *gl.New(api),
37 }
38}
39
40func (f *Chip) GetInstance(zeta gl.QuadraticExtensionVariable) InstanceInfo {
41 zetaBatch := BatchInfo{
42 Point: zeta,
43 Polynomials: friAllPolys(f.commonData),
44 }
45
46 g := gl.PrimitiveRootOfUnity(f.commonData.DegreeBits)
47 zetaNext := f.gl.MulExtension(
48 gl.NewVariable(g.Uint64()).ToQuadraticExtension(),
49 zeta,
50 )
51
52 zetaNextBath := BatchInfo{
53 Point: zetaNext,
54 Polynomials: friZSPolys(f.commonData),
55 }
56
57 return InstanceInfo{
58 Oracles: friOracles(f.commonData),
59 Batches: []BatchInfo{zetaBatch, zetaNextBath},
60 }
61}
62
63func (f *Chip) ToOpenings(c variables.OpeningSet) Openings {
64 values := c.Constants // num_constants + 1
65 values = append(values, c.PlonkSigmas...) // num_routed_wires
66 values = append(values, c.Wires...) // num_wires
67 values = append(values, c.PlonkZs...) // num_challenges
68 values = append(values, c.PartialProducts...) // num_challenges * num_partial_products
69 values = append(values, c.QuotientPolys...) // num_challenges * quotient_degree_factor
70 zetaBatch := OpeningBatch{Values: values}
71 zetaNextBatch := OpeningBatch{Values: c.PlonkZsNext}
72 return Openings{Batches: []OpeningBatch{zetaBatch, zetaNextBatch}}
73}
74
75func (f *Chip) assertLeadingZeros(powWitness gl.Variable, friConfig types.FriConfig) {
76 // Asserts that powWitness'es big-endian bit representation has at least `leading_zeros` leading zeros.
77 // Note that this is assuming that the Goldilocks field is being used. Specfically that the
78 // field is 64 bits long
79 maxPowWitness := uint64(math.Pow(2, float64(64-friConfig.ProofOfWorkBits))) - 1
80 reducedPowWitness := f.gl.Reduce(powWitness)
81 f.api.AssertIsLessOrEqual(reducedPowWitness.Limb, frontend.Variable(maxPowWitness))
82}
83
84func (f *Chip) fromOpeningsAndAlpha(
85 openings *Openings,
86 alpha gl.QuadraticExtensionVariable,
87) []gl.QuadraticExtensionVariable {
88 // One reduced opening for all openings evaluated at point Zeta.
89 // Another one for all openings evaluated at point Zeta * Omega (which is only PlonkZsNext polynomial)
90
91 reducedOpenings := make([]gl.QuadraticExtensionVariable, 0, 2)
92 for _, batch := range openings.Batches {
93 reducedOpenings = append(reducedOpenings, f.gl.ReduceWithPowers(batch.Values, alpha))
94 }
95
96 return reducedOpenings
97}
98
99func (f *Chip) verifyMerkleProofToCapWithCapIndex(
100 leafData []gl.Variable,
101 leafIndexBits []frontend.Variable,
102 capIndexBits []frontend.Variable,
103 merkleCap variables.FriMerkleCap,
104 proof *variables.FriMerkleProof,
105) {
106 currentDigest := f.poseidonBN254Chip.HashOrNoop(leafData)
107 for i, sibling := range proof.Siblings {
108 bit := leafIndexBits[i]
109
110 var inputs poseidon.BN254State
111 inputs[0] = frontend.Variable(0)
112 inputs[1] = frontend.Variable(0)
113 inputs[2] = f.api.Select(bit, sibling, currentDigest)
114 inputs[3] = f.api.Select(bit, currentDigest, sibling)
115 state := f.poseidonBN254Chip.Poseidon(inputs)
116
117 currentDigest = state[0]
118 }
119
120 // We assume that the cap_height is 4. Create two levels of the Lookup2 circuit
121 if len(capIndexBits) != 4 || len(merkleCap) != 16 {
122 errorMsg, _ := fmt.Printf(
123 "capIndexBits length should be 4 and the merkleCap length should be 16. Actual values (capIndexBits: %d, merkleCap: %d)\n",
124 len(capIndexBits),
125 len(merkleCap),
126 )
127 panic(errorMsg)
128 }
129
130 const NUM_LEAF_LOOKUPS = 4
131 var leafLookups [NUM_LEAF_LOOKUPS]poseidon.BN254HashOut
