def Inv(a):
""" Invert a non-zero value """
t = [types.sint() for i in range(3)]
c = [types.cint() for i in range(2)]
one = types.cint()
ldi(one, 1)
inverse(t[0], t[1])
s = t[0]*a
asm_open(c[0], s)
# avoid division by zero for benchmarking
divc(c[1], one, c[0])
#divc(c[1], c[0], one)
return c[1]*t[0]
def Trunc(a, l, m, kappa, compute_modulo=False):
""" Oblivious truncation by secret m """
if l == 1:
if compute_modulo:
return a * m, 1 + m
else:
return a * (1 - m)
r = [types.sint() for i in range(l)]
r_dprime = types.sint(0)
r_prime = types.sint(0)
rk = types.sint()
c = types.cint()
ci = [types.cint() for i in range(l)]
d = types.sint()
x, pow2m = B2U(m, l, kappa)
#assert(pow2m.value == 2**m.value)
#assert(sum(b.value for b in x) == m.value)
for i in range(l):
bit(r[i])
t1 = two_power(i) * r[i]
t2 = t1*x[i]
r_prime += t2
r_dprime += t1 - t2
#assert(r_prime.value == (sum(2**i*x[i].value*r[i].value for i in range(l)) % comparison.program.P))
comparison.PRandInt(rk, kappa)
r_dprime += two_power(l) * rk
#assert(r_dprime.value == (2**l * rk.value + sum(2**i*(1 - x[i].value)*r[i].value for i in range(l)) % comparison.program.P))
asm_open(c, a + r_dprime + r_prime)
for i in range(1,l):
ci[i] = c % two_power(i)
#assert(ci[i].value == c.value % 2**i)
c_dprime = sum(ci[i]*(x[i-1] - x[i]) for i in range(1,l))
#assert(c_dprime.value == (sum(ci[i].value*(x[i-1].value - x[i].value) for i in range(1,l)) % comparison.program.P))
lts(d, c_dprime, r_prime, l, kappa)
if compute_modulo:
b = c_dprime - r_prime + pow2m * d
return b, pow2m
else:
to_shift = a - c_dprime + r_prime
if program.Program.prog.options.ring:
shifted = TruncInRing(to_shift, l, pow2m)
else:
pow2inv = Inv(pow2m)
#assert(pow2inv.value * pow2m.value % comparison.program.P == 1)
shifted = to_shift * pow2inv
b = shifted - d
return b
def maskField(a, k, kappa):
r_dprime = types.sint()
r_prime = types.sint()
c = types.cint()
r = [types.sint() for i in range(k)]
comparison.PRandM(r_dprime, r_prime, r, k, k, kappa)
asm_open(c, a + two_power(k) * r_dprime + r_prime)# + 2**(k-1))
return c, r
def Pow2(a, l, kappa):
m = int(ceil(log(l, 2)))
t = BitDec(a, m, m, kappa)
x = [types.sint() for i in range(m)]
pow2k = [types.cint() for i in range(m)]
for i in range(m):
pow2k[i] = two_power(2**i)
t[i] = t[i]*pow2k[i] + 1 - t[i]
return KMul(t)
def two_power(n):
if isinstance(n, int) and n < 31:
return 2**n
else:
max = types.cint(1) << 31
res = 2**(n%31)
for i in range(n / 31):
res *= max
return res
def AppRcr(b, k, f, kappa):
"""
Approximate reciprocal of [b]:
Given [b], compute [1/b]
"""
alpha = types.cint(int(2.9142 * (2**k)))
c, v = Norm(b, k, f, kappa)
d = alpha - 2 * c
w = d * v
w = TruncPr(w, 2 * k, 2 * (k - f))
return w
def SDiv(a, b, l, kappa):
theta = int(ceil(log(l / 3.5) / log(2)))
alpha = two_power(2*l)
beta = 1 / types.cint(two_power(l))
w = types.cint(int(2.9142 * two_power(l))) - 2 * b
x = alpha - b * w
y = a * w
y = TruncPr(y, 2 * l, l, kappa)
x2 = types.sint()
comparison.Mod2m(x2, x, 2 * l + 1, l, kappa, False)
x1 = (x - x2) * beta
for i in range(theta-1):
y = y * (x1 + two_power(l)) + TruncPr(y * x2, 2 * l, l, kappa)
y = TruncPr(y, 2 * l + 1, l + 1, kappa)
x = x1 * x2 + TruncPr(x2**2, 2 * l + 1, l + 1, kappa)
x = x1 * x1 + TruncPr(x, 2 * l + 1, l - 1, kappa)
x2 = types.sint()
comparison.Mod2m(x2, x, 2 * l, l, kappa, False)
x1 = (x - x2) * beta
y = y * (x1 + two_power(l)) + TruncPr(y * x2, 2 * l, l, kappa)
y = TruncPr(y, 2 * l + 1, l - 1, kappa)
return y
def TruncRoundNearest(a, k, m, kappa):
"""
Returns a / 2^m, rounded to the nearest integer.
