def union(self, interval):
check_intervals_digits_coincide(self, interval)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) < mpfr(interval.lower):
min = self.lower
include_min = self.include_lower
elif mpfr(self.lower) > mpfr(interval.lower):
min = interval.lower
include_min = interval.include_lower
else:
min = interval.lower
include_min = interval.include_lower or self.include_lower
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.upper) < mpfr(interval.upper):
max = interval.upper
include_max = interval.include_upper
elif mpfr(self.upper) > mpfr(interval.upper):
max = self.upper
include_max = self.include_upper
else:
max = self.upper
include_max = self.include_upper or interval.include_upper
return Interval(min, max, include_min, include_max, self.digits)
def intersection(self, interval):
check_intervals_digits_coincide(self, interval)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundToNearest,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) > mpfr(interval.upper) or mpfr(
self.upper) < mpfr(interval.lower):
return empty_interval
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) > mpfr(interval.upper) or mpfr(
self.upper) < mpfr(interval.lower):
return empty_interval
if mpfr(self.lower) > mpfr(interval.lower):
min_bound = self.lower
else:
min_bound = interval.lower
#min_bound=round_number_down_to_digits(max(mpfr(self.lower), mpfr(interval.lower)), self.digits)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) > mpfr(interval.upper) or mpfr(
self.upper) < mpfr(interval.lower):
return empty_interval
if mpfr(self.upper) < mpfr(interval.upper):
max_bound = self.upper
else:
max_bound = interval.upper
#max_bound=round_number_up_to_digits(min(mpfr(self.upper),mpfr(interval.upper)), self.digits)
return Interval(min_bound, max_bound, True, True, self.digits)
def adjust_ret_list(retlist):
retlist[0].cdf_low="0.0"
retlist[-1].cdf_up="1.0"
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
min_value=gmpy2.exp10(-digits_for_input_cdf)
current=min_value
for pbox in retlist:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_low)) or gmpy2.mpfr(pbox.cdf_low)<current:
pbox.cdf_low=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
current=current+min_value
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_up)) or gmpy2.mpfr(pbox.cdf_up)<current:
pbox.cdf_up=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
current=gmpy2.sub(gmpy2.mpfr("1.0"), min_value)
for pbox in retlist[::-1]:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.mpfr(pbox.cdf_up)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_up)>current:
pbox.cdf_up=round_number_up_to_digits(current, digits_for_input_cdf)
current=gmpy2.sub(current, min_value)
if gmpy2.mpfr(pbox.cdf_low)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_low)>current:
pbox.cdf_low=round_number_up_to_digits(current, digits_for_input_cdf)
retlist[0].cdf_low = "0.0"
retlist[-1].cdf_up = "1.0"
return retlist
def subtraction(self, interval):
reset_default_precision()
res_inc_left = False
res_inc_right = False
if self.include_lower and interval.include_lower:
res_inc_left = True
if self.include_upper and interval.include_upper:
res_inc_right = True
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(mpfr(self.lower), mpfr(interval.upper))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.sub(mpfr(self.upper), mpfr(interval.lower))
if res_left <= res_right:
res_right = round_number_up_to_digits(res_right, self.digits)
res_left = round_number_down_to_digits(res_left, self.digits)
return Interval(res_left, res_right, res_inc_left, res_inc_right,
self.digits)
else:
res_right = round_number_down_to_digits(res_right, self.digits)
res_left = round_number_up_to_digits(res_left, self.digits)
