Makefile, ocbgen: Handle 512-bit blocks.

[ocb-tv] / ocbgen

#! /usr/bin/python
### -*-python-*-
###
### Generalization of OCB mode for other block sizes
###
### (c) 2017 Mark Wooding
###

###----- Licensing notice ---------------------------------------------------
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or
### (at your option) any later version.
###
### This program is distributed in the hope that it will be useful,
### but WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
### GNU General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software Foundation,
### Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

from sys import argv, stderr
from struct import pack
from itertools import izip
from contextlib import contextmanager
import catacomb as C

R = C.FibRand(0)

###--------------------------------------------------------------------------
### Utilities.

def combs(things, k):
  ii = range(k)
  n = len(things)
  while True:
    yield [things[i] for i in ii]
    for j in xrange(k):
      if j == k - 1: lim = n
      else: lim = ii[j + 1]
      i = ii[j] + 1
      if i < lim:
        ii[j] = i
        break
      ii[j] = j
    else:
      return

POLYMAP = {}

def poly(nbits):
  try: return POLYMAP[nbits]
  except KeyError: pass
  base = C.GF(0).setbit(nbits).setbit(0)
  for k in xrange(1, nbits, 2):
    for cc in combs(range(1, nbits), k):
      p = base + sum(C.GF(0).setbit(c) for c in cc)
      if p.irreduciblep(): POLYMAP[nbits] = p; return p
  raise ValueError, nbits

def prim(nbits):
  ## No fancy way to do this: I'd need a much cleverer factoring algorithm
  ## than I have in my pockets.
  if nbits == 64: cc = [64, 4, 3, 1, 0]
  elif nbits == 96: cc = [96, 10, 9, 6, 0]
  elif nbits == 128: cc = [128, 7, 2, 1, 0]
  elif nbits == 192: cc = [192, 15, 11, 5, 0]
  elif nbits == 256: cc = [256, 10, 5, 2, 0]
  else: raise ValueError, 'no field for %d bits' % nbits
  p = C.GF(0)
  for c in cc: p = p.setbit(c)
  return p

def Z(n):
  return C.ByteString.zero(n)

def mul_blk_gf(m, x, p): return ((C.GF.loadb(m)*x)%p).storeb((p.nbits + 6)/8)

def with_lastp(it):
  it = iter(it)
  try: j = next(it)
  except StopIteration: raise ValueError, 'empty iter'
  lastp = False
  while not lastp:
    i = j
    try: j = next(it)
    except StopIteration: lastp = True
    yield i, lastp

def safehex(x):
  if len(x): return hex(x)
  else: return '""'

def keylens(ksz):
  sel = []
  if isinstance(ksz, C.KeySZSet): kk = ksz.set
  elif isinstance(ksz, C.KeySZRange): kk = range(ksz.min, ksz.max, ksz.mod)
  elif isinstance(ksz, C.KeySZAny): kk = range(64); sel = [0]
  kk = list(kk); kk = kk[:]
  n = len(kk)
  while n and len(sel) < 4:
    i = R.range(n)
    n -= 1
    kk[i], kk[n] = kk[n], kk[i]
    sel.append(kk[n])
  return sel

def pad0star(m, w):
  n = len(m)
  if not n: r = w
  else: r = (-len(m))%w
  if r: m += Z(r)
  return C.ByteString(m)

def pad10star(m, w):
  r = w - len(m)%w
  if r: m += '\x80' + Z(r - 1)
  return C.ByteString(m)

def ntz(i):
  j = 0
  while (i&1) == 0: i >>= 1; j += 1
  return j

def blocks(x, w):
  v, i, n = [], 0, len(x)
  while n - i > w:
    v.append(C.ByteString(x[i:i + w]))
    i += w
  return v, C.ByteString(x[i:])

EMPTY = C.bytes('')

def blocks0(x, w):
  v, tl = blocks(x, w)
  if len(tl) == w: v.append(tl); tl = EMPTY
  return v, tl

###--------------------------------------------------------------------------
### Luby--Rackoff large-block ciphers.

class LubyRackoffCipher (type):
  def __new__(cls, bc, blksz):
    assert blksz%2 == 0
    assert blksz <= 2*bc.blksz
    name = '%s-lr[%d]' % (bc.name, 8*blksz)
    me = type(name, (LubyRackoffBase,), {})
    me.name = name
    me.blksz = blksz
    me.keysz = bc.keysz
    me.bc = bc
    return me

