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t642_sat.py
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t642_sat.py
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# tango642 4.3.9 SAT solving simulation -
# finds a key specified in seed_i and hcv[].
# requires autosat from https://github.com/petersn/autosat
# and python-sat
#
# use "time python t642_sat.py" to measure solving time.
# increase "bits" (an even value) to estimate solving complexity. "bits=64"
# corresponds to real tango642 variable size. a minimal reasonable "bits"
# value is 6; lower values solve instantly. base exponential time increase can
# be assessed by setting hci=0 and incrementally assigning various "bits"
# values. note that the SAT solver may have to consider most of the system
# anyway, so a time difference between various "hci" values may not be
# pronounced. the time exponent dependence on "hci" itself depends on "bits"
# asymptotically, with higher "bits" values producing a more linear "hci*bits"
# exponent.
import autosat
##### simulation parameters
bits = 6 # state variable size
hci = 2 # number of keyed hash elements in use (key length-1)
ivlen = 4 # nonce vector length
seed_i = 4 # keyed prng init (key value 1)
hcv = [3,14,3,13,14,4,2,15,2,5,6,11,9,1,11,5,8,6,10,7,5,6,3,10,3,0,2,9,9,12,15,11] # key values
iv = [15,9,4,6] # nonce vector
hc = 16 # keyed hash array length
fc = 15 # firewall prng init length
num_obs = 16 # number of observations to use for solving (*4)
#####
def inibits(inst,l,ini):
result = []
for i in range(l):
if( (ini>>i)&1 ):
v=True
else:
v=False
result.append(inst.get_constant(v))
return result
@autosat.sat
def full_adder(a, b, carry_in):
r = a + b + carry_in
return r & 1, (r & 2) >> 1
def add(a, b):
assert len(a) == len(b)
carry = False
result = []
for a_bit, b_bit in zip(a, b):
sum_bit, carry = full_adder(a_bit, b_bit, carry)
result.append(sum_bit)
return result
def xor(a, b):
assert len(a) == len(b)
return [i ^ j for i, j in zip(a, b)]
def and_(a, b):
assert len(a) == len(b)
return [i & j for i, j in zip(a, b)]
def mul(a, b):
assert len(a) == len(b)
result = [a[0] & bit for bit in b]
for i in range(1, len(a)):
addend = [a[i] & bit for bit in b[:-i]]
result[i:] = add(result[i:], addend)
return result
obs = [] # observations
bits2 = bits>>1
bmask = (1<<bits)-1
rawbits5 = 0
rawbitsA = 0
for i in range(bits2):
rawbits5 <<= 2
rawbits5 |= 0x1
rawbitsA <<= 2
rawbitsA |= 0x2
def prvhash_core_calc(seed, lcg, h):
seed = seed * ( lcg * 2 + 1 )
seed &= bmask
rs = seed>>bits2 | seed<<bits2
rs &= bmask
h += rs + rawbitsA
h &= bmask
lcg += seed + rawbits5
lcg &= bmask
seed ^= h
out = lcg ^ rs
return seed, lcg, h, out
# calculate real outputs
calc_seed = seed_i&bmask
calc_lcg = 0
calc_h = []
calc_seed1 = 0
calc_lcg1 = 0
calc_seed2 = 0
calc_lcg2 = 0
calc_seed3 = 0
calc_lcg3 = 0
calc_seed4 = 0
calc_lcg4 = 0
calc_h2 = [0,0,0,0,0]
for i in range(hc):
if(i < hci):
calc_h.append(hcv[i]&bmask)
else:
calc_h.append(0)
calc_x = 0
calc_x2 = 0
ivpos = 0
for i in range(5):
calc_seed, calc_lcg, calc_h[calc_x%hc], out1 = prvhash_core_calc(calc_seed, calc_lcg, calc_h[calc_x%hc])
for i in range(hc):
if((i&1)==1 and ivpos < ivlen):
calc_seed ^= iv[ivpos]&bmask
calc_lcg ^= iv[ivpos]&bmask
ivpos += 1
calc_seed, calc_lcg, calc_h[calc_x%hc], out1 = prvhash_core_calc(calc_seed, calc_lcg, calc_h[calc_x%hc])