k: bit length of m
m: compile-time integer
"""
from types import sint, cint
from library import reveal, load_int_to_secret
if m == 1:
if program.options.ring:
lsb = Mod2mRing(None, a, k, 1, False)
return TruncRing(None, a + lsb, k + 1, 1, False)
else:
lsb = sint()
Mod2(lsb, a, k, kappa, False)
return (a + lsb) / 2
r_dprime = sint()
r_prime = sint()
r = [sint() for i in range(m)]
u = sint()
PRandM(r_dprime, r_prime, r, k, m, kappa)
c = reveal((cint(1) << (k - 1)) + a + (cint(1) << m) * r_dprime + r_prime)
c_prime = c % (cint(1) << (m - 1))
if const_rounds:
BitLTC1(u, c_prime, r[:-1], kappa)
else:
BitLTL(u, c_prime, r[:-1], kappa)
bit = ((c - c_prime) >> (m - 1)) % 2
xor = bit + u - 2 * bit * u
prod = xor * r[-1]
# u_prime = xor * u + (1 - xor) * r[-1]
u_prime = bit * u + u - 2 * bit * u + r[-1] - prod
a_prime = (c % (cint(1) << m)) - r_prime + (cint(1) << m) * u_prime
d = (a - a_prime) >> m
rounding = xor + r[-1] - 2 * prod
return d + rounding
def B2U_from_Pow2(pow2a, l, kappa):
#assert(pow2a.value == 2**a.value)
r = [types.sint() for i in range(l)]
t = types.sint()
c = types.cint()
for i in range(l):
bit(r[i])
comparison.PRandInt(t, kappa)
asm_open(c, pow2a + two_power(l) * t + sum(two_power(i)*r[i] for i in range(l)))
comparison.program.curr_tape.require_bit_length(l + kappa)
c = list(bits(c, l))
x = [c[i] + r[i] - 2*c[i]*r[i] for i in range(l)]
#print ' '.join(str(b.value) for b in x)
y = PreOR(x, kappa)
#print ' '.join(str(b.value) for b in y)
return [1 - y[i] for i in range(l)]
def SDiv_mono(a, b, l, kappa):
theta = int(ceil(log(l / 3.5) / log(2)))
alpha = two_power(2*l)
w = types.cint(int(2.9142 * two_power(l))) - 2 * b
x = alpha - b * w
y = a * w
y = TruncPr(y, 2 * l + 1, l + 1, kappa)
for i in range(theta-1):
y = y * (alpha + x)
# keep y with l bits
y = TruncPr(y, 3 * l, 2 * l, kappa)
x = x**2
# keep x with 2l bits
x = TruncPr(x, 4 * l, 2 * l, kappa)
y = y * (alpha + x)
y = TruncPr(y, 3 * l, 2 * l, kappa)
return y
def SDiv_mono(a, b, l, kappa):
theta = int(ceil(log(l / 3.5) / log(2)))
alpha = two_power(2*l)
w = types.cint(int(2.9142 * two_power(l))) - 2 * b
x = alpha - b * w
y = a * w
y = TruncPr(y, 2 * l + 1, l + 1, kappa)
for i in range(theta-1):
y = y * (alpha + x)
# keep y with l bits
y = TruncPr(y, 3 * l, 2 * l, kappa)
x = x**2
# keep x with 2l bits
x = TruncPr(x, 4 * l, 2 * l, kappa)
y = y * (alpha + x)
y = TruncPr(y, 3 * l, 2 * l, kappa)
return y
def B2U(a, l, kappa):
pow2a = Pow2(a, l, kappa)
#assert(pow2a.value == 2**a.value)
r = [types.sint() for i in range(l)]
t = types.sint()
c = types.cint()
for i in range(l):
bit(r[i])
comparison.PRandInt(t, kappa)
asm_open(c, pow2a + two_power(l) * t + sum(two_power(i)*r[i] for i in range(l)))
comparison.program.curr_tape.require_bit_length(l + kappa)
c = list(bits(c, l))
x = [c[i] + r[i] - 2*c[i]*r[i] for i in range(l)]
#print ' '.join(str(b.value) for b in x)
y = PreOR(x, kappa)
#print ' '.join(str(b.value) for b in y)
return [1 - y[i] for i in range(l)], pow2a
def FPDiv(a, b, k, f, kappa):
theta = int(ceil(log(k / 3.5)))
alpha = types.cint(1 * two_power(2 * f))
w = AppRcr(b, k, f, kappa)
x = alpha - b * w
y = a * w
y = TruncPr(y, 2 * k, f, kappa)