132 // First create the "leaf" lookup2 circuits
133 // The will use the least significant bits of the capIndexBits array
134 for i := 0; i < NUM_LEAF_LOOKUPS; i++ {
135 leafLookups[i] = f.api.Lookup2(
136 capIndexBits[0], capIndexBits[1],
137 merkleCap[i*NUM_LEAF_LOOKUPS], merkleCap[i*NUM_LEAF_LOOKUPS+1], merkleCap[i*NUM_LEAF_LOOKUPS+2], merkleCap[i*NUM_LEAF_LOOKUPS+3],
138 )
139 }
140
141 // Use the most 2 significant bits of the capIndexBits array for the "root" lookup
142 merkleCapEntry := f.api.Lookup2(capIndexBits[2], capIndexBits[3], leafLookups[0], leafLookups[1], leafLookups[2], leafLookups[3])
143 f.api.AssertIsEqual(currentDigest, merkleCapEntry)
144}
145
146func (f *Chip) verifyInitialProof(xIndexBits []frontend.Variable, proof *variables.FriInitialTreeProof, initialMerkleCaps []variables.FriMerkleCap, capIndexBits []frontend.Variable) {
147 if len(proof.EvalsProofs) != len(initialMerkleCaps) {
148 panic("length of eval proofs in fri proof should equal length of initial merkle caps")
149 }
150
151 for i := 0; i < len(initialMerkleCaps); i++ {
152 evals := proof.EvalsProofs[i].Elements
153 merkleProof := proof.EvalsProofs[i].MerkleProof
154 cap := initialMerkleCaps[i]
155 f.verifyMerkleProofToCapWithCapIndex(evals, xIndexBits, capIndexBits, cap, &merkleProof)
156 }
157}
158
159func (f *Chip) expFromBitsConstBase(
160 base goldilocks.Element,
161 exponentBits []frontend.Variable,
162) gl.Variable {
163 product := gl.One()
164 for i, bit := range exponentBits {
165 // If the bit is on, we multiply product by base^pow.
166 // We can arithmetize this as:
167 // product *= 1 + bit (base^pow - 1)
168 // product = (base^pow - 1) product bit + product
169 pow := int64(1 << i)
170 basePow := goldilocks.NewElement(0)
171 basePow.Exp(base, big.NewInt(pow))
172 basePowVariable := gl.NewVariable(basePow.Uint64() - 1)
173 product = f.gl.Add(
174 f.gl.Mul(
175 f.gl.Mul(
176 basePowVariable,
177 product,
178 ),
179 gl.NewVariable(bit),
180 ),
181 product,
182 )
183 }
184 return product
185}
186
187func (f *Chip) calculateSubgroupX(
188 xIndexBits []frontend.Variable,
189 nLog uint64,
190) gl.Variable {
191 // Compute x from its index
192 // `subgroup_x` is `subgroup[x_index]`, i.e., the actual field element in the domain.
193 // OPTIMIZE - Make these as global values
194 g := gl.NewVariable(gl.MULTIPLICATIVE_GROUP_GENERATOR.Uint64())
195 base := gl.PrimitiveRootOfUnity(nLog)
196
197 // Create a reverse list of xIndexBits
198 xIndexBitsRev := make([]frontend.Variable, 0)
199 for i := len(xIndexBits) - 1; i >= 0; i-- {
200 xIndexBitsRev = append(xIndexBitsRev, xIndexBits[i])
201 }
202
203 product := f.expFromBitsConstBase(base, xIndexBitsRev)
204
205 return f.gl.Mul(g, product)
206}
207
208func (f *Chip) friCombineInitial(
209 instance InstanceInfo,
210 proof variables.FriInitialTreeProof,
211 friAlpha gl.QuadraticExtensionVariable,
212 subgroupX_QE gl.QuadraticExtensionVariable,
213 precomputedReducedEval []gl.QuadraticExtensionVariable,
214) gl.QuadraticExtensionVariable {
215 sum := gl.ZeroExtension()
216
217 if len(instance.Batches) != len(precomputedReducedEval) {
218 panic("len(openings) != len(precomputedReducedEval)")
219 }
220
221 for i := 0; i < len(instance.Batches); i++ {
222 batch := instance.Batches[i]
223 reducedOpenings := precomputedReducedEval[i]
224
225 point := batch.Point
226 evals := make([]gl.QuadraticExtensionVariable, 0)
227 for _, polynomial := range batch.Polynomials {
228 evals = append(
229 evals,
230 gl.QuadraticExtensionVariable{