calc_x += 1
for i in range(hc+1):
calc_seed, calc_lcg, calc_h[calc_x%hc], out1 = prvhash_core_calc(calc_seed, calc_lcg, calc_h[calc_x%hc])
calc_x += 1
for i in range(fc+num_obs):
calc_seed, calc_lcg, calc_h[calc_x%hc], out1 = prvhash_core_calc(calc_seed, calc_lcg, calc_h[calc_x%hc])
calc_x += 1
calc_seed4 ^= out1
calc_seed1, calc_lcg1, calc_h2[(calc_x2+0)%5], outf1 = prvhash_core_calc(calc_seed1, calc_lcg1, calc_h2[(calc_x2+0)%5])
calc_seed2, calc_lcg2, calc_h2[(calc_x2+1)%5], outf2 = prvhash_core_calc(calc_seed2, calc_lcg2, calc_h2[(calc_x2+1)%5])
calc_seed3, calc_lcg3, calc_h2[(calc_x2+2)%5], outf3 = prvhash_core_calc(calc_seed3, calc_lcg3, calc_h2[(calc_x2+2)%5])
calc_seed4, calc_lcg4, calc_h2[(calc_x2+3)%5], outf4 = prvhash_core_calc(calc_seed4, calc_lcg4, calc_h2[(calc_x2+3)%5])
calc_x2 += 1
if(i>=fc):
obs.append(outf1)
obs.append(outf2)
obs.append(outf3)
obs.append(outf4)
print("----")
# solve initial state
inst = autosat.Instance()
BITR5 = inibits(inst, bits, rawbits5)
BITRA = inibits(inst, bits, rawbitsA)
def prvhash_core_sat(seed, lcg, h):
seed = mul(seed, [True] + lcg[:-1])
rs = seed[bits2:] + seed[:bits2]
h = add(h, add(rs, BITRA))
lcg = add(lcg, add(seed, BITR5))
seed = xor(seed, h)
out = xor(lcg, rs)
return seed, lcg, h, out
start_seed = inst.new_vars(bits)
start_h = []
seed = start_seed[:]
h = []
for i in range(hc):
if(i < hci):
start_h.append(inst.new_vars(bits))
h.append(start_h[i][:])
else:
h.append(inibits(inst, bits, 0))
lcg = inibits(inst, bits, 0)
seed1 = inibits(inst, bits, 0)
lcg1 = inibits(inst, bits, 0)
seed2 = inibits(inst, bits, 0)
lcg2 = inibits(inst, bits, 0)
seed3 = inibits(inst, bits, 0)
lcg3 = inibits(inst, bits, 0)
seed4 = inibits(inst, bits, 0)
lcg4 = inibits(inst, bits, 0)
h2 = [inibits(inst, bits, 0),inibits(inst, bits, 0),inibits(inst, bits, 0),inibits(inst, bits, 0),inibits(inst, bits, 0)]
x = 0
x2 = 0
ivpos = 0
for k in range(5):
seed, lcg, h[x % hc], out1 = prvhash_core_sat(seed, lcg, h[x % hc])
for k in range(hc):
if((k&1)==1 and ivpos < ivlen):
seed = xor(seed, inibits(inst,bits,iv[ivpos]))
lcg = xor(lcg, inibits(inst,bits,iv[ivpos]))
ivpos += 1
seed, lcg, h[x % hc], out1 = prvhash_core_sat(seed, lcg, h[x % hc])
x += 1
for k in range(hc+1):
seed, lcg, h[x % hc], out1 = prvhash_core_sat(seed, lcg, h[x % hc])
x += 1
for k in range(fc+num_obs):
seed, lcg, h[x % hc], out1 = prvhash_core_sat(seed, lcg, h[x % hc])
x += 1
seed4 = xor(seed4, out1)
seed1, lcg1, h2[(x2+0)%5], outf1 = prvhash_core_sat(seed1, lcg1, h2[(x2+0)%5])
seed2, lcg2, h2[(x2+1)%5], outf2 = prvhash_core_sat(seed2, lcg2, h2[(x2+1)%5])
seed3, lcg3, h2[(x2+2)%5], outf3 = prvhash_core_sat(seed3, lcg3, h2[(x2+2)%5])
seed4, lcg4, h2[(x2+3)%5], outf4 = prvhash_core_sat(seed4, lcg4, h2[(x2+3)%5])
x2 += 1
if(k>=fc):
for i, b in enumerate(outf1):
b.make_equal(bool((obs[(k-fc)*4+0] >> i) & 1))
for i, b in enumerate(outf2):
b.make_equal(bool((obs[(k-fc)*4+1] >> i) & 1))
for i, b in enumerate(outf3):
b.make_equal(bool((obs[(k-fc)*4+2] >> i) & 1))
for i, b in enumerate(outf4):
b.make_equal(bool((obs[(k-fc)*4+3] >> i) & 1))
model = inst.solve(solver_name="Glucose3",decode_model=False)
#print(model)
print("seed = %4i (%4i)" % (autosat.decode_number(start_seed, model), (seed_i&bmask)))
for i in range(hci):
print("hash = %4i (%4i)" % (autosat.decode_number(start_h[i], model), (hcv[i]&bmask)))