mdw@git.distorted.org.uk Git - catacomb/blob - utils/advmodes

   1 #! /usr/bin/python
   2
   3 from sys import argv, exit
   4 from struct import unpack, pack
   5 from itertools import izip
   6 import catacomb as C
   7
   8 R = C.FibRand(0)
   9
  10 ###--------------------------------------------------------------------------
  11 ### Utilities.
  12
  13 def combs(things, k):
  14   ii = range(k)
  15   n = len(things)
  16   while True:
  17     yield [things[i] for i in ii]
  18     for j in xrange(k):
  19       if j == k - 1: lim = n
  20       else: lim = ii[j + 1]
  21       i = ii[j] + 1
  22       if i < lim:
  23         ii[j] = i
  24         break
  25       ii[j] = j
  26     else:
  27       return
  28
  29 POLYMAP = {}
  30
  31 def poly(nbits):
  32   try: return POLYMAP[nbits]
  33   except KeyError: pass
  34   base = C.GF(0).setbit(nbits).setbit(0)
  35   for k in xrange(1, nbits, 2):
  36     for cc in combs(range(1, nbits), k):
  37       p = base + sum((C.GF(0).setbit(c) for c in cc), C.GF(0))
  38       if p.irreduciblep(): POLYMAP[nbits] = p; return p
  39   raise ValueError, nbits
  40
  41 def prim(nbits):
  42   ## No fancy way to do this: I'd need a much cleverer factoring algorithm
  43   ## than I have in my pockets.
  44   if nbits == 64: cc = [64, 4, 3, 1, 0]
  45   elif nbits == 96: cc = [96, 10, 9, 6, 0]
  46   elif nbits == 128: cc = [128, 7, 2, 1, 0]
  47   elif nbits == 192: cc = [192, 15, 11, 5, 0]
  48   elif nbits == 256: cc = [256, 10, 5, 2, 0]
  49   else: raise ValueError, 'no field for %d bits' % nbits
  50   p = C.GF(0)
  51   for c in cc: p = p.setbit(c)
  52   return p
  53
  54 def Z(n):
  55   return C.ByteString.zero(n)
  56
  57 def mul_blk_gf(m, x, p): return ((C.GF.loadb(m)*x)%p).storeb((p.nbits + 6)/8)
  58
  59 def with_lastp(it):
  60   it = iter(it)
  61   try: j = next(it)
  62   except StopIteration: raise ValueError, 'empty iter'
  63   lastp = False
  64   while not lastp:
  65     i = j
  66     try: j = next(it)
  67     except StopIteration: lastp = True
  68     yield i, lastp
  69
  70 def safehex(x):
  71   if len(x): return hex(x)
  72   else: return '""'
  73
  74 def keylens(ksz):
  75   sel = []
  76   if isinstance(ksz, C.KeySZSet): kk = ksz.set
  77   elif isinstance(ksz, C.KeySZRange): kk = range(ksz.min, ksz.max, ksz.mod)
  78   elif isinstance(ksz, C.KeySZAny): kk = range(64); sel = [0]
  79   kk = list(kk); kk = kk[:]
  80   n = len(kk)
  81   while n and len(sel) < 4:
  82     i = R.range(n)
  83     n -= 1
  84     kk[i], kk[n] = kk[n], kk[i]
  85     sel.append(kk[n])
  86   return sel
  87
  88 def pad0star(m, w):
  89   n = len(m)
  90   if not n: r = w
  91   else: r = (-len(m))%w
  92   if r: m += Z(r)
  93   return C.ByteString(m)
  94
  95 def pad10star(m, w):
  96   r = w - len(m)%w
  97   if r: m += '\x80' + Z(r - 1)
  98   return C.ByteString(m)
  99
 100 def ntz(i):
 101   j = 0
 102   while (i&1) == 0: i >>= 1; j += 1
 103   return j
 104
 105 def blocks(x, w):
 106   v, i, n = [], 0, len(x)
 107   while n - i > w:
 108     v.append(C.ByteString(x[i:i + w]))
 109     i += w
 110   return v, C.ByteString(x[i:])
 111
 112 EMPTY = C.bytes('')
 113
 114 def blocks0(x, w):
 115   v, tl = blocks(x, w)
 116   if len(tl) == w: v.append(tl); tl = EMPTY
 117   return v, tl
 118
 119 def dummygen(bc): return []
 120
 121 CUSTOM = {}
 122
 123 ###--------------------------------------------------------------------------
 124 ### RC6.
 125
 126 class RC6Cipher (type):
 127   def __new__(cls, w, r):
 128     name = 'rc6-%d/%d' % (w, r)
 129     me = type(name, (RC6Base,), {})
 130     me.name = name
 131     me.r = r
 132     me.w = w
 133     me.blksz = w/2
 134     me.keysz = C.KeySZRange(me.blksz, 1, 255, 1)
 135     return me
 136
 137 def rotw(w):
 138   return w.bit_length() - 1
 139
 140 def rol(w, x, n):
 141   m0, m1 = C.MP(0).setbit(w - n) - 1, C.MP(0).setbit(n) - 1
 142   return ((x&m0) << n) | (x >> (w - n))&m1
 143
 144 def ror(w, x, n):
 145   m0, m1 = C.MP(0).setbit(n) - 1, C.MP(0).setbit(w - n) - 1
 146   return ((x&m0) << (w - n)) | (x >> n)&m1
 147
 148 class RC6Base (object):
 149
 150   ## Magic constants.
 151   P400 = C.MP(0xb7e151628aed2a6abf7158809cf4f3c762e7160f38b4da56a784d9045190cfef324e7738926cfbe5f4bf8d8d8c31d763da06)
 152   Q400 = C.MP(0x9e3779b97f4a7c15f39cc0605cedc8341082276bf3a27251f86c6a11d0c18e952767f0b153d27b7f0347045b5bf1827f0188)
 153
 154   def __init__(me, k):
 155
 156     ## Build the magic numbers.