return Interval(res_right, res_left, res_inc_right, res_inc_left,
self.digits)
def check_interval_is_zero(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
left = mpfr(interval.lower)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
right = mpfr(interval.upper)
if gmpy2.is_zero(left) and gmpy2.is_zero(right):
return True
return False
def round_value_to_interval(str_value):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = mpfr(str_value)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = mpfr(str_value)
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True,
digits_for_range)
def check_sterbenz_apply(interval1, interval2):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
two_y_left = gmpy2.mul(mpfr("2.0"), mpfr(interval2.lower))
two_x_left = gmpy2.mul(mpfr("2.0"), mpfr(interval1.lower))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
y_right = mpfr(interval2.upper)
x_right = mpfr(interval1.upper)
if x_right <= two_y_left and y_right <= two_x_left:
return True
return False
def compute_middle_point_given_interval(low, upper):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.add(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.add(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True,
digits_for_range)
def compute_uncertainty_given_interval(low, upper):
coefficients = {}
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.sub(gmpy2.div(mpfr(upper), mpfr("2.0")),
gmpy2.div(mpfr(low), mpfr("2.0")))
coefficients[AffineManager.get_new_error_index()]=\
Interval(round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True, True, digits_for_range)
return coefficients
def initConstants(cls): from math import sqrt def nextPrime(n=2): while True: for factor in range(2,int(sqrt(n))+1): if n % factor == 0: break else: yield n n += 1 # Find the first nRounds primes npgen = nextPrime() primes = [next(npgen) for x in range(cls.nRounds)] fb_mul = 2 ** cls.wordBits def getFractionalBits(n): return int((n - int(n)) * fb_mul) if cls.use_gmp: from gmpy2 import context,set_context,sqrt,cbrt set_context(context(precision=75)) else: cbrt = lambda n: pow(n, 1 / 3) # First wordBits bits of the fractional parts of the square roots of the first 8 primes H = (getFractionalBits(sqrt(n)) for n in primes[:8]) # First wordBits bits of the fractional parts of the cube roots of the first nRounds primes K = (getFractionalBits(cbrt(n)) for n in primes) cls.H_init = tuple(H) cls.K = tuple(K)
def main23(N):
c=gmpy2.context()
c.precision=len(str(N))+20
c.real_prec=len(str(N))+20
gmpy2.set_context(c)
assert N==gmpy2.mpz(N)
N=gmpy2.mpz(N)
A=find_sqrt(6*N)
A = gmpy2.mpz(A)
assert ( (A-1)**2<6*N<A**2 ),'not found'
Atag = A
for iA in xrange(-2**20,2**20):
A = Atag + iA
s =A**2-N
x = gmpy2.sqrt(s)
try:
x = gmpy2.mpz(x)
except:continue
'''print x**2 > s , x**2 < s
while x**2>s:
x-=1
print 1,
print x**2 > s , x**2 < s'''
for p in [(A-x)/2,(A-x)/3,(A+x)/2,(A+x)/3 ]:
q = N/p
if p*q==N:
print gmpy2.is_prime(q)
print gmpy2.is_prime(p)
print min(p,q)
assert False,'bla'
def main(N):
c=gmpy2.context()
c.precision=len(str(N))+20
c.real_prec=len(str(N))+20
gmpy2.set_context(c)
assert N==gmpy2.mpz(N)
N=gmpy2.mpz(N)
A=find_sqrt(N)
A = gmpy2.mpz(A)
assert ( (A-1)**2<N<A**2 ),'not found'
Atag = A
for iA in xrange(-2**20,2**20):
A = Atag + iA
s =A**2-N
x = gmpy2.sqrt(s)
try:
x = gmpy2.mpz(x)
except:continue
print x**2 > s , x**2 < s
'''while x**2>s:
x-=1
print 1,'''
print x**2 > s , x**2 < s
p = A-x
q = A+x
q = N/p
if p*q==N:
print gmpy2.is_prime(q)
print gmpy2.is_prime(p)
print min(p,q)
break
def set_prec(prc=None):
"""
set the precision
pass None to get current precision
prc is the number of digits that should be accurate in base two
"""
#note:
