plonkfri

type Proof struct {

	// commitments to the solution vectors
	LROpp [3]fri.ProofOfProximity

	// commitment to Z (permutation polynomial)
	// Z   Commitment
	Zpp fri.ProofOfProximity

	// commitment to h1,h2,h3 such that h = h1 + X**n*h2 + X**2nh3 the quotient polynomial
	Hpp [3]fri.ProofOfProximity

	// opening proofs for L, R, O
	OpeningsLROmp [3]fri.OpeningProof

	// opening proofs for Z, Zu
	OpeningsZmp [2]fri.OpeningProof

	// opening proof for H
	OpeningsHmp [3]fri.OpeningProof

	// opening proofs for ql, qr, qm, qo, qk
	OpeningsQlQrQmQoQkincompletemp [5]fri.OpeningProof

	// openings of S1, S2, S3
	// OpeningsS1S2S3   [3]OpeningProof
	OpeningsS1S2S3mp [3]fri.OpeningProof

	// openings of Id1, Id2, Id3
	OpeningsId1Id2Id3mp [3]fri.OpeningProof
}

type ProvingKey struct {

	// Verifying Key is embedded into the proving key (needed by Prove)
	Vk *VerifyingKey

	// qr,ql,qm,qo and Qk incomplete (Ls=Lagrange basis big domain, L=Lagrange basis small domain, C=canonical basis)
	EvaluationQlDomainBigBitReversed  []fr.Element
	EvaluationQrDomainBigBitReversed  []fr.Element
	EvaluationQmDomainBigBitReversed  []fr.Element
	EvaluationQoDomainBigBitReversed  []fr.Element
	LQkIncompleteDomainSmall          []fr.Element
	CQl, CQr, CQm, CQo, CQkIncomplete []fr.Element

	// Domains used for the FFTs
	// 0 -> "small" domain, used for individual polynomials
	// 1 -> "big" domain, used for the computation of the quotient
	Domain [2]fft.Domain

	// s1, s2, s3 (L=Lagrange basis small domain, C=canonical basis, Ls=Lagrange Shifted big domain)
	LId                                                                    []fr.Element
	EvaluationId1BigDomain, EvaluationId2BigDomain, EvaluationId3BigDomain []fr.Element
	EvaluationS1BigDomain, EvaluationS2BigDomain, EvaluationS3BigDomain    []fr.Element

	// position -> permuted position (position in [0,3*sizeSystem-1])
	Permutation []int64
}

type VerifyingKey struct {

	// Size circuit, that is the closest power of 2 bounding above
	// number of constraints+number of public inputs
	Size              uint64
	SizeInv           fr.Element
	Generator         fr.Element
	NbPublicVariables uint64

	// cosetShift generator of the coset on the small domain
	CosetShift fr.Element

	// S commitments to S1, S2, S3
	SCanonical [3][]fr.Element
	Spp        [3]fri.ProofOfProximity

	// Id commitments to Id1, Id2, Id3
	// Id   [3]Commitment
	IdCanonical [3][]fr.Element
	Idpp        [3]fri.ProofOfProximity

	// Commitments to ql, qr, qm, qo prepended with as many zeroes (ones for l) as there are public inputs.
	// In particular Qk is not complete.
	Qpp [5]fri.ProofOfProximity // Ql, Qr, Qm, Qo, Qk

	// Iopp scheme (currently one for each size of polynomial)
	Iopp fri.Iopp

	// generator of the group on which the Iopp works. If i is the opening position,
	// the polynomials will be opened at genOpening^{i}.
	GenOpening fr.Element
}