 157     P = me.P400 >> (400 - me.w)
 158     if P%2 == 0: P += 1
 159     Q = me.Q400 >> (400 - me.w)
 160     if Q%2 == 0: Q += 1
 161     M = C.MP(0).setbit(me.w) - 1
 162
 163     ## Convert the key into words.
 164     wb = me.w/8
 165     c = (len(k) + wb - 1)/wb
 166     kb, ktl = blocks(k, me.w/8)
 167     L = map(C.MP.loadl, kb + [ktl])
 168     assert c == len(L)
 169
 170     ## Build the subkey table.
 171     me.d = rotw(me.w)
 172     n = 2*me.r + 4
 173     S = [(P + i*Q)&M for i in xrange(n)]
 174
 175     ##for j in xrange(c):
 176     ##  print 'L[%3d] = %s' % (j, hex(L[j]).upper()[2:].rjust(2*wb, '0'))
 177     ##for i in xrange(n):
 178     ##  print 'S[%3d] = %s' % (i, hex(S[i]).upper()[2:].rjust(2*wb, '0'))
 179
 180     i = j = 0
 181     A = B = C.MP(0)
 182
 183     for s in xrange(3*max(c, n)):
 184       A = S[i] = rol(me.w, S[i] + A + B, 3)
 185       B = L[j] = rol(me.w, L[j] + A + B, (A + B)%(1 << me.d))
 186       ##print 'S[%3d] = %s' % (i, hex(S[i]).upper()[2:].rjust(2*wb, '0'))
 187       ##print 'L[%3d] = %s' % (j, hex(L[j]).upper()[2:].rjust(2*wb, '0'))
 188       i = (i + 1)%n
 189       j = (j + 1)%c
 190
 191     ## Done.
 192     me.s = S
 193
 194   def encrypt(me, x):
 195     M = C.MP(0).setbit(me.w) - 1
 196     a, b, c, d = map(C.MP.loadl, blocks0(x, me.blksz/4)[0])
 197     b = (b + me.s[0])&M
 198     d = (d + me.s[1])&M
 199     ##print 'B = %s' % (hex(b).upper()[2:].rjust(me.w/4, '0'))
 200     ##print 'D = %s' % (hex(d).upper()[2:].rjust(me.w/4, '0'))
 201     for i in xrange(2, 2*me.r + 2, 2):
 202       t = rol(me.w, 2*b*b + b, me.d)
 203       u = rol(me.w, 2*d*d + d, me.d)
 204       a = (rol(me.w, a ^ t, u%(1 << me.d)) + me.s[i + 0])&M
 205       c = (rol(me.w, c ^ u, t%(1 << me.d)) + me.s[i + 1])&M
 206       ##print 'A = %s' % (hex(a).upper()[2:].rjust(me.w/4, '0'))
 207       ##print 'C = %s' % (hex(c).upper()[2:].rjust(me.w/4, '0'))
 208       a, b, c, d = b, c, d, a
 209     a = (a + me.s[2*me.r + 2])&M
 210     c = (c + me.s[2*me.r + 3])&M
 211     ##print 'A = %s' % (hex(a).upper()[2:].rjust(me.w/4, '0'))
 212     ##print 'C = %s' % (hex(c).upper()[2:].rjust(me.w/4, '0'))
 213     return C.ByteString(a.storel(me.blksz/4) + b.storel(me.blksz/4) +
 214                         c.storel(me.blksz/4) + d.storel(me.blksz/4))
 215
 216   def decrypt(me, x):
 217     M = C.MP(0).setbit(me.w) - 1
 218     a, b, c, d = map(C.MP.loadl, blocks0(x, me.blksz/4))
 219     c = (c - me.s[2*me.r + 3])&M
 220     a = (a - me.s[2*me.r + 2])&M
 221     for i in xrange(2*me.r + 1, 1, -2):
 222       a, b, c, d = d, a, b, c
 223       u = rol(me.w, 2*d*d + d, me.d)
 224       t = rol(me.w, 2*b*b + b, me.d)
 225       c = ror(me.w, (c - me.s[i + 1])&M, t%(1 << me.d)) ^ u
 226       a = ror(me.w, (a - me.s[i + 0])&M, u%(1 << me.d)) ^ t
 227     a = (a + s[2*me.r + 2])&M
 228     c = (c + s[2*me.r + 3])&M
 229     return C.ByteString(a.storel(me.blksz/4) + b.storel(me.blksz/4) +
 230                         c.storel(me.blksz/4) + d.storel(me.blksz/4))
 231
 232 for (w, r) in [(8, 16), (16, 16), (24, 16), (32, 16),
 233                (32, 20), (48, 16), (64, 16), (96, 16), (128, 16),
 234                (192, 16), (256, 16), (400, 16)]:
 235   CUSTOM['rc6-%d/%d' % (w, r)] = RC6Cipher(w, r)
 236
 237 ###--------------------------------------------------------------------------
 238 ### OMAC (or CMAC).