@contextmanager
def muffle():
  global VERBOSE, LRVERBOSE
  _v, _lrv = VERBOSE, LRVERBOSE
  try:
    VERBOSE = LRVERBOSE = False
    yield None
  finally:
    VERBOSE, LRVERBOSE = _v, _lrv

class LubyRackoffBase (object):
  NR = 4 # for strong-PRP security
  def __init__(me, k):
    if LRVERBOSE: print 'K = %s' % hex(k)
    bc, blksz = me.__class__.bc, me.__class__.blksz
    with muffle(): E = bc(k)
    me.f = []
    ksz = len(k)
    i = C.MP(0)
    for j in xrange(me.NR):
      b = C.WriteBuffer()
      while b.size < ksz:
        with muffle(): x = E.encrypt(i.storeb(bc.blksz))
        b.put(x)
        if LRVERBOSE: print 'E(K; [%d]) = %s' % (i, hex(x))
        i += 1
      kj = C.ByteString(C.ByteString(b)[0:ksz])
      if LRVERBOSE: print 'K_%d = %s' % (j, hex(kj))
      with muffle(): me.f.append(bc(kj))
  def encrypt(me, m):
    bc, blksz = me.__class__.bc, me.__class__.blksz
    assert len(m) == blksz
    l, r = C.ByteString(m[:blksz/2]), C.ByteString(m[blksz/2:])
    if LRVERBOSE: print 'L_0, R_0 = %s, %s' % (hex(l), hex(r))
    for j in xrange(me.NR):
      l0 = pad0star(l, bc.blksz)
      with muffle(): t = me.f[j].encrypt(l0)
      l, r = r ^ t[:blksz/2], l
      if LRVERBOSE:
        print 'E(K_%d; L_%d || 0^*) = %s' % (j, j, hex(t))
        print 'L_%d, R_%d = %s, %s' % (j + 1, j + 1, hex(l), hex(r))
    return C.ByteString(r + l)
  def decrypt(me, c):
    bc, blksz = me.__class__.bc, me.__class__.blksz
    assert len(c) == blksz
    l, r = C.ByteString(c[:blksz/2]), C.ByteString(c[blksz/2:])
    for j in xrange(me.NR - 1, -1, -1):
      l0 = pad0star(l, bc.blksz)
      with muffle(): t = me.f[j].encrypt(l0)
      if LRVERBOSE:
        print 'L_%d, R_%d = %s, %s' % (j + 1, j + 1, hex(l), hex(r))
        print 'E(K_%d; L_%d || 0^*) = %s' % (j + 1, j + 1, hex(t))
      l, r = r ^ t[:blksz/2], l
    if LRVERBOSE: print 'L_0, R_0 = %s, %s' % (hex(l), hex(r))
    return C.ByteString(r + l)

LRAES = {}
for i in [8, 12, 16, 24, 32]:
  LRAES['lraes%d' % (8*i)] = LubyRackoffCipher(C.rijndael, i)
LRAES['dlraes512'] = LubyRackoffCipher(LubyRackoffCipher(C.rijndael, 32), 64)

###--------------------------------------------------------------------------
### PMAC.

def ocb_masks(E):
  blksz = E.__class__.blksz
  p = poly(8*blksz)
  x = C.GF(2); xinv = p.modinv(x)
  z = Z(blksz)
  L = E.encrypt(z)
  Lxinv = mul_blk_gf(L, xinv, p)
  Lgamma = 66*[L]
  for i in xrange(1, len(Lgamma)):
    Lgamma[i] = mul_blk_gf(Lgamma[i - 1], x, p)
  return Lgamma, Lxinv

def dump_ocb(E):
  Lgamma, Lxinv = ocb_masks(E)
  print 'L x^-1 = %s' % hex(Lxinv)
  for i, lg in enumerate(Lgamma):
    print 'L x^%d = %s' % (i, hex(lg))

def pmac1(E, m):
  blksz = E.__class__.blksz
  Lgamma, Lxinv = ocb_masks(E)
  a = o = Z(blksz)
  i = 1
  v, tl = blocks(m, blksz)
  for x in v:
    b = ntz(i)
    o ^= Lgamma[b]
    a ^= E.encrypt(x ^ o)
    if VERBOSE:
      print 'Z[%d]: %d -> %s' % (i - 1, b, hex(o))
      print 'A[%d]: %s' % (i - 1, hex(a))
    i += 1
  if len(tl) == blksz: a ^= tl ^ Lxinv
  else: a ^= pad10star(tl, blksz)
  return E.encrypt(a)