# precision is defined in base 2. It needs to be redefined in the base
# that is being used so as the number in the new base so it doesn't lose
# precision. That is, the number shouldn't return with trailing garbage
# (45.0000000000000000052...). The conversions are automatically done in
# the functions that need the precision - it is not done here.
global prec
if prc is None: return prec
prc = int(abs(prc))
if backend == 'mpmath': # base ten precision
mp.prec = int(prc * log(2, 10))
elif backend == 'gmpy2': # base two precision
gm.set_context(gm.context(precision=prc))
elif backend == 'decimal': # base ten precision
dm.getcontext().prec = int(prc * log(2, 10))
else:
pass
prec = prc
return prc
def check_zero_is_in_interval(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
left = mpfr(interval.lower)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
right = mpfr(interval.upper)
if gmpy2.is_zero(left) and interval.include_lower:
return True
if gmpy2.is_zero(right) and interval.include_upper:
return True
if left < mpfr("0.0") < right:
return True
return False
def main():
gmpy2.set_context(gmpy2.context())
gmpy2.get_context().precision = 75
T = int(input())
if T < 1 or T > 100:
raise RuntimeError("T is not within the valid range")
for i in range(T):
n = int(input())
r = Numbers(n)
print("Case #" + str(i + 1) + ": " + r)
def add_all_coefficients_upper_abs(self):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundAwayZero,
precision=mpfr_proxy_precision) as ctx:
res_right = mpfr("0.0")
for coeff in self.coefficients:
res_right = gmpy2.add(
res_right, abs(mpfr(self.coefficients[coeff].upper)))
# now the number is positive so we can round up
return round_number_up_to_digits(res_right, digits_for_range)
def recover_msg(N1, N2, N3, C1, C2, C3):
m = 42
# your code starts here: to calculate the original message - m
# Note 'm' should be an integer
N = N1 * N2 * N3
#y1 = N / N1
#y2 = N / N2
#y3 = N / N3
s = [1, 0]
r = [(N / N1), N1]
i = 2
temp = (N / N1) % N1
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(temp)
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z1 = s[i - 2]
s = [1, 0]
r = [(N / N2), N2]
i = 2
temp = (N / N2) % N2
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(temp)
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z2 = s[i - 2]
s = [1, 0]
r = [(N / N3), N3]
i = 2
temp = (N / N3) % N3
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(r[i - 2] % r[i - 1])
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z3 = s[i - 2]
if z1 < 0: z1 += N1
if z2 < 0: z2 += N2
if z3 < 0: z3 += N3
x = (z1 * C1 * (N / N1) + z2 * C2 * (N / N2) + z3 * C3 * (N / N3)) % N
gmpy2.set_context(gmpy2.context())
gmpy2.get_context().precision = 1000000
m = int(gmpy2.cbrt(x))
# your code ends here
# convert the int to message string
msg = hex(m).rstrip('L')[2:].decode('hex')
return msg
def createDSIfromDistribution(distribution, n=50):
#np.logspace(-9, 5, base=2, num=50) spacing should be done by powers of 2
if distribution.range_()[0]==0.0 and distribution.range_()[-1]==1.0 and use_powers_of_two_spacing:
lin_space = powers_of_two_spacing()
elif "FTE" in distribution.name and use_powers_of_two_spacing:
lin_space = powers_of_two_error(distribution.d.precision)
else:
lin_space = np.linspace(distribution.range_()[0], distribution.range_()[-1], num=n + 1, endpoint=True)
if custom_spacing:
try:
lin_space = distribution.get_my_spacing()
except:
lin_space = np.linspace(distribution.range_()[0], distribution.range_()[-1], num=n + 1, endpoint=True)
cdf_distr=distribution.get_piecewise_cdf()
ret_list=[]
for i in range(0, len(lin_space)-1):
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
lower=round_number_down_to_digits(gmpy2.mpfr(lin_space[i]), digits_for_input_discretization)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
upper=round_number_up_to_digits(gmpy2.mpfr(lin_space[i+1]), digits_for_input_discretization)
cdf_low_bound=min(1.0, max(0.0, cdf_distr(float(lin_space[i]))))
cdf_up_bound=min(1.0, max(0.0, cdf_distr(float(lin_space[i+1]))))
cdf_low_string=dec2Str(round_near(cdf_low_bound, digits_for_input_cdf))
cdf_up_string=dec2Str(round_near(cdf_up_bound, digits_for_input_cdf))
pbox = PBox(Interval(lower, upper, True, False, digits_for_range),
cdf_low_string, cdf_up_string)
ret_list.append(pbox)
ret_list=adjust_ret_list(ret_list)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
ret_list[0].interval.lower = \