 239
 240 def omac_masks(E):
 241   blksz = E.__class__.blksz
 242   p = poly(8*blksz)
 243   z = Z(blksz)
 244   L = E.encrypt(z)
 245   m0 = mul_blk_gf(L, C.GF(2), p)
 246   m1 = mul_blk_gf(m0, C.GF(2), p)
 247   return m0, m1
 248
 249 def dump_omac(E):
 250   blksz = E.__class__.blksz
 251   m0, m1 = omac_masks(E)
 252   print 'L = %s' % hex(E.encrypt(Z(blksz)))
 253   print 'm0 = %s' % hex(m0)
 254   print 'm1 = %s' % hex(m1)
 255   for t in xrange(3):
 256     print 'v%d = %s' % (t, hex(E.encrypt(C.MP(t).storeb(blksz))))
 257     print 'z%d = %s' % (t, hex(omac(E, t, '')))
 258
 259 def omac(E, t, m):
 260   blksz = E.__class__.blksz
 261   m0, m1 = omac_masks(E)
 262   a = Z(blksz)
 263   if t is not None: m = C.MP(t).storeb(blksz) + m
 264   v, tl = blocks(m, blksz)
 265   for x in v: a = E.encrypt(a ^ x)
 266   r = blksz - len(tl)
 267   if r == 0:
 268     a = E.encrypt(a ^ tl ^ m0)
 269   else:
 270     pad = pad10star(tl, blksz)
 271     a = E.encrypt(a ^ pad ^ m1)
 272   return a
 273
 274 def cmac(E, m):
 275   if VERBOSE: dump_omac(E)
 276   return omac(E, None, m),
 277
 278 def cmacgen(bc):
 279   return [(0,), (1,),
 280           (3*bc.blksz,),
 281           (3*bc.blksz - 5,)]
 282
 283 ###--------------------------------------------------------------------------
 284 ### Counter mode.
 285
 286 def ctr(E, m, c0):
 287   blksz = E.__class__.blksz
 288   y = C.WriteBuffer()
 289   c = C.MP.loadb(c0)
 290   while y.size < len(m):
 291     y.put(E.encrypt(c.storeb(blksz)))
 292     c += 1
 293   return C.ByteString(m) ^ C.ByteString(y)[:len(m)]
 294
 295 ###--------------------------------------------------------------------------
 296 ### GCM.
 297
 298 def gcm_mangle(x):
 299   y = C.WriteBuffer()
 300   for b in x:
 301     b = ord(b)
 302     bb = 0
 303     for i in xrange(8):
 304       bb <<= 1
 305       if b&1: bb |= 1
 306       b >>= 1
 307     y.putu8(bb)
 308   return C.ByteString(y)
 309
 310 def gcm_mul(x, y):
 311   w = len(x)
 312   p = poly(8*w)
 313   u, v = C.GF.loadl(gcm_mangle(x)), C.GF.loadl(gcm_mangle(y))
 314   z = (u*v)%p
 315   return gcm_mangle(z.storel(w))
 316
 317 def gcm_pow(x, n):
 318   w = len(x)
 319   p = poly(8*w)
 320   u = C.GF.loadl(gcm_mangle(x))
 321   z = pow(u, n, p)
 322   return gcm_mangle(z.storel(w))
 323
 324 def gcm_ctr(E, m, c0):
 325   y = C.WriteBuffer()
 326   pre = c0[:-4]
 327   c, = unpack('>L', c0[-4:])
 328   while y.size < len(m):
 329     c += 1
 330     y.put(E.encrypt(pre + pack('>L', c)))
 331   return C.ByteString(m) ^ C.ByteString(y)[:len(m)]
 332
 333 def g(what, x, m, a0 = None):
 334   n = len(x)
 335   if a0 is None: a = Z(n)
 336   else: a = a0
 337   i = 0
 338   for b in blocks0(m, n)[0]:
 339     a = gcm_mul(a ^ b, x)
 340     if VERBOSE: print '%s[%d] = %s -> %s' % (what, i, hex(b), hex(a))
 341     i += 1
 342   return a
 343
 344 def gcm_pad(w, x):
 345   return C.ByteString(x + Z(-len(x)%w))
 346
 347 def gcm_lens(w, a, b):
 348   if w < 12: n = w
 349   else: n = w/2
 350   return C.ByteString(C.MP(a).storeb(n) + C.MP(b).storeb(n))
 351
 352 def ghash(whata, whatb, x, a, b):
 353   w = len(x)
 354   ha = g(whata, x, gcm_pad(w, a))
 355   hb = g(whatb, x, gcm_pad(w, b))
 356   if a:
 357     hc = gcm_mul(ha, gcm_pow(x, (len(b) + w - 1)/w)) ^ hb
 358     if VERBOSE: print '%s || %s -> %s' % (whata, whatb, hex(hc))
 359   else:
 360     hc = hb
 361   return g(whatb, x, gcm_lens(w, 8*len(a), 8*len(b)), hc)
 362
 363 def gcmenc(E, n, h, m, tsz = None):
 364   w = E.__class__.blksz
 365   x = E.encrypt(Z(w))
 366   if VERBOSE: print 'x = %s' % hex(x)
 367   if len(n) + 4 == w: c0 = C.ByteString(n + pack('>L', 1))
 368   else: c0 = ghash('?', 'n', x, EMPTY, n)
 369   if VERBOSE: print 'c0 = %s' % hex(c0)
 370   y = gcm_ctr(E, m, c0)
 371   t = ghash('h', 'y', x, h, y) ^ E.encrypt(c0)
 372   return y, t
 373
 374 def gcmdec(E, n, h, y, t):
 375   w = E.__class__.blksz
 376   x = E.encrypt(Z(w))
 377   if VERBOSE: print 'x = %s' % hex(x)
 378   if len(n) + 4 == w: c0 = C.ByteString(n + pack('>L', 1))
 379   else: c0 = ghash('?', 'n', x, EMPTY, n)
 380   if VERBOSE: print 'c0 = %s' % hex(c0)
 381   m = gcm_ctr(E, y, c0)
 382   tt = ghash('h', 'y', x, h, y) ^ E.encrypt(c0)
 383   if t == tt: return m,
 384   else: return None,
 385
 386 def gcmgen(bc):
 387   return [(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1),
 388           (bc.blksz, 3*bc.blksz, 3*bc.blksz),
 389           (bc.blksz - 4, bc.blksz + 3, 3*bc.blksz + 9),
 390           (bc.blksz - 1, 3*bc.blksz - 5, 3*bc.blksz + 5)]
 391
 392 def gcm_mul_tests(nbits):
 393   print 'gcm-mul%d {' % nbits
 394   for i in xrange(64):
 395     x = R.block(nbits/8)
 396     y = R.block(nbits/8)
 397     z = gcm_mul(x, y)
 398     print '  %s\n    %s\n    %s;' % (hex(x), hex(y), hex(z))
 399   print '}'
 400
 401 ###--------------------------------------------------------------------------
 402 ### CCM.
