# Public domain.

import sys
import random
import signatures
import doublescalarmult

def multiscalarmult(scalars,points):
  while True:
    maxscalarpos = 0
    for i in range(len(scalars)):
      if scalars[i] > scalars[maxscalarpos]:
        maxscalarpos = i
    secondscalarpos = 0
    if secondscalarpos == maxscalarpos: secondscalarpos = 1
    for i in range(len(scalars)):
      if i != maxscalarpos:
        if scalars[i] > scalars[secondscalarpos]:
          secondscalarpos = i
    if scalars[secondscalarpos] == 0:
      return points[maxscalarpos] * scalars[maxscalarpos]
    points[secondscalarpos] += points[maxscalarpos]
    scalars[maxscalarpos] -= scalars[secondscalarpos]

def verifybatch(smvector):
  results = []
  randomizers = [random.randrange(2**signatures.b) for i in range(len(smvector))]

  points = [signatures.B]
  scalars = [0]
  for i in range(len(smvector)):
    sm = smvector[i]
    R,S,A,M = sm[0],sm[1],sm[2],sm[3]
    h = signatures.inthash(str(R) + str(A) + M)
    points.append(signatures.groupelt(R))
    scalars.append(randomizers[i])
    points.append(signatures.groupelt(A))
    scalars.append((h * randomizers[i]) % signatures.l)
    scalars[0] = (scalars[0] - S * randomizers[i]) % signatures.l

  if multiscalarmult(scalars,points).x == 0:
    return [True] * len(smvector)

  for sm in smvector:
    R,S,A,M = sm[0],sm[1],sm[2],sm[3]
    h = signatures.inthash(str(R) + str(A) + M)
    checkR = doublescalarmult.doublescalarmult(S,signatures.B,(-h) % signatures.l,signatures.groupelt(A))
    results.append(R == checkR.x)
  return results

signatures.benchmark(verifybatch,int(sys.argv[1]))