round_number_down_to_digits(gmpy2.mpfr(distribution.a_real), digits_for_input_discretization)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
ret_list[-1].interval.upper = \
round_number_up_to_digits(gmpy2.mpfr(distribution.b_real), digits_for_input_discretization)
ret_list[-1].interval.include_upper = True
mixarith=MixedArithmetic(ret_list[0].interval.lower,ret_list[-1].interval.upper,ret_list)
return mixarith
def check_zero_is_in_interval(self):
zero_is_included = False
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) < mpfr("0.0") < mpfr(self.upper):
zero_is_included = True
if mpfr(self.lower) == mpfr("0.0") and self.include_lower:
zero_is_included = True
if mpfr(self.upper) == mpfr("0.0") and self.include_upper:
zero_is_included = True
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
if mpfr(self.lower) < mpfr("0.0") < mpfr(self.upper):
zero_is_included = True
if mpfr(self.lower) == mpfr("0.0") and self.include_lower:
zero_is_included = True
if mpfr(self.upper) == mpfr("0.0") and self.include_upper:
zero_is_included = True
return zero_is_included
def clean_affine_operation(self):
keys = []
for key in self.coefficients:
value = self.coefficients[key]
remove = [False, False]
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(mpfr(value.lower)):
remove[0] = True
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(mpfr(value.upper)):
remove[1] = True
if remove[0] and remove[1]:
keys.append(key)
for delete in keys:
del self.coefficients[delete]
self.update_interval()
return self
def find_min_abs_interval(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundToZero,
precision=mpfr_proxy_precision) as ctx:
left = abs(mpfr(interval.lower))
right = abs(mpfr(interval.upper))
if left < right:
#Now the number is positive so we can round down
return round_number_down_to_digits(left, digits_for_range)
else:
#Now the number is positive so we can round down
return round_number_down_to_digits(right, digits_for_range)
def compute_interval(self):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
res_left = gmpy2.sub(mpfr(self.center.lower),
mpfr(self.add_all_coefficients_lower_abs()))
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
res_right = gmpy2.add(mpfr(self.center.upper),
mpfr(self.add_all_coefficients_upper_abs()))
if res_left <= res_right:
return Interval(
round_number_down_to_digits(res_left, digits_for_range),
round_number_up_to_digits(res_right, digits_for_range), True,
True, digits_for_range)
else:
return Interval(
round_number_down_to_digits(res_right, digits_for_range),
round_number_up_to_digits(res_left, digits_for_range), True,
True, digits_for_range)
def powers_of_two_spacing():
exp_spacing=[]
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundToNearest, precision=mpfr_proxy_precision) as ctx:
exponent=gmpy2.mpfr("0")
while abs(exponent)<discretization_points:
value=gmpy2.exp2(exponent)
exp_spacing.insert(0, round_number_nearest_to_digits(value, digits_for_input_discretization))
exponent=gmpy2.sub(exponent,gmpy2.mpfr("1"))
exp_spacing.insert(0, "0.0")
for index, value in enumerate(exp_spacing[:-1]):
if value==exp_spacing[index+1]:
print("Problem with digits in powers of 2")
exit(-1)
return exp_spacing
def __init_subclass__(cls, **kwargs):
if cls.is_bound:
if cls.ieee_compliance:
precision = cls.mantissa_size + 1
emax = 1 << (cls.exponent_size - 1)
emin = 4 - emax - precision
subnormalize = True
else:
precision = cls.mantissa_size + 1
emax = 1 << (cls.exponent_size - 1)
emin = 3 - emax
subnormalize = False
ctx = gmpy2.context(
precision=precision,
emin=emin,
emax=emax,
round=_mode_2_gmpy2[cls.mode],
subnormalize=cls.ieee_compliance,
allow_complex=False,
)
if hasattr(cls, '_ctx_'):
c_ctx = cls._ctx_
if not isinstance(c_ctx, type(ctx)):
raise TypeError(
'class attribute _ctx_ is reversed by FPVector')
#stupid compare because contexts aren't comparable
elif (c_ctx.precision != ctx.precision
or c_ctx.real_prec != ctx.real_prec
or c_ctx.imag_prec != ctx.imag_prec
or c_ctx.round != ctx.round
or c_ctx.real_round != ctx.real_round
or c_ctx.imag_round != ctx.imag_round
or c_ctx.emax != ctx.emax or c_ctx.emin != ctx.emin
or c_ctx.subnormalize != ctx.subnormalize
or c_ctx.trap_underflow != ctx.trap_underflow
or c_ctx.trap_overflow != ctx.trap_overflow
or c_ctx.trap_inexact != ctx.trap_inexact
or c_ctx.trap_erange != ctx.trap_erange
or c_ctx.trap_divzero != ctx.trap_divzero
or c_ctx.trap_expbound != ctx.trap_expbound
or c_ctx.allow_complex != ctx.allow_complex):