 403
 404 def stbe(n, w): return C.MP(n).storeb(w)
 405
 406 def ccm_fmthdr(blksz, n, hsz, msz, tsz):
 407   b = C.WriteBuffer()
 408   if blksz == 8:
 409     q = blksz - len(n) - 1
 410     f = 0
 411     if hsz: f |= 0x40
 412     f |= (tsz - 1) << 3
 413     f |= q - 1
 414     b.putu8(f).put(n).put(stbe(msz, q))
 415   elif blksz == 16:
 416     q = blksz - len(n) - 1
 417     f = 0
 418     if hsz: f |= 0x40
 419     f |= (tsz - 2)/2 << 3
 420     f |= q - 1
 421     b.putu8(f).put(n).put(stbe(msz, q))
 422   else:
 423     q = blksz - len(n) - 2
 424     f0 = f1 = 0
 425     if hsz: f1 |= 0x80
 426     f0 |= tsz
 427     f1 |= q
 428     b.putu8(f0).putu8(f1).put(n).put(stbe(msz, q))
 429   b = C.ByteString(b)
 430   if VERBOSE: print 'hdr = %s' % hex(b)
 431   return b
 432
 433 def ccm_fmtctr(blksz, n, i = 0):
 434   b = C.WriteBuffer()
 435   if blksz == 8 or blksz == 16:
 436     q = blksz - len(n) - 1
 437     b.putu8(q - 1).put(n).put(stbe(i, q))
 438   else:
 439     q = blksz - len(n) - 2
 440     b.putu8(0).putu8(q).put(n).put(stbe(i, q))
 441   b = C.ByteString(b)
 442   if VERBOSE: print 'ctr = %s' % hex(b)
 443   return b
 444
 445 def ccmaad(b, h, blksz):
 446   hsz = len(h)
 447   if not hsz: pass
 448   elif hsz < 0xfffe: b.putu16(hsz)
 449   elif hsz <= 0xffffffff: b.putu16(0xfffe).putu32(hsz)
 450   else: b.putu16(0xffff).putu64(hsz)
 451   b.put(h); b.zero((-b.size)%blksz)
 452
 453 def ccmenc(E, n, h, m, tsz = None):
 454   blksz = E.__class__.blksz
 455   if tsz is None: tsz = blksz
 456   b = C.WriteBuffer()
 457   b.put(ccm_fmthdr(blksz, n, len(h), len(m), tsz))
 458   ccmaad(b, h, blksz)
 459   b.put(m); b.zero((-b.size)%blksz)
 460   b = C.ByteString(b)
 461   a = Z(blksz)
 462   v, _ = blocks0(b, blksz)
 463   i = 0
 464   for x in v:
 465     a = E.encrypt(a ^ x)
 466     if VERBOSE:
 467       print 'b[%d] = %s' % (i, hex(x))
 468       print 'a[%d] = %s' % (i + 1, hex(a))
 469     i += 1
 470   y = ctr(E, a + m, ccm_fmtctr(blksz, n))
 471   return C.ByteString(y[blksz:]), C.ByteString(y[0:tsz])
 472
 473 def ccmdec(E, n, h, y, t):
 474   blksz = E.__class__.blksz
 475   tsz = len(t)
 476   b = C.WriteBuffer()
 477   b.put(ccm_fmthdr(blksz, n, len(h), len(y), tsz))
 478   ccmaad(b, h, blksz)
 479   mm = ctr(E, t + Z(blksz - tsz) + y, ccm_fmtctr(blksz, n))
 480   u, m = C.ByteString(mm[0:tsz]), C.ByteString(mm[blksz:])
 481   b.put(m); b.zero((-b.size)%blksz)
 482   b = C.ByteString(b)
 483   a = Z(blksz)
 484   v, _ = blocks0(b, blksz)
 485   i = 0
 486   for x in v:
 487     a = E.encrypt(a ^ x)
 488     if VERBOSE:
 489       print 'b[%d] = %s' % (i, hex(x))
 490       print 'a[%d] = %s' % (i + 1, hex(a))
 491     i += 1
 492   if u == a[:tsz]: return m,
 493   else: return None,
 494
 495 def ccmgen(bc):
 496   bsz = bc.blksz
 497   return [(bsz - 5, 0, 0, 4), (bsz - 5, 1, 0, 4), (bsz - 5, 0, 1, 4),
 498           (bsz/2 + 1, 3*bc.blksz, 3*bc.blksz),
 499           (bsz/2 + 1, 3*bc.blksz - 5, 3*bc.blksz + 5)]
 500
 501 ###--------------------------------------------------------------------------
 502 ### EAX.
 503
 504 def eaxenc(E, n, h, m, tsz = None):
 505   if VERBOSE:
 506     print 'k = %s' % hex(k)
 507     print 'n = %s' % hex(n)
 508     print 'h = %s' % hex(h)
 509     print 'm = %s' % hex(m)
 510     dump_omac(E)
 511   if tsz is None: tsz = E.__class__.blksz
 512   c0 = omac(E, 0, n)
 513   y = ctr(E, m, c0)
 514   ht = omac(E, 1, h)
 515   yt = omac(E, 2, y)
 516   if VERBOSE:
 517     print 'c0 = %s' % hex(c0)
 518     print 'ht = %s' % hex(ht)
 519     print 'yt = %s' % hex(yt)
 520   return y, C.ByteString((c0 ^ ht ^ yt)[:tsz])
 521
 522 def eaxdec(E, n, h, y, t):
 523   if VERBOSE:
 524     print 'k = %s' % hex(k)
 525     print 'n = %s' % hex(n)
 526     print 'h = %s' % hex(h)
 527     print 'y = %s' % hex(y)
 528     print 't = %s' % hex(t)
 529     dump_omac(E)
 530   c0 = omac(E, 0, n)
 531   m = ctr(E, y, c0)
 532   ht = omac(E, 1, h)
 533   yt = omac(E, 2, y)
 534   if VERBOSE:
 535     print 'c0 = %s' % hex(c0)
 536     print 'ht = %s' % hex(ht)
 537     print 'yt = %s' % hex(yt)
 538   if t == (c0 ^ ht ^ yt)[:len(t)]: return m,
 539   else: return None,
 540
 541 def eaxgen(bc):
 542   return [(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1),
 543           (bc.blksz, 3*bc.blksz, 3*bc.blksz),
 544           (bc.blksz - 1, 3*bc.blksz - 5, 3*bc.blksz + 5)]
 545
 546 ###--------------------------------------------------------------------------
 547 ### PMAC.