for i in range(theta):
y = y * (alpha + x)
x = x * x
y = TruncPr(y, 2 * k, 2 * f, kappa)
x = TruncPr(x, 2 * k, 2 * f, kappa)
y = y * (alpha + x)
y = TruncPr(y, 2 * k, 2 * f, kappa)
return y
def FPDiv(a, b, k, f, kappa):
theta = int(ceil(log(k/3.5)))
alpha = types.cint(1 * two_power(2*f))
w = AppRcr(b, k, f, kappa)
x = alpha - b * w
y = a * w
y = TruncPr(y, 2*k, f, kappa)
for i in range(theta):
y = y * (alpha + x)
x = x * x
y = TruncPr(y, 2*k, 2*f, kappa)
x = TruncPr(x, 2*k, 2*f, kappa)
y = y * (alpha + x)
y = TruncPr(y, 2*k, 2*f, kappa)
return y
def BitDec(a, k, m, kappa, bits_to_compute=None):
r_dprime = types.sint()
r_prime = types.sint()
c = types.cint()
r = [types.sint() for i in range(m)]
comparison.PRandM(r_dprime, r_prime, r, k, m, kappa)
#assert(r_prime.value == sum(r[i].value*2**i for i in range(m)) % comparison.program.P)
pow2 = two_power(k + kappa)
asm_open(c, pow2 + two_power(k) + a - two_power(m) * r_dprime - r_prime)
#rval = 2**m*r_dprime.value + r_prime.value
#assert(rval % 2**m == r_prime.value)
#assert(rval == (2**m*r_dprime.value + sum(r[i].value*2**i for i in range(m)) % comparison.program.P ))
try:
pass #assert(c.value == (2**(k + kappa) + 2**k + (a.value%2**k) - rval) % comparison.program.P)
except AssertionError:
print 'BitDec assertion failed'
print 'a =', a.value
print 'a mod 2^%d =' % k, (a.value % 2**k)
return BitAdd(list(bits(c, m)), r, bits_to_compute)[:-1]
def BitDecField(a, k, m, kappa, bits_to_compute=None):
r_dprime = types.sint()
r_prime = types.sint()
c = types.cint()
r = [types.sint() for i in range(m)]
comparison.PRandM(r_dprime, r_prime, r, k, m, kappa)
#assert(r_prime.value == sum(r[i].value*2**i for i in range(m)) % comparison.program.P)
pow2 = two_power(k + kappa)
asm_open(c, pow2 + two_power(k) + a - two_power(m)*r_dprime - r_prime)
#rval = 2**m*r_dprime.value + r_prime.value
#assert(rval % 2**m == r_prime.value)
#assert(rval == (2**m*r_dprime.value + sum(r[i].value*2**i for i in range(m)) % comparison.program.P ))
try:
pass#assert(c.value == (2**(k + kappa) + 2**k + (a.value%2**k) - rval) % comparison.program.P)
except AssertionError:
print 'BitDec assertion failed'
print 'a =', a.value
print 'a mod 2^%d =' % k, (a.value % 2**k)
return types.intbitint.bit_adder(list(bits(c,m)), r)
def SDiv(a, b, l, kappa, round_nearest=False):
theta = int(ceil(log(l / 3.5) / log(2)))
alpha = two_power(2 * l)
w = types.cint(int(2.9142 * two_power(l))) - 2 * b
x = alpha - b * w
y = a * w
y = y.round(2 * l + 1, l, kappa, round_nearest)
x2 = types.sint()
comparison.Mod2m(x2, x, 2 * l + 1, l, kappa, False)
x1 = comparison.TruncZeroes(x - x2, 2 * l + 1, l, True)
for i in range(theta - 1):
y = y * (x1 + two_power(l)) + (y * x2).round(2 * l, l, kappa,
round_nearest)
y = y.round(2 * l + 1, l + 1, kappa, round_nearest)
x = x1 * x2 + (x2**2).round(2 * l + 1, l + 1, kappa, round_nearest)
x = x1 * x1 + x.round(2 * l + 1, l - 1, kappa, round_nearest)
x2 = types.sint()
comparison.Mod2m(x2, x, 2 * l, l, kappa, False)
x1 = comparison.TruncZeroes(x - x2, 2 * l + 1, l, True)
y = y * (x1 + two_power(l)) + (y * x2).round(2 * l, l, kappa,
round_nearest)
y = y.round(2 * l + 1, l - 1, kappa, round_nearest)
return y