def pmac2(E, m):
  blksz = E.__class__.blksz
  p = prim(8*blksz)
  L = E.encrypt(Z(blksz))
  o = mul_blk_gf(L, 10, p)
  a = Z(blksz)
  v, tl = blocks(m, blksz)
  for x in v:
    a ^= E.encrypt(x ^ o)
    o = mul_blk_gf(o, 2, p)
  if len(tl) == blksz: a ^= tl ^ mul_blk_gf(o, 3, p)
  else: a ^= pad10star(tl, blksz) ^ mul_blk_gf(o, 5, p)
  return E.encrypt(a)

def ocb3_masks(E):
  Lgamma, _ = ocb_masks(E)
  Lstar = Lgamma[0]
  Ldollar = Lgamma[1]
  return Lstar, Ldollar, Lgamma[2:]

def dump_ocb3(E):
  Lstar, Ldollar, Lgamma = ocb3_masks(E)
  print 'L_*       : %s' % hex(Lstar)
  print 'L_$       : %s' % hex(Ldollar)
  for i, lg in enumerate(Lgamma[:4]):
    print 'L_%-8d: %s' % (i, hex(lg))

def pmac3(E, m):
  blksz = E.__class__.blksz
  Lstar, Ldollar, Lgamma = ocb3_masks(E)
  a = o = Z(blksz)
  i = 1
  v, tl = blocks0(m, blksz)
  for x in v:
    b = ntz(i)
    o ^= Lgamma[b]
    a ^= E.encrypt(x ^ o)
    if VERBOSE:
      print 'Offset\'_%-2d: %s' % (i, hex(o))
      print 'AuthSum_%-2d: %s' % (i, hex(a))
    i += 1
  if tl:
    o ^= Lstar
    a ^= E.encrypt(pad10star(tl, blksz) ^ o)
    if VERBOSE:
      print 'Offset\'_* : %s' % hex(o)
      print 'AuthSum_* : %s' % hex(a)
  return a

def pmac1_pub(E, m):
  if VERBOSE: dump_ocb(E)
  return pmac1(E, m),

def pmac2_pub(E, m):
  return pmac2(E, m),

def pmac3_pub(E, m):
  return pmac3(E, m),

def pmacgen(bc):
  return [(0,), (1,),
          (3*bc.blksz,),
          (3*bc.blksz - 5,)]

###--------------------------------------------------------------------------
### OCB.

## For OCB2, it's important for security that n = log_x (x + 1) is large in
## the field representations of GF(2^w) used -- in fact, we need more, that
## i n (mod 2^w - 1) is large for i in {4, -3, -2, -1, 1, 2, 3, 4}.  The
## original paper lists the values for 64 and 128, but we support other block
## sizes, so here's the result of the (rather large, in some cases)
## computation.
##
## Block size           log_x (x + 1)
##
##       64             9686038906114705801
##       96             63214690573408919568138788065
##      128             338793687469689340204974836150077311399
##      192             161110085006042185925119981866940491651092686475226538785
##      256             22928580326165511958494515843249267194111962539778797914076675796261938307298

def ocb1(E, n, h, m, tsz = None):
  ## This is OCB1.PMAC1 from Rogaway's `Authenticated-Encryption with
  ## Associated-Data'.
  blksz = E.__class__.blksz
  if VERBOSE: dump_ocb(E)
  Lgamma, Lxinv = ocb_masks(E)
  if tsz is None: tsz = blksz
  a = Z(blksz)
  o = E.encrypt(n ^ Lgamma[0])
  if VERBOSE: print 'R = %s' % hex(o)
  i = 1
  y = C.WriteBuffer()
  v, tl = blocks(m, blksz)
  for x in v:
    b = ntz(i)
    o ^= Lgamma[b]
    a ^= x
    if VERBOSE:
      print 'Z[%d]: %d -> %s' % (i - 1, b, hex(o))
      print 'A[%d]: %s' % (i - 1, hex(a))
    y.put(E.encrypt(x ^ o) ^ o)
    i += 1
  b = ntz(i)
  o ^= Lgamma[b]
  n = len(tl)
  if VERBOSE:
    print 'Z[%d]: %d -> %s' % (i - 1, b, hex(o))
    print 'LEN = %s' % hex(C.MP(8*n).storeb(blksz))
  yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ Lxinv ^ o)
  cfinal = tl ^ yfinal[:n]
  a ^= o ^ (tl + yfinal[n:])
  y.put(cfinal)
  t = E.encrypt(a)
  if h: t ^= pmac1(E, h)
  return C.ByteString(y), C.ByteString(t[:tsz])