 548
 549 def ocb_masks(E):
 550   blksz = E.__class__.blksz
 551   p = poly(8*blksz)
 552   x = C.GF(2); xinv = p.modinv(x)
 553   z = Z(blksz)
 554   L = E.encrypt(z)
 555   Lxinv = mul_blk_gf(L, xinv, p)
 556   Lgamma = 66*[L]
 557   for i in xrange(1, len(Lgamma)):
 558     Lgamma[i] = mul_blk_gf(Lgamma[i - 1], x, p)
 559   return Lgamma, Lxinv
 560
 561 def dump_ocb(E):
 562   Lgamma, Lxinv = ocb_masks(E)
 563   print 'L x^-1 = %s' % hex(Lxinv)
 564   for i, lg in enumerate(Lgamma[:16]):
 565     print 'L x^%d = %s' % (i, hex(lg))
 566
 567 def pmac1(E, m):
 568   blksz = E.__class__.blksz
 569   Lgamma, Lxinv = ocb_masks(E)
 570   a = o = Z(blksz)
 571   i = 0
 572   v, tl = blocks(m, blksz)
 573   for x in v:
 574     i += 1
 575     b = ntz(i)
 576     o ^= Lgamma[b]
 577     a ^= E.encrypt(x ^ o)
 578     if VERBOSE:
 579       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 580       print 'A[%d]: %s' % (i, hex(a))
 581   if len(tl) == blksz: a ^= tl ^ Lxinv
 582   else: a ^= pad10star(tl, blksz)
 583   return E.encrypt(a)
 584
 585 def pmac2(E, m):
 586   blksz = E.__class__.blksz
 587   p = prim(8*blksz)
 588   L = E.encrypt(Z(blksz))
 589   o = mul_blk_gf(L, C.GF(10), p)
 590   a = Z(blksz)
 591   v, tl = blocks(m, blksz)
 592   for x in v:
 593     a ^= E.encrypt(x ^ o)
 594     o = mul_blk_gf(o, C.GF(2), p)
 595   if len(tl) == blksz: a ^= tl ^ mul_blk_gf(o, C.GF(3), p)
 596   else: a ^= pad10star(tl, blksz) ^ mul_blk_gf(o, C.GF(5), p)
 597   return E.encrypt(a)
 598
 599 def ocb3_masks(E):
 600   Lgamma, _ = ocb_masks(E)
 601   Lstar = Lgamma[0]
 602   Ldollar = Lgamma[1]
 603   return Lstar, Ldollar, Lgamma[2:]
 604
 605 def dump_ocb3(E):
 606   Lstar, Ldollar, Lgamma = ocb3_masks(E)
 607   print 'L_* = %s' % hex(Lstar)
 608   print 'L_$ = %s' % hex(Ldollar)
 609   for i, lg in enumerate(Lgamma[:16]):
 610     print 'L x^%d = %s' % (i, hex(lg))
 611
 612 def pmac3(E, m):
 613   ## Note that `PMAC3' is /not/ a secure MAC.  It depends on other parts of
 614   ## OCB3 to prevent a rather easy linear-algebra attack.
 615   blksz = E.__class__.blksz
 616   Lstar, Ldollar, Lgamma = ocb3_masks(E)
 617   a = o = Z(blksz)
 618   i = 0
 619   v, tl = blocks0(m, blksz)
 620   for x in v:
 621     i += 1
 622     b = ntz(i)
 623     o ^= Lgamma[b]
 624     a ^= E.encrypt(x ^ o)
 625     if VERBOSE:
 626       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 627       print 'A[%d]: %s' % (i, hex(a))
 628   if tl:
 629     o ^= Lstar
 630     a ^= E.encrypt(pad10star(tl, blksz) ^ o)
 631     if VERBOSE:
 632       print 'Z[%d]: * -> %s' % (i, hex(o))
 633       print 'A[%d]: %s' % (i, hex(a))
 634   return a
 635
 636 def pmac1_pub(E, m):
 637   if VERBOSE: dump_ocb(E)
 638   return pmac1(E, m),
 639
 640 def pmacgen(bc):
 641   return [(0,), (1,),
 642           (3*bc.blksz,),
 643           (3*bc.blksz - 5,)]
 644
 645 ###--------------------------------------------------------------------------
 646 ### OCB.
 647
 648 def ocb1enc(E, n, h, m, tsz = None):
 649   ## This is OCB1.PMAC1 from Rogaway's `Authenticated-Encryption with
 650   ## Associated-Data'.