# this basically should never happen unless some one does
# class Foo(FPVector):
# _ctx_ = gmpy2.context(....)
raise TypeError('Incompatible context types')
cls._ctx_ = ctx
def powers_of_two_error(precision):
exp_spacing=[]
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundToNearest, precision=mpfr_proxy_precision) as ctx:
exponent=gmpy2.mpfr(-precision)
counter=0
while counter<discretization_points//2:
value=gmpy2.exp2(exponent)
exp_spacing.insert(0, round_number_nearest_to_digits(value, digits_for_input_discretization))
exponent=gmpy2.sub(exponent,gmpy2.mpfr("1"))
counter=counter+1
exp_spacing_reverse=copy.deepcopy(exp_spacing)
exp_spacing_reverse.reverse()
exp_spacing_reverse=["-"+s for s in exp_spacing_reverse]
exp_spacing=exp_spacing_reverse+["0.0"]+exp_spacing
for index, value in enumerate(exp_spacing[:-1]):
if value==exp_spacing[index+1]:
print("Problem with digits in powers of 2")
exit(-1)
return exp_spacing
def calculate_curve_constants():
"""
Calculate the curve constants $\ell_i$
:return:
"""
expected_values = [
50127518246259276682880317011538934615153226543083896339791,
22358026531042503310338016640572204942053343837521088510715,
5105580562119000402467322500999592531749084507000101675068,
19494034873545274265741574254707851381713530791194721254848
]
ells = []
alpha_hats = calculate_alpha_hats()
gmpy2.context().real_round = gmpy2.RoundToNearest
for i in range(4):
alpha_hat_i = alpha_hats[i]
ell_i = round(mpq(alpha_hat_i * mu, N))
# Verify results what precomputed values
assert ell_i == expected_values[i]
ells.append(ell_i)
return ells
def initConstants(cls):
from math import sqrt
def nextPrime(n=2):
while True:
for factor in range(2, int(sqrt(n)) + 1):
if n % factor == 0:
break
else:
yield n
n += 1
# Find the first nRounds primes
npgen = nextPrime()
primes = [next(npgen) for x in range(cls.nRounds)]
fb_mul = 2**cls.wordBits
def getFractionalBits(n):
return int((n - int(n)) * fb_mul)
if cls.use_gmp:
from gmpy2 import context, set_context, sqrt, cbrt
# context() parameters are platform-dependent!
set_context(context(precision=75,
round=1)) # OK for gmp 6.1.2 / gmpy 2.1.0
else:
cbrt = lambda n: pow(n, 1 / 3)
# First wordBits bits of the fractional parts of the square roots of the first 8 primes
H = (getFractionalBits(sqrt(n)) for n in primes[:8])
# First wordBits bits of the fractional parts of the cube roots of the first nRounds primes
K = (getFractionalBits(cbrt(n)) for n in primes)
cls.H_init = tuple(H)
cls.K = tuple(K)
import gmpy2
from gmpy2 import mpfr, const_pi, const_euler
from numpy import meshgrid, array
import matplotlib.pyplot as plt
import seaborn as sns
import matplotlib.animation as anim
import os
import cv2 # conda install -c conda-forge opencv=4.1.0
bits = 32
# bits = 64
gmpy2.set_context(gmpy2.context(precision=bits))
# ------------------------------------------------
### FUNCTIONS ###
def mp(num):
return mpfr(str(num))
def backf(num, digits=5):
return float(round(num, digits))
def listf(l):
return list(map(backf, l))
def regions_binary(ra, rd, pf_plus, pf_minus, precision=1000):
"""
Construct (px, px_tilde, px/px_tilde) regions used to find the certified radius for binary data.
Intuitively, pf_minus controls rd and pf_plus controls ra.