def ocb2(E, n, h, m, tsz = None):
  blksz = E.__class__.blksz
  if tsz is None: tsz = blksz
  p = prim(8*blksz)
  L = E.encrypt(n)
  o = mul_blk_gf(L, 2, p)
  a = Z(blksz)
  v, tl = blocks(m, blksz)
  y = C.WriteBuffer()
  for x in v:
    a ^= x
    y.put(E.encrypt(x ^ o) ^ o)
    o = mul_blk_gf(o, 2, p)
  n = len(tl)
  yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ o)
  cfinal = tl ^ yfinal[:n]
  a ^= (tl + yfinal[n:]) ^ mul_blk_gf(o, 3, p)
  y.put(cfinal)
  t = E.encrypt(a)
  if h: t ^= pmac2(E, h)
  return C.ByteString(y), C.ByteString(t[:tsz])

OCB3_STRETCH = { 8: (5, 25),
                 12: (6, 33),
                 16: (6, 8),
                 24: (7, 40),
                 32: (7, 120),
                 64: (8, 240) }

def ocb3(E, n, h, m, tsz = None):
  blksz = E.__class__.blksz
  if tsz is None: tsz = blksz
  Lstar, Ldollar, Lgamma = ocb3_masks(E)
  if VERBOSE: dump_ocb3(E)

  ## Figure out how much we need to glue onto the nonce.  This ends up being
  ## [t mod w]_v || 0^p || 1 || N, where w is the block size in bits, t is
  ## the tag length in bits, v = floor(log_2(w - 1)) + 1, and p = w - l(N) -
  ## v - 1.  But this is an annoying way to think about it because of the
  ## byte misalignment.  Instead, think of it as a byte-aligned prefix
  ## encoding the tag and an `is the nonce full-length' flag, followed by
  ## optional padding, and then the nonce:
  ##
  ##    F || N                  if l(N) = w - f
  ##    F || 0^p || 1 || N      otherwise
  ##
  ## where F is [t mod w]_v || 0^{f-v-1} || b; f = floor(log_2(w - 1)) + 2;
  ## b is 1 if l(N) = w - f, or 0 otherwise; and p = w - f - l(N) - 1.
  tszbits = C.MP(8*blksz - 1).nbits
  fwd = tszbits/8 + 1
  f = tsz << 3 + 8*fwd - tszbits

  ## Form the augmented nonce.
  nb = C.WriteBuffer()
  nsz, nwd = len(n), blksz - fwd
  if nsz == nwd: f |= 1
  nb.put(C.MP(f).storeb(fwd))
  if nsz < nwd: nb.zero(nwd - nsz - 1).putu8(1)
  nb.put(n)
  nn = C.ByteString(nb)
  if VERBOSE: print 'N\'        : %s' % hex(nn)

  ## Calculate the initial offset.
  split, shift = OCB3_STRETCH[blksz]
  splitbits = 1 << split
  t2ps = C.MP(0).setbit(splitbits)
  lomask = (C.MP(0).setbit(split) - 1)
  himask = ~lomask
  top, bottom = nn&himask.storeb2c(blksz), C.MP.loadb(nn)&lomask
  ktop = C.MP.loadb(E.encrypt(top))
  stretch = (ktop << splitbits) | \
      (((ktop ^ (ktop << shift)) >> (8*blksz - splitbits))%t2ps)
  o = (stretch >> splitbits - bottom).storeb(blksz)
  a = C.ByteString.zero(blksz)
  if VERBOSE:
    print 'bottom    : %d' % bottom
    print 'Ktop      : %s' % hex(ktop.storeb(blksz))
    print 'Stretch   : %s' % hex(stretch.storeb(blksz + (1 << split - 3)))
    print 'Offset_0  : %s' % hex(o)