 651   blksz = E.__class__.blksz
 652   if VERBOSE: dump_ocb(E)
 653   Lgamma, Lxinv = ocb_masks(E)
 654   if tsz is None: tsz = blksz
 655   a = Z(blksz)
 656   o = E.encrypt(n ^ Lgamma[0])
 657   if VERBOSE: print 'R = %s' % hex(o)
 658   i = 0
 659   y = C.WriteBuffer()
 660   v, tl = blocks(m, blksz)
 661   for x in v:
 662     i += 1
 663     b = ntz(i)
 664     o ^= Lgamma[b]
 665     a ^= x
 666     if VERBOSE:
 667       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 668       print 'A[%d]: %s' % (i, hex(a))
 669     y.put(E.encrypt(x ^ o) ^ o)
 670   i += 1
 671   b = ntz(i)
 672   o ^= Lgamma[b]
 673   n = len(tl)
 674   if VERBOSE:
 675     print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 676     print 'LEN = %s' % hex(C.MP(8*n).storeb(blksz))
 677   yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ Lxinv ^ o)
 678   cfinal = tl ^ yfinal[:n]
 679   a ^= o ^ (tl + yfinal[n:])
 680   y.put(cfinal)
 681   t = E.encrypt(a)
 682   if h: t ^= pmac1(E, h)
 683   return C.ByteString(y), C.ByteString(t[:tsz])
 684
 685 def ocb1dec(E, n, h, y, t):
 686   ## This is OCB1.PMAC1 from Rogaway's `Authenticated-Encryption with
 687   ## Associated-Data'.
 688   blksz = E.__class__.blksz
 689   if VERBOSE: dump_ocb(E)
 690   Lgamma, Lxinv = ocb_masks(E)
 691   a = Z(blksz)
 692   o = E.encrypt(n ^ Lgamma[0])
 693   if VERBOSE: print 'R = %s' % hex(o)
 694   i = 0
 695   m = C.WriteBuffer()
 696   v, tl = blocks(y, blksz)
 697   for x in v:
 698     i += 1
 699     b = ntz(i)
 700     o ^= Lgamma[b]
 701     if VERBOSE:
 702       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 703       print 'A[%d]: %s' % (i, hex(a))
 704     u = E.decrypt(x ^ o) ^ o
 705     m.put(u)
 706     a ^= u
 707   i += 1
 708   b = ntz(i)
 709   o ^= Lgamma[b]
 710   n = len(tl)
 711   if VERBOSE:
 712     print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 713     print 'LEN = %s' % hex(C.MP(8*n).storeb(blksz))
 714   yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ Lxinv ^ o)
 715   mfinal = tl ^ yfinal[:n]
 716   a ^= o ^ (mfinal + yfinal[n:])
 717   m.put(mfinal)
 718   u = E.encrypt(a)
 719   if h: u ^= pmac1(E, h)
 720   if t == u[:len(t)]: return C.ByteString(m),
 721   else: return None,
 722
 723 def ocb2enc(E, n, h, m, tsz = None):
 724   ## For OCB2, it's important for security that n = log_x (x + 1) is large in
 725   ## the field representations of GF(2^w) used -- in fact, we need more, that
 726   ## i n (mod 2^w - 1) is large for i in {4, -3, -2, -1, 1, 2, 3, 4}.  The
 727   ## original paper lists the values for 64 and 128, but we support other
 728   ## block sizes, so here's the result of the (rather large, in some cases)
 729   ## computation.
 730   ##
 731   ## Block size           log_x (x + 1)
 732   ##
 733   ##       64             9686038906114705801
 734   ##       96             63214690573408919568138788065
 735   ##      128             338793687469689340204974836150077311399
 736   ##      192             161110085006042185925119981866940491651092686475226538785
 737   ##      256             22928580326165511958494515843249267194111962539778797914076675796261938307298
 738
 739   blksz = E.__class__.blksz
 740   if tsz is None: tsz = blksz
 741   p = prim(8*blksz)
 742   L = E.encrypt(n)
 743   o = mul_blk_gf(L, C.GF(2), p)
 744   a = Z(blksz)
 745   v, tl = blocks(m, blksz)
 746   y = C.WriteBuffer()
 747   for x in v:
 748     a ^= x
 749     y.put(E.encrypt(x ^ o) ^ o)
 750     o = mul_blk_gf(o, C.GF(2), p)
 751   n = len(tl)
 752   yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ o)
 753   cfinal = tl ^ yfinal[:n]
 754   a ^= (tl + yfinal[n:]) ^ mul_blk_gf(o, C.GF(3), p)
 755   y.put(cfinal)
 756   t = E.encrypt(a)
 757   if h: t ^= pmac2(E, h)
 758   return C.ByteString(y), C.ByteString(t[:tsz])
 759
 760 def ocb2dec(E, n, h, y, t):
 761   blksz = E.__class__.blksz
 762   p = prim(8*blksz)
 763   L = E.encrypt(n)
 764   o = mul_blk_gf(L, C.GF(2), p)
 765   a = Z(blksz)
 766   v, tl = blocks(y, blksz)
 767   m = C.WriteBuffer()
 768   for x in v:
 769     u = E.encrypt(x ^ o) ^ o
 770     y.put(u)
 771     a ^= u
 772     o = mul_blk_gf(o, C.GF(2), p)
 773   n = len(tl)
 774   yfinal = E.encrypt(C.MP(8*n).storeb(blksz) ^ o)
 775   mfinal = tl ^ yfinal[:n]
 776   a ^= (mfinal + yfinal[n:]) ^ mul_blk_gf(o, C.GF(3), p)
 777   m.put(mfinal)
 778   u = E.encrypt(a)
 779   if h: u ^= pmac2(E, h)
 780   if t == u[:len(t)]: return C.ByteString(m),
 781   else: return None,
 782
 783 OCB3_STRETCH = {  4: ( 4,  17),
 784                   8: ( 5,  25),
 785                  12: ( 6,  33),
 786                  16: ( 6,   8),
 787                  24: ( 7,  40),
 788                  32: ( 8,   1),
 789                  48: ( 8,  80),
 790                  64: ( 8, 176),
 791                  96: ( 9, 160),
 792                 128: ( 9, 352),
 793                 200: (10, 192) }
 794
 795 def ocb3nonce(E, n, tsz):
 796
 797   ## Figure out how much we need to glue onto the nonce.  This ends up being
 798   ## [t mod w]_v || 0^p || 1 || N, where w is the block size in bits, t is
 799   ## the tag length in bits, v = floor(log_2(w - 1)) + 1, and p = w - l(N) -
 800   ## v - 1.  But this is an annoying way to think about it because of the
 801   ## byte misalignment.  Instead, think of it as a byte-aligned prefix
 802   ## encoding the tag and an `is the nonce full-length' flag, followed by
 803   ## optional padding, and then the nonce:
 804   ##
 805   ##    F || N                  if l(N) = w - f
 806   ##    F || 0^p || 1 || N      otherwise
 807   ##
 808   ## where F is [t mod w]_v || 0^{f-v-1} || b; f = floor(log_2(w - 1)) + 2;
 809   ## b is 1 if l(N) = w - f, or 0 otherwise; and p = w - f - l(N) - 1.
