nim-groth16/groth16/prover.nim
2024-03-02 16:44:54 -07:00

298 lines
9.4 KiB
Nim

#
# Groth16 prover
#
# WARNING!
# the points H in `.zkey` are *NOT* what normal people would think they are
# See <https://geometry.xyz/notebook/the-hidden-little-secret-in-snarkjs>
#
#[
import sugar
import constantine/math/config/curves
import constantine/math/io/io_fields
import constantine/math/io/io_bigints
import ./zkey
]#
import std/os
import std/times
import std/cpuinfo
import system
import taskpools
import constantine/math/arithmetic except Fp, Fr
#import constantine/math/io/io_extfields except Fp12
#import constantine/math/extension_fields/towers except Fp2, Fp12
import groth16/bn128
import groth16/math/domain
import groth16/math/poly
import groth16/zkey_types
import groth16/files/witness
import groth16/misc
#-------------------------------------------------------------------------------
type
Proof* = object
publicIO* : seq[Fr]
pi_a* : G1
pi_b* : G2
pi_c* : G1
curve* : string
#-------------------------------------------------------------------------------
# Az, Bz, Cz column vectors
#
type
ABC = object
valuesAz : seq[Fr]
valuesBz : seq[Fr]
valuesCz : seq[Fr]
# computes the vectors A*z, B*z, C*z where z is the witness
func buildABC( zkey: ZKey, witness: seq[Fr] ): ABC =
let hdr: GrothHeader = zkey.header
let domSize = hdr.domainSize
var valuesAz : seq[Fr] = newSeq[Fr](domSize)
var valuesBz : seq[Fr] = newSeq[Fr](domSize)
for entry in zkey.coeffs:
case entry.matrix
of MatrixA: valuesAz[entry.row] += entry.coeff * witness[entry.col]
of MatrixB: valuesBz[entry.row] += entry.coeff * witness[entry.col]
else: raise newException(AssertionDefect, "fatal error")
var valuesCz : seq[Fr] = newSeq[Fr](domSize)
for i in 0..<domSize:
valuesCz[i] = valuesAz[i] * valuesBz[i]
return ABC( valuesAz:valuesAz, valuesBz:valuesBz, valuesCz:valuesCz )
#-------------------------------------------------------------------------------
# quotient poly
#
# interpolates A,B,C, and computes the quotient polynomial Q = (A*B - C) / Z
func computeQuotientNaive( abc: ABC ): Poly=
let n = abc.valuesAz.len
assert( abc.valuesBz.len == n )
assert( abc.valuesCz.len == n )
let D = createDomain(n)
let polyA : Poly = polyInverseNTT( abc.valuesAz , D )
let polyB : Poly = polyInverseNTT( abc.valuesBz , D )
let polyC : Poly = polyInverseNTT( abc.valuesCz , D )
let polyBig = polyMulFFT( polyA , polyB ) - polyC
var polyQ = polyDivideByVanishing(polyBig, D.domainSize)
polyQ.coeffs.add( zeroFr ) # make it a power of two
return polyQ
#---------------------------------------
# returns [ eta^i * xs[i] | i<-[0..n-1] ]
func multiplyByPowers( xs: seq[Fr], eta: Fr ): seq[Fr] =
let n = xs.len
assert(n >= 1)
var ys : seq[Fr] = newSeq[Fr](n)
ys[0] = xs[0]
if n >= 1: ys[1] = eta * xs[1]
var spow : Fr = eta
for i in 2..<n:
spow *= eta
ys[i] = spow * xs[i]
return ys
# interpolates a polynomial, shift the variable by `eta`, and compute the shifted values
func shiftEvalDomain( values: seq[Fr], D: Domain, eta: Fr ): seq[Fr] =
echo "task: abc.values: ", values[0].unsafeAddr.pointer.repr
let poly : Poly = polyInverseNTT( values , D )
let cs : seq[Fr] = poly.coeffs
var ds : seq[Fr] = multiplyByPowers( cs, eta )
return polyForwardNTT( Poly(coeffs:ds), D )
# computes the quotient polynomial Q = (A*B - C) / Z
# by computing the values on a shifted domain, and interpolating the result
# remark: Q has degree `n-2`, so it's enough to use a domain of size n
proc computeQuotientPointwise( nthreads: int, abc: ABC ): Poly =
let n = abc.valuesAz.len
assert( abc.valuesBz.len == n )
assert( abc.valuesCz.len == n )
let D = createDomain(n)
# (eta*omega^j)^n - 1 = eta^n - 1
# 1 / [ (eta*omega^j)^n - 1] = 1/(eta^n - 1)
let eta = createDomain(2*n).domainGen
let invZ1 = invFr( smallPowFr(eta,n) - oneFr )
var pool = Taskpool.new(num_threads = nthreads)
echo "main: abc.valuesAz: ", abc.valuesAz[0].unsafeAddr.pointer.repr
echo "main: abc.valuesBz: ", abc.valuesBz[0].unsafeAddr.pointer.repr
echo "main: abc.valuesCz: ", abc.valuesCz[0].unsafeAddr.pointer.repr
var A1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesAz, D, eta )
var B1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesBz, D, eta )
var C1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesCz, D, eta )
pool.syncAll()
let A1 = sync A1fv
let B1 = sync B1fv
let C1 = sync C1fv
var ys : seq[Fr] = newSeq[Fr]( n )
for j in 0..<n: ys[j] = ( A1[j]*B1[j] - C1[j] ) * invZ1
let Q1 = polyInverseNTT( ys, D )
let cs = multiplyByPowers( Q1.coeffs, invFr(eta) )
pool.shutdown()
return Poly(coeffs: cs)