  ## Split the message into blocks.
  i = 1
  y = C.WriteBuffer()
  v, tl = blocks0(m, blksz)
  for x in v:
    b = ntz(i)
    o ^= Lgamma[b]
    a ^= x
    if VERBOSE:
      print 'Offset_%-3d: %s' % (i, hex(o))
      print 'Checksum_%d: %s' % (i, hex(a))
    y.put(E.encrypt(x ^ o) ^ o)
    i += 1
  if tl:
    o ^= Lstar
    n = len(tl)
    pad = E.encrypt(o)
    a ^= pad10star(tl, blksz)
    if VERBOSE:
      print 'Offset_*  : %s' % hex(o)
      print 'Checksum_*: %s' % hex(a)
    y.put(tl ^ pad[0:n])
  o ^= Ldollar
  t = E.encrypt(a ^ o) ^ pmac3(E, h)
  return C.ByteString(y), C.ByteString(t[:tsz])

def ocbgen(bc):
  w = bc.blksz
  return [(w, 0, 0), (w, 1, 0), (w, 0, 1),
          (w, 0, 3*w),
          (w, 3*w, 3*w),
          (w, 0, 3*w + 5),
          (w, 3*w - 5, 3*w + 5)]

def ocb3gen(bc):
  w = bc.blksz
  return [(w - 2, 0, 0), (w - 2, 1, 0), (w - 2, 0, 1),
          (w - 5, 0, 3*w),
          (w - 3, 3*w, 3*w),
          (w - 2, 0, 3*w + 5),
          (w - 2, 3*w - 5, 3*w + 5)]

###--------------------------------------------------------------------------
### Main program.

VERBOSE = LRVERBOSE = False

class struct (object):
  def __init__(me, **kw):
    me.__dict__.update(kw)

def mct(ocb, bc, ksz, nsz, tsz):
  k = C.MP(8*tsz).storeb(ksz)
  E = bc(k)
  e = C.ByteString('')
  n = C.MP(1)
  cbuf = C.WriteBuffer()
  for i in xrange(128):
    s = C.ByteString.zero(i)
    y, t = ocb(E, n.storeb(nsz), s, s, tsz); n += 1; cbuf.put(y).put(t)
    y, t = ocb(E, n.storeb(nsz), e, s, tsz); n += 1; cbuf.put(y).put(t)
    y, t = ocb(E, n.storeb(nsz), s, e, tsz); n += 1; cbuf.put(y).put(t)
  _, t = ocb(E, n.storeb(nsz), C.ByteString(cbuf), e, tsz)
  print hex(t)

argc = len(argv)
argi = 1

def usage():
  print >>stderr, """\
usage: %s [-v] OCB BLKC OP ARGS...
        mct KSZ NSZ TSZ
        kat K N0 TSZ HSZ,MSZ ...
        lraes W K M""" % argv[0]
  exit(2)

def arg(must = True, default = None):
  global argi
  if argi < argc: argi += 1; return argv[argi - 1]
  elif not must: return default
  else: usage()

MODEMAP = { 'ocb1': ocb1,
            'ocb2': ocb2,
            'ocb3': ocb3 }

def pat(sz):
  b = C.WriteBuffer()
  for i in xrange(sz): b.putu8(i%256)
  return C.ByteString(b)

opt = arg()
if opt == '-v': VERBOSE = True; opt = arg()
ocb = MODEMAP[opt]

bcname = arg()
bc = None
for d in LRAES, C.gcprps:
  try: bc = d[bcname]
  except KeyError: pass
  else: break
if bc is None: raise KeyError, bcname

mode = arg()
if mode == 'mct':
  ksz = int(arg()); nsz = int(arg()); tsz = int(arg())
  mct(ocb, bc, ksz, nsz, tsz)
  exit(0)

elif mode == 'kat':
  k = C.bytes(arg())
  E = bc(k)
  nspec = arg()
  if nspec.endswith('+'): ninc = 1; nspec = nspec[:-1]
  else: ninc = 0
  n0 = C.bytes(nspec)
  nz = C.MP.loadb(n0)
  nsz = len(n0)
  tsz = int(arg())

  print 'K: %s' % hex(k)

  while True:
    hmsz = arg(must = False)
    if hmsz is None: break
    hsz, msz = map(int, hmsz.split(','))
    n = nz.storeb(nsz)
    h = pat(hsz)
    m = pat(msz)
    y, t = ocb(E, n, h, m, tsz)
    print
    print 'N: %s' % hex(n)
    print 'A: %s' % hex(h)
    print 'P: %s' % hex(m)
    print 'C: %s%s' % (hex(y), hex(t))
    nz += ninc

elif mode == 'lraes':
  w = int(arg())
  k = C.bytes(arg())
  m = C.bytes(arg())
  LRVERBOSE = True
  lr = LubyRackoffCipher(bc, w)
  E = lr(k)
  print
  c = E.encrypt(m)
  print 'E\'(K, m) = %s' % hex(c)

else:
  usage()

###----- That's all, folks --------------------------------------------------