# randfake(m, j) = fake random number generator for interval [0, m-1],
#                  j = calling order

def randfake(m, j):
  return (127*j + 307)%m


# c2a(s) = list of ASCII codes for string s

def c2a(s):
  return [ord(j) for j in s]


# a2c(v) = string represented by list of ASCII codes v

def a2c(v):
  u = [chr(j) for j in v]
  w = join(u, "")
  return(w)


# numell(E, q=0) = number of points on elliptic curve E
#                  in finite field of size q
#
#     For now if E is tied to a finite field and q is provided, insist
#     that q is the size of the field.

def numell(E, q=0):
  En = E.base_field().order()
  if q > 0:
    if En < +Infinity:
      if q != En:
        print "Curve is attached to field of size ", En
        return(-1)
      num = E.order()
      return num
    else:
      Er = E.reduction(q)
      num = Er.order()
      return num
  else:
    if En < +Infinity:
      return E.order()
    else:
      return +Infinity


# pointstocodes(tries, ptlist) = list of ascii codes
# Subtle point: the coordinates of points in this context are integer_mods

def pointstocodes(tries, ptlist):
  codes = []
  for q in ptlist:
    t = floor( ( lift(q[0])-1 )/tries )
    codes.append(t)
  return codes

# codestopoints(curve, prime, tries, codelist)
#      = list of points on "curve" over field of "prime" elements based
#        on finding the first x-coordinate among mx+1, mx+2, mx+m

def codestopoints(curve, prime, tries, codelist):
  pts = []
  e = curve.reduction(prime)
  for c in codelist:
    flag = False
    for j in range(1, tries+1):
      x = tries*c + j
      if e.is_x_coord(x):
        ptt = e.lift_x(x)
        flag = True
        break
    if flag == True:
      if ptt.order() == 1:
        print "Origin shows up on curve for code ", c
        return []
      else:
        pt = [ptt[0], ptt[1]]
    else:
      print "Failed to find a point on curve for code ", c
      return []
    pts.append(pt)
  return pts