# Public domain.

import sys
import random
import signatures
import doublescalarmult

c = 5
twoc = 2**c
# XXX: tune c and twoc for b

def digits(n):
  result = []
  while n != 0:
    nk = n % twoc
    n /= twoc
    if nk + nk >= twoc:
      nk -= twoc
      n += 1
    result.append(nk)
  return result

def multiscalarmult(scalars,points):
  s = [digits(n) for n in scalars]
  words = max([len(d) for d in s])

  needmultiples = [0] * len(scalars)
  for j in range(len(scalars)):
    for i in range(len(s[j])):
      if s[j][i] > needmultiples[j]:
        needmultiples[j] = s[j][i]
      if -s[j][i] > needmultiples[j]:
        needmultiples[j] = -s[j][i]

  multiples = [False,points]
  for i in range(2,2**c):
    newmultiples = [i <= needmultiples[j] and points[j] + multiples[i - 1][j] for j in range(len(points))]
    multiples.append(newmultiples)

  result = signatures.groupelt(0)
  for i in reversed(range(words)):
    for j in range(c):
      result = result + result
    for j in range(len(scalars)):
      if len(s[j]) > i:
        digit = s[j][i]
        if digit > 0:
          result = result + multiples[digit][j]
        elif digit < 0:
          result = result - multiples[-digit][j]
  return result

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]))