#---------------------------------------
# Snarkjs does something different, not actually computing the quotient poly
# they can get away with this, because during the trusted setup, they
# replace the points encoding the values `delta^-1 * tau^i * Z(tau)` by
# (shifted) Lagrange bases.
# see <https://geometry.xyz/notebook/the-hidden-little-secret-in-snarkjs>
#
proc computeSnarkjsScalarCoeffs( nthreads: int, abc: ABC ): seq[Fr] =
let n = abc.valuesAz.len
assert( abc.valuesBz.len == n )
assert( abc.valuesCz.len == n )
let D = createDomain(n)
let eta = createDomain(2*n).domainGen
var pool = Taskpool.new(num_threads = nthreads)
GCref(abc.valuesAz)
GCref(abc.valuesBz)
GCref(abc.valuesCz)
var A1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesAz, D, eta )
var B1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesBz, D, eta )
var C1fv : FlowVar[seq[Fr]] = pool.spawn shiftEvalDomain( abc.valuesCz, D, eta )
pool.syncAll()
GCunref(abc.valuesAz)
GCunref(abc.valuesBz)
GCunref(abc.valuesCz)
let A1 = sync A1fv
let B1 = sync B1fv
let C1 = sync C1fv
var ys : seq[Fr] = newSeq[Fr]( n )
for j in 0..<n: ys[j] = ( A1[j] * B1[j] - C1[j] )
pool.shutdown()
return ys
#-------------------------------------------------------------------------------
# the prover
#
type
Mask* = object
r*: Fr # masking coefficients
s*: Fr # for zero knowledge
proc generateProofWithMask*( nthreads: int, printTimings: bool, zkey: ZKey, wtns: Witness, mask: Mask ): Proof =
# if (zkey.header.curve != wtns.curve):
# echo( "zkey.header.curve = " & ($zkey.header.curve) )
# echo( "wtns.curve = " & ($wtns.curve ) )
assert( zkey.header.curve == wtns.curve )
var start : float = 0
let witness = wtns.values
let hdr : GrothHeader = zkey.header
let spec : SpecPoints = zkey.specPoints
let pts : ProverPoints = zkey.pPoints
let nvars = hdr.nvars
let npubs = hdr.npubs
assert( nvars == witness.len , "wrong witness length" )
# remark: with the special variable "1" we actuall have (npub+1) public IO variables
var pubIO : seq[Fr] = newSeq[Fr]( npubs + 1)
for i in 0..npubs: pubIO[i] = witness[i]
start = cpuTime()
var abc : ABC
withMeasureTime(printTimings,"building 'ABC'"):
abc = buildABC( zkey, witness )
start = cpuTime()
var qs : seq[Fr]
withMeasureTime(printTimings,"computing the quotient (FFTs)"):
case zkey.header.flavour
# the points H are [delta^-1 * tau^i * Z(tau)]
of JensGroth:
let polyQ = computeQuotientPointwise( nthreads, abc )
qs = polyQ.coeffs
# the points H are `[delta^-1 * L_{2i+1}(tau)]_1`
# where L_i are Lagrange basis polynomials on the double-sized domain
of Snarkjs:
qs = computeSnarkjsScalarCoeffs( nthreads, abc )
var zs : seq[Fr] = newSeq[Fr]( nvars - npubs - 1 )
for j in npubs+1..<nvars:
zs[j-npubs-1] = witness[j]
# masking coeffs
let r = mask.r
let s = mask.s
assert( witness.len == pts.pointsA1.len )
assert( witness.len == pts.pointsB1.len )
assert( witness.len == pts.pointsB2.len )
assert( hdr.domainSize == qs.len )
assert( hdr.domainSize == pts.pointsH1.len )
assert( nvars - npubs - 1 == zs.len )
assert( nvars - npubs - 1 == pts.pointsC1.len )
var pi_a : G1
withMeasureTime(printTimings,"computing pi_A (G1 MSM)"):
pi_a = spec.alpha1
pi_a += r ** spec.delta1
pi_a += msmMultiThreadedG1( nthreads , witness , pts.pointsA1 )
var rho : G1
withMeasureTime(printTimings,"computing rho (G1 MSM)"):
rho = spec.beta1
rho += s ** spec.delta1
rho += msmMultiThreadedG1( nthreads , witness , pts.pointsB1 )
var pi_b : G2
withMeasureTime(printTimings,"computing pi_B (G2 MSM)"):
pi_b = spec.beta2
pi_b += s ** spec.delta2
pi_b += msmMultiThreadedG2( nthreads , witness , pts.pointsB2 )
var pi_c : G1
withMeasureTime(printTimings,"computing pi_C (2x G1 MSM)"):
pi_c = s ** pi_a
pi_c += r ** rho
pi_c += negFr(r*s) ** spec.delta1
pi_c += msmMultiThreadedG1( nthreads, qs , pts.pointsH1 )
pi_c += msmMultiThreadedG1( nthreads, zs , pts.pointsC1 )
return Proof( curve:"bn128", publicIO:pubIO, pi_a:pi_a, pi_b:pi_b, pi_c:pi_c )
#-------------------------------------------------------------------------------
proc generateProofWithTrivialMask*( nthreads: int, printTimings: bool, zkey: ZKey, wtns: Witness ): Proof =
let mask = Mask(r: intToFr(0), s: intToFr(0))
return generateProofWithMask( nthreads, printTimings, zkey, wtns, mask )
proc generateProof*( nthreads: int, printTimings: bool, zkey: ZKey, wtns: Witness ): Proof =
# masking coeffs
let r : Fr = randFr()
let s : Fr = randFr()
let mask = Mask(r: r, s: s)
return generateProofWithMask( nthreads, printTimings, zkey, wtns, mask )