Parameters
----------
ra: int
Number of ones y has added to x
rd : int
Number of ones y has deleted from x
pf_plus : float, 0 <= p_plus <= 1
The probability to flip a zero to a one
pf_minus: float, 0 <= p_plus <= 1
The probability to flip a one to a zero
precision: int
Numerical precision for floating point calculations
Returns
-------
regions: array-like, [None, 3]
Regions of constant probability under px and px_tilde,
"""
pf_plus, pf_minus = gmpy2.mpfr(pf_plus), gmpy2.mpfr(pf_minus)
with gmpy2.context(precision=precision):
if pf_plus == 0:
px = pf_minus**rd
px_tilde = pf_minus**ra
return np.array([[1 - px, 0, float('inf')],
[px, px_tilde, px / px_tilde],
[0, 1 - px_tilde, 0]])
if pf_minus == 0:
px = pf_plus**ra
px_tilde = pf_plus**rd
return np.array([
[1 - px, 0, float('inf')],
[px, px_tilde, px / px_tilde],
[0, 1 - px_tilde, 0],
])
max_q = ra + rd
i_vec = np.arange(0, max_q + 1)
T = ra * ((pf_plus / (1 - pf_plus)) ** i_vec) + \
rd * ((pf_minus / (1 - pf_minus)) ** i_vec)
ratio = np.zeros_like(T)
px = np.zeros_like(T)
px[0] = 1
for q in range(0, max_q + 1):
ratio[q] = (pf_plus/(1-pf_minus)) ** (q - rd) * \
(pf_minus/(1-pf_plus)) ** (q - ra)
if q == 0:
continue
for i in range(1, q + 1):
px[q] = px[q] + ((-1)**(i + 1)) * T[i] * px[q - i]
px[q] = px[q] / q
scale = ((1 - pf_plus)**ra) * ((1 - pf_minus)**rd)
px = px * scale
regions = np.column_stack((px, px / ratio, ratio))
if pf_plus + pf_minus > 1:
# reverse the order to maintain decreasing sorting
regions = regions[::-1]
return regions
def regions_discrete(ra, rd, rc, k, pf_plus, pf_minus, precision=1000):
"""
Construct (px, px_tilde, px/px_tilde) regions used to find the certified radius for general discrete data.
Note: if pf_plus = pf_minus any combination of ra+rd+rc=r gives the same result.
ra: int
Number of zeros changed to non-zeros from x to x_tilde.
rd : int
Number of non-zeros changed to zeros from x to x_tilde.
rc : int
Number of non-zeros changed to other non-zero values from x to x_tilde.
k: int
Number of discrete categories.
pf_plus : float, 0 <= p_plus <= 1
The probability to flip a zero to a non-zero.
pf_minus: float, 0 <= p_plus <= 1
The probability to flip a non-zero to a zero.
precision: int
Numerical precision for floating point calculations.
"""
with gmpy2.context(precision=precision):
pf_plus, pf_minus = gmpy2.mpfr(pf_plus), gmpy2.mpfr(pf_minus)
one = gmpy2.mpfr(1)
ra, rd, rc = int(ra), int(rd), int(rc)
a0 = (one - pf_plus)
b0 = pf_plus / (k - 1)
c0 = one - a0 - b0
dist_0 = [a0, b0, c0]
a1 = (one - pf_minus)
b1 = pf_minus / (k - 1)
c1 = one - a1 - b1
dist_1 = [a1, b1, c1]
regions = defaultdict(float)
for triplet in product(triplets(ra, k), triplets(rd, k), triplets(rc, k)):
q0, p0, m0 = triplet[0]
q1, p1, m1 = triplet[1]
q2, p2, m2 = triplet[2]
ratio = 1
ratio *= (a0 / b1)**(q0 - p1)
ratio *= (b0 / a1)**(p0 - q1)
ratio *= (c0 / c1)**(m0 - m1)
ratio *= (a1 / b1)**(q2 - p2)
# compute the product of three multinomial distributions
px = 1
for (qi, pi, mi), ri, dist in zip(triplet, [ra, rd, rc],
[dist_0, dist_1, dist_1]):
px *= dist[0]**qi
px *= dist[1]**pi
px *= dist[2]**mi
px *= gmpy2.fac(ri) / gmpy2.fac(qi) / gmpy2.fac(pi) / gmpy2.fac(mi)
regions[float(ratio)] += px
regions = np.array(list(regions.items()))
srt = regions[:, 0].argsort()[::-1]
return np.column_stack(
(regions[srt, 1], regions[srt, 1] / regions[srt, 0], regions[srt, 0]))
cipher = 2780321436921227845269766067805604547641764672251687438825498122989499386967784164108893743279610287605669769995594639683212592165536863280639528420328182048065518360606262307313806591343147104009274770408926901136562839153074067955850912830877064811031354484452546219065027914838811744269912371819665118277221