231 proof.EvalsProofs[polynomial.OracleIndex].Elements[polynomial.PolynomialInfo],
232 gl.Zero(),
233 },
234 )
235 }
236
237 reducedEvals := f.gl.ReduceWithPowers(evals, friAlpha)
238 numerator := f.gl.SubExtensionNoReduce(reducedEvals, reducedOpenings)
239 denominator := f.gl.SubExtension(subgroupX_QE, point)
240 sum = f.gl.MulExtension(f.gl.ExpExtension(friAlpha, uint64(len(evals))), sum)
241 inv, hasInv := f.gl.InverseExtension(denominator)
242 f.api.AssertIsEqual(hasInv, frontend.Variable(1))
243 sum = f.gl.MulAddExtension(
244 numerator,
245 inv,
246 sum,
247 )
248 }
249
250 return sum
251}
252
253func (f *Chip) finalPolyEval(finalPoly variables.PolynomialCoeffs, point gl.QuadraticExtensionVariable) gl.QuadraticExtensionVariable {
254 ret := gl.ZeroExtension()
255 for i := len(finalPoly.Coeffs) - 1; i >= 0; i-- {
256 ret = f.gl.MulAddExtension(ret, point, finalPoly.Coeffs[i])
257 }
258 return ret
259}
260
261func (f *Chip) interpolate(
262 x gl.QuadraticExtensionVariable,
263 xPoints []gl.QuadraticExtensionVariable,
264 yPoints []gl.QuadraticExtensionVariable,
265 barycentricWeights []gl.QuadraticExtensionVariable,
266) gl.QuadraticExtensionVariable {
267 if len(xPoints) != len(yPoints) || len(xPoints) != len(barycentricWeights) {
268 panic("length of xPoints, yPoints, and barycentricWeights are inconsistent")
269 }
270
271 lX := gl.OneExtension()
272 for i := 0; i < len(xPoints); i++ {
273 lX = f.gl.SubMulExtension(x, xPoints[i], lX)
274 }
275
276 sum := gl.ZeroExtension()
277
278 lookupFromPoints := frontend.Variable(1)
279 for i := 0; i < len(xPoints); i++ {
280 quotient, hasQuotient := f.gl.DivExtension(
281 barycentricWeights[i],
282 f.gl.SubExtension(
283 x,
284 xPoints[i],
285 ),
286 )
287
288 lookupFromPoints = f.api.Mul(hasQuotient, lookupFromPoints)
289
290 sum = f.gl.AddExtension(
291 f.gl.MulExtension(
292 yPoints[i],
293 quotient,
294 ),
295 sum,
296 )
297 }
298
299 interpolation := f.gl.MulExtension(lX, sum)
300
301 lookupVal := gl.ZeroExtension()
302 // Now check if x is already within the xPoints
303 for i := 0; i < len(xPoints); i++ {
304 lookupVal = f.gl.Lookup(
305 f.gl.IsZero(f.gl.SubExtension(x, xPoints[i])),
306 lookupVal,
307 yPoints[i],
308 )
309 }
310
311 return f.gl.Lookup(lookupFromPoints, lookupVal, interpolation)
312}
313
314func (f *Chip) computeEvaluation(
315 x gl.Variable,
316 xIndexWithinCosetBits []frontend.Variable,
317 arityBits uint64,
318 evals []gl.QuadraticExtensionVariable,
319 beta gl.QuadraticExtensionVariable,
320) gl.QuadraticExtensionVariable {
321 arity := 1 << arityBits
322 if (len(evals)) != arity {
323 panic("len(evals) ! arity")
324 }
325 if arityBits > 8 {
326 panic("currently assuming that arityBits is <= 8")
327 }
328
329 g := gl.PrimitiveRootOfUnity(arityBits)
330 gInv := goldilocks.NewElement(0)
331 gInv.Exp(g, big.NewInt(int64(arity-1)))
332
333 // The evaluation vector needs to be reordered first. Permute the evals array such that each
334 // element's new index is the bit reverse of it's original index.
335 // OPTIMIZE - Since the size of the evals array should be constant (e.g. 2^arityBits),
336 // we can just hard code the permutation.
337 permutedEvals := make([]gl.QuadraticExtensionVariable, len(evals))
338 for i := uint8(0); i < uint8(len(evals)); i++ {
339 newIndex := bits.Reverse8(i) >> arityBits
340 permutedEvals[newIndex] = evals[i]
341 }
342
343 // Want `g^(arity - rev_x_index_within_coset)` as in the out-of-circuit version. Compute it
344 // as `(g^-1)^rev_x_index_within_coset`.