 810   blksz = E.__class__.blksz
 811   tszbits = min(C.MP(8*blksz - 1).nbits, 8)
 812   fwd = tszbits/8 + 1
 813   f = 8*(tsz%blksz) << + 8*fwd - tszbits
 814
 815   ## Form the augmented nonce.
 816   nb = C.WriteBuffer()
 817   nsz, nwd = len(n), blksz - fwd
 818   if nsz == nwd: f |= 1
 819   nb.put(C.MP(f).storeb(fwd))
 820   if nsz < nwd: nb.zero(nwd - nsz - 1).putu8(1)
 821   nb.put(n)
 822   nn = C.ByteString(nb)
 823   if VERBOSE: print 'aug-nonce = %s' % hex(nn)
 824
 825   ## Calculate the initial offset.
 826   split, shift = OCB3_STRETCH[blksz]
 827   t2pw = C.MP(0).setbit(8*blksz) - 1
 828   lomask = (C.MP(0).setbit(split) - 1)
 829   himask = ~lomask
 830   top, bottom = nn&himask.storeb2c(blksz), C.MP.loadb(nn)&lomask
 831   ktop = C.MP.loadb(E.encrypt(top))
 832   stretch = (ktop << 8*blksz) | (ktop ^ (ktop << shift)&t2pw)
 833   o = (stretch >> 8*blksz - bottom).storeb(blksz)
 834   if VERBOSE:
 835     print 'stretch = %s' % hex(stretch.storeb(2*blksz))
 836     print 'Z[0] = %s' % hex(o)
 837
 838   return o
 839
 840 def ocb3enc(E, n, h, m, tsz = None):
 841   blksz = E.__class__.blksz
 842   if tsz is None: tsz = blksz
 843   Lstar, Ldollar, Lgamma = ocb3_masks(E)
 844   if VERBOSE: dump_ocb3(E)
 845
 846   ## Set things up.
 847   o = ocb3nonce(E, n, tsz)
 848   a = C.ByteString.zero(blksz)
 849
 850   ## Split the message into blocks.
 851   i = 0
 852   y = C.WriteBuffer()
 853   v, tl = blocks0(m, blksz)
 854   for x in v:
 855     i += 1
 856     b = ntz(i)
 857     o ^= Lgamma[b]
 858     a ^= x
 859     if VERBOSE:
 860       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 861       print 'A[%d]: %s' % (i, hex(a))
 862     y.put(E.encrypt(x ^ o) ^ o)
 863   if tl:
 864     o ^= Lstar
 865     n = len(tl)
 866     pad = E.encrypt(o)
 867     a ^= pad10star(tl, blksz)
 868     if VERBOSE:
 869       print 'Z[%d]: * -> %s' % (i, hex(o))
 870       print 'A[%d]: %s' % (i, hex(a))
 871     y.put(tl ^ pad[0:n])
 872   o ^= Ldollar
 873   t = E.encrypt(a ^ o) ^ pmac3(E, h)
 874   return C.ByteString(y), C.ByteString(t[:tsz])
 875
 876 def ocb3dec(E, n, h, y, t):
 877   blksz = E.__class__.blksz
 878   tsz = len(t)
 879   Lstar, Ldollar, Lgamma = ocb3_masks(E)
 880   if VERBOSE: dump_ocb3(E)
 881
 882   ## Set things up.
 883   o = ocb3nonce(E, n, tsz)
 884   a = C.ByteString.zero(blksz)
 885
 886   ## Split the message into blocks.