345 revXIndexWithinCosetBits := make([]frontend.Variable, len(xIndexWithinCosetBits))
346 for i := 0; i < len(xIndexWithinCosetBits); i++ {
347 revXIndexWithinCosetBits[len(xIndexWithinCosetBits)-1-i] = xIndexWithinCosetBits[i]
348 }
349 start := f.expFromBitsConstBase(gInv, revXIndexWithinCosetBits)
350 cosetStart := f.gl.Mul(start, x)
351
352 xPoints := make([]gl.QuadraticExtensionVariable, len(evals))
353 yPoints := permutedEvals
354
355 // OPTIMIZE: Make g_F a constant
356 g_F := gl.NewVariable(g.Uint64()).ToQuadraticExtension()
357 xPoints[0] = gl.QuadraticExtensionVariable{cosetStart, gl.Zero()}
358 for i := 1; i < len(evals); i++ {
359 xPoints[i] = f.gl.MulExtension(xPoints[i-1], g_F)
360 }
361
362 // OPTIMIZE: This is n^2. Is there a way to do this better?
363 // Compute the barycentric weights
364 barycentricWeights := make([]gl.QuadraticExtensionVariable, len(xPoints))
365 for i := 0; i < len(xPoints); i++ {
366 barycentricWeights[i] = gl.OneExtension()
367 for j := 0; j < len(xPoints); j++ {
368 if i != j {
369 barycentricWeights[i] = f.gl.SubMulExtension(
370 xPoints[i],
371 xPoints[j],
372 barycentricWeights[i],
373 )
374 }
375 }
376 // Take the inverse of the barycentric weights
377 // OPTIMIZE: Can provide a witness to this value
378 inv, hasInv := f.gl.InverseExtension(barycentricWeights[i])
379 f.api.AssertIsEqual(hasInv, frontend.Variable(1))
380 barycentricWeights[i] = inv
381 }
382
383 return f.interpolate(beta, xPoints, yPoints, barycentricWeights)
384}
385
386func (f *Chip) verifyQueryRound(
387 instance InstanceInfo,
388 challenges *variables.FriChallenges,
389 precomputedReducedEval []gl.QuadraticExtensionVariable,
390 initialMerkleCaps []variables.FriMerkleCap,
391 proof *variables.FriProof,
392 xIndex gl.Variable,
393 n uint64,
394 nLog uint64,
395 roundProof *variables.FriQueryRound,
396) {
397 // Note assertNoncanonicalIndicesOK does not add any constraints, it's a sanity check on the config
398 assertNoncanonicalIndicesOK(*f.friParams)
399
400 xIndex = f.gl.Reduce(xIndex)
401 xIndexBits := f.api.ToBinary(xIndex.Limb, 64)[0 : f.friParams.DegreeBits+f.friParams.Config.RateBits]
402 capIndexBits := xIndexBits[len(xIndexBits)-int(f.friParams.Config.CapHeight):]
403
404 f.verifyInitialProof(xIndexBits, &roundProof.InitialTreesProof, initialMerkleCaps, capIndexBits)
405
406 subgroupX := f.calculateSubgroupX(
407 xIndexBits,
408 nLog,
409 )
410
411 subgroupX_QE := subgroupX.ToQuadraticExtension()
412
413 oldEval := f.friCombineInitial(
414 instance,
415 roundProof.InitialTreesProof,
416 challenges.FriAlpha,
417 subgroupX_QE,
418 precomputedReducedEval,
419 )
420
421 for i, arityBits := range f.friParams.ReductionArityBits {
422 evals := roundProof.Steps[i].Evals
423
424 cosetIndexBits := xIndexBits[arityBits:]
425 xIndexWithinCosetBits := xIndexBits[:arityBits]
426
427 // Assumes that the arity bits will be 4. That means that the range of
428 // xIndexWithCoset is [0,2^4-1]. This is based on plonky2's circuit recursive
429 // config: https://github.com/mir-protocol/plonky2/blob/main/plonky2/src/plonk/circuit_data.rs#L63
430 // Will use a two levels tree of 4-selector gadgets.
431 if arityBits != 4 {
432 panic("assuming arity bits is 4")
433 }
434
435 const NUM_LEAF_LOOKUPS = 4
436 var leafLookups [NUM_LEAF_LOOKUPS]gl.QuadraticExtensionVariable
437 // First create the "leaf" lookup2 circuits
438 // The will use the least significant bits of the xIndexWithCosetBits array
439 for i := 0; i < NUM_LEAF_LOOKUPS; i++ {
440 leafLookups[i] = f.gl.Lookup2(
441 xIndexWithinCosetBits[0],
442 xIndexWithinCosetBits[1],
443 evals[i*NUM_LEAF_LOOKUPS],
444 evals[i*NUM_LEAF_LOOKUPS+1],
445 evals[i*NUM_LEAF_LOOKUPS+2],
446 evals[i*NUM_LEAF_LOOKUPS+3],
447 )
448 }
449
450 // Use the most 2 significant bits of the xIndexWithCosetBits array for the "root" lookup
451 newEval := f.gl.Lookup2(
452 xIndexWithinCosetBits[2],
453 xIndexWithinCosetBits[3],
454 leafLookups[0],
455 leafLookups[1],
456 leafLookups[2],
457 leafLookups[3],
458 )
459
460 f.gl.AssertIsEqual(newEval[0], oldEval[0])
461 f.gl.AssertIsEqual(newEval[1], oldEval[1])
462
463 oldEval = f.computeEvaluation(
464 subgroupX,
465 xIndexWithinCosetBits,
466 arityBits,
467 evals,
468 challenges.FriBetas[i],
469 )
470
471 // Convert evals (array of QE) to fields by taking their 0th degree coefficients
472 fieldEvals := make([]gl.Variable, 0, 2*len(evals))
473 for j := 0; j < len(evals); j++ {
474 fieldEvals = append(fieldEvals, evals[j][0])
475 fieldEvals = append(fieldEvals, evals[j][1])
476 }
477 f.verifyMerkleProofToCapWithCapIndex(
478 fieldEvals,
479 cosetIndexBits,
480 capIndexBits,
481 proof.CommitPhaseMerkleCaps[i],
482 &roundProof.Steps[i].MerkleProof,
483 )
484
485 // Update the point x to x^arity.
486 for j := uint64(0); j < arityBits; j++ {
487 subgroupX = f.gl.Mul(subgroupX, subgroupX)
488 }
489
490 xIndexBits = cosetIndexBits
491 }
492
493 subgroupX_QE = subgroupX.ToQuadraticExtension()
494 finalPolyEval := f.finalPolyEval(proof.FinalPoly, subgroupX_QE)
495
496 f.gl.AssertIsEqual(oldEval[0], finalPolyEval[0])
497 f.gl.AssertIsEqual(oldEval[1], finalPolyEval[1])
498}
499
500func (f *Chip) VerifyFriProof(
501 instance InstanceInfo,
502 openings Openings,
503 friChallenges *variables.FriChallenges,
504 initialMerkleCaps []variables.FriMerkleCap,
505 friProof *variables.FriProof,
506) {
507 // Not adding any constraints but a sanity check on the proof shape matching the friParams (constant).
508 validateFriProofShape(friProof, instance, f.friParams)
509
510 // Check POW
511 f.assertLeadingZeros(friChallenges.FriPowResponse, f.friParams.Config)
512
513 // Check that parameters are coherent. Not adding any constraints but a sanity check
514 // on the proof shape matching the friParams.
515 if int(f.friParams.Config.NumQueryRounds) != len(friProof.QueryRoundProofs) {
516 panic("Number of query rounds does not match config.")
517 }
518
519 precomputedReducedEvals := f.fromOpeningsAndAlpha(&openings, friChallenges.FriAlpha)
520
521 // Size of the LDE domain.
522 nLog := f.friParams.DegreeBits + f.friParams.Config.RateBits
523 n := uint64(math.Pow(2, float64(nLog)))
524
525 if len(friChallenges.FriQueryIndices) != len(friProof.QueryRoundProofs) {
526 panic(fmt.Sprintf(
527 "Number of query indices (%d) should equal number of query round proofs (%d)",
528 len(friChallenges.FriQueryIndices),
529 len(friProof.QueryRoundProofs),
530 ))
531 }
532
533 for idx, xIndex := range friChallenges.FriQueryIndices {
534 roundProof := friProof.QueryRoundProofs[idx]
535
536 f.verifyQueryRound(
537 instance,
538 friChallenges,
539 precomputedReducedEvals,
540 initialMerkleCaps,
541 friProof,
542 xIndex,
543 n,
544 nLog,
545 &roundProof,
546 )
547 }
548}