 887   i = 0
 888   m = C.WriteBuffer()
 889   v, tl = blocks0(y, blksz)
 890   for x in v:
 891     i += 1
 892     b = ntz(i)
 893     o ^= Lgamma[b]
 894     if VERBOSE:
 895       print 'Z[%d]: %d -> %s' % (i, b, hex(o))
 896       print 'A[%d]: %s' % (i, hex(a))
 897     u = E.encrypt(x ^ o) ^ o
 898     m.put(u)
 899     a ^= u
 900   if tl:
 901     o ^= Lstar
 902     n = len(tl)
 903     pad = E.encrypt(o)
 904     if VERBOSE:
 905       print 'Z[%d]: * -> %s' % (i, hex(o))
 906       print 'A[%d]: %s' % (i, hex(a))
 907     u = tl ^ pad[0:n]
 908     m.put(u)
 909     a ^= pad10star(u, blksz)
 910   o ^= Ldollar
 911   u = E.encrypt(a ^ o) ^ pmac3(E, h)
 912   if t == u[:tsz]: return C.ByteString(m),
 913   else: return None,
 914
 915 def ocbgen(bc):
 916   w = bc.blksz
 917   return [(w, 0, 0), (w, 1, 0), (w, 0, 1),
 918           (w, 0, 3*w),
 919           (w, 3*w, 3*w),
 920           (w, 0, 3*w + 5),
 921           (w, 3*w - 5, 3*w + 5)]
 922
 923 def ocb3gen(bc):
 924   w = bc.blksz
 925   return [(w - 2, 0, 0), (w - 2, 1, 0), (w - 2, 0, 1),
 926           (w - 5, 0, 3*w),
 927           (w - 3, 3*w, 3*w),
 928           (w - 2, 0, 3*w + 5),
 929           (w - 2, 3*w - 5, 3*w + 5)]
 930
 931 def ocb3_mct(bc, ksz, tsz):
 932   k = C.ByteString(C.WriteBuffer().zero(ksz - 4).putu32(8*tsz))
 933   E = bc(k)
 934   n = C.MP(1)
 935   nw = bc.blksz - 4
 936   cbuf = C.WriteBuffer()
 937   for i in xrange(128):
 938     s = C.ByteString.zero(i)
 939     y, t = ocb3enc(E, n.storeb(nw), s, s, tsz); n += 1; cbuf.put(y).put(t)
 940     y, t = ocb3enc(E, n.storeb(nw), EMPTY, s, tsz); n += 1; cbuf.put(y).put(t)
 941     y, t = ocb3enc(E, n.storeb(nw), s, EMPTY, tsz); n += 1; cbuf.put(y).put(t)
 942   _, t = ocb3enc(E, n.storeb(nw), C.ByteString(cbuf), EMPTY, tsz)
 943   print hex(t)
 944
 945 def ocb3_mct2(bc):
 946   k = C.bytes('000102030405060708090a0b0c0d0e0f')
 947   E = bc(k)
 948   tsz = min(E.blksz, 32)
 949   n = C.MP(1)
 950   cbuf = C.WriteBuffer()
 951   for i in xrange(128):
 952     sbuf = C.WriteBuffer()
 953     for j in xrange(i): sbuf.putu8(j)
 954     s = C.ByteString(sbuf)
 955     y, t = ocb3enc(E, n.storeb(2), s, s, tsz); n += 1; cbuf.put(y).put(t)
 956     y, t = ocb3enc(E, n.storeb(2), EMPTY, s, tsz); n += 1; cbuf.put(y).put(t)
 957     y, t = ocb3enc(E, n.storeb(2), s, EMPTY, tsz); n += 1; cbuf.put(y).put(t)
 958   _, t = ocb3enc(E, n.storeb(2), C.ByteString(cbuf), EMPTY, tsz)
 959   print hex(t)
 960
 961 ###--------------------------------------------------------------------------
 962 ### Main program.
 963
 964 class struct (object):
 965   def __init__(me, **kw):
 966     me.__dict__.update(kw)
 967
 968 binarg = struct(mk = R.block, parse = C.bytes, show = safehex)
 969 intarg = struct(mk = lambda x: x, parse = int, show = None)
 970
 971 MODEMAP = { 'eax-enc': (eaxgen, 3*[binarg] + [intarg], eaxenc),
 972             'eax-dec': (dummygen, 4*[binarg], eaxdec),
 973             'ccm-enc': (ccmgen, 3*[binarg] + [intarg], ccmenc),
 974             'ccm-dec': (dummygen, 4*[binarg], ccmdec),
 975             'cmac': (cmacgen, [binarg], cmac),
 976             'gcm-enc': (gcmgen, 3*[binarg] + [intarg], gcmenc),
 977             'gcm-dec': (dummygen, 4*[binarg], gcmdec),
 978             'ocb1-enc': (ocbgen, 3*[binarg] + [intarg], ocb1enc),
 979             'ocb1-dec': (dummygen, 4*[binarg], ocb1dec),
 980             'ocb2-enc': (ocbgen, 3*[binarg] + [intarg], ocb2enc),
 981             'ocb2-dec': (dummygen, 4*[binarg], ocb2dec),
 982             'ocb3-enc': (ocb3gen, 3*[binarg] + [intarg], ocb3enc),
 983             'ocb3-dec': (dummygen, 4*[binarg], ocb3dec),
 984             'pmac1': (pmacgen, [binarg], pmac1_pub) }
 985
 986 mode = argv[1]
 987 if len(argv) == 3 and mode == 'gcm-mul':
 988   VERBOSE = False
 989   nbits = int(argv[2])
 990   gcm_mul_tests(nbits)
 991   exit(0)
 992 bc = None
 993 for d in CUSTOM, C.gcprps:
 994   try: bc = d[argv[2]]
 995   except KeyError: pass
 996   else: break
 997 if bc is None: raise KeyError, argv[2]
 998 if len(argv) == 5 and mode == 'ocb3-mct':
 999   VERBOSE = False
1000   ksz, tsz = int(argv[3]), int(argv[4])
1001   ocb3_mct(bc, ksz, tsz)
1002   exit(0)
1003 if len(argv) == 3 and mode == 'ocb3-mct2':
1004   VERBOSE = False
1005   ocb3_mct2(bc)
1006   exit(0)
1007 if len(argv) == 3:
1008   VERBOSE = False
1009   gen, argty, func = MODEMAP[mode]
1010   if mode.endswith('-enc'): mode = mode[:-4]
1011   print '%s-%s {' % (bc.name, mode)
1012   for ksz in keylens(bc.keysz):
1013     for argvals in gen(bc):
1014       k = R.block(ksz)
1015       args = [t.mk(a) for t, a in izip(argty, argvals)]
1016       rets = func(bc(k), *args)
1017       print '  %s' % safehex(k)
1018       for t, a in izip(argty, args):
1019         if t.show: print '    %s' % t.show(a)
1020       for r, lastp in with_lastp(rets):
1021         print '    %s%s' % (safehex(r), lastp and ';' or '')
1022   print '}'
1023 else:
1024   VERBOSE = True
1025   k = C.bytes(argv[3])
1026   gen, argty, func = MODEMAP[mode]
1027   args = [t.parse(a) for t, a in izip(argty, argv[4:])]
1028   rets = func(bc(k), *args)
1029   for r in rets:
1030     if r is None: print "X"
1031     else: print hex(r)
1032
1033 ###----- That's all, folks --------------------------------------------------