n = 23571113171923293137414347535961677173798389971011031071091131271311371391491511571631671731791811911931971992112232272292332392412512572632692712772812832933073113133173313373473493533593673733793833893974014094194214314334394434494574614634674794874914995035095215235415475575635695715775875935996016076136176196316416436476536596616736776836917017097197277337397437517577617697737877978098118218238278298398538578598638778818838879079119199299379419479539679719779839919971009101310191431936117404941729571877755575331917062752829306305198341421305376800954281557410379953262534149212590443063350628712530148541217933209759909975139820841212346188350112608680453894647472456216566674289561525527394398888860917887112180144144965154878409149321280697460295807024856510864232914981820173542223592901476958693572703687098161888680486757805443187028074386001621827485207065876653623459779938558845775617779542038109532989486603799040658192890612331485359615639748042902366550066934348195272617921683
Low Public Exponent Attack
"""
import sys
try:
import gmpy2
except ImportError:
print("Install gmpy2 first to run this program")
sys.exit()
e = 3
cipher = 2780321436921227845269766067805604547641764672251687438825498122989499386967784164108893743279610287605669769995594639683212592165536863280639528420328182048065518360606262307313806591343147104009274770408926901136562839153074067955850912830877064811031354484452546219065027914838811744269912371819665118277221
n = 23571113171923293137414347535961677173798389971011031071091131271311371391491511571631671731791811911931971992112232272292332392412512572632692712772812832933073113133173313373473493533593673733793833893974014094194214314334394434494574614634674794874914995035095215235415475575635695715775875935996016076136176196316416436476536596616736776836917017097197277337397437517577617697737877978098118218238278298398538578598638778818838879079119199299379419479539679719779839919971009101310191431936117404941729571877755575331917062752829306305198341421305376800954281557410379953262534149212590443063350628712530148541217933209759909975139820841212346188350112608680453894647472456216566674289561525527394398888860917887112180144144965154878409149321280697460295807024856510864232914981820173542223592901476958693572703687098161888680486757805443187028074386001621827485207065876653623459779938558845775617779542038109532989486603799040658192890612331485359615639748042902366550066934348195272617921683
n = hex(n)
import gmpy2
with gmpy2.local_context(gmpy2.context(), precision=800) as ctx:
ctx.precision += 800
root = gmpy2.cbrt(cipher)
try:
print(str('%x' % +int(root)).decode('hex'))
except AttributeError:
print(bytes.fromhex(str('%x' % +int(root))).decode('utf-8'))
# answer!!
# dsc{t0-m355-w1th-m4th-t4k35-4-l0t-0f-sp1n3}
import gmpy2
from gmpy2 import mpz
__author__ = 'Qubo'
N1 = '17976931348623159077293051907890247336179769789423065727343008115'
N1 += '77326758055056206869853794492129829595855013875371640157101398586'
N1 += '47833778606925583497541085196591615128057575940752635007475935288'
N1 += '71082364994994077189561705436114947486504671101510156394068052754'
N1 += '0071584560878577663743040086340742855278549092581'
gmpy2.set_context(gmpy2.context(precision=2000))
N = mpz(N1)
A = gmpy2.ceil(gmpy2.sqrt(N))
SquareA = gmpy2.square(A)
if gmpy2.is_square(mpz(gmpy2.sub(SquareA, N))):
x = gmpy2.sqrt(gmpy2.sub(SquareA, N))
print 'p = ' + str(mpz(gmpy2.sub(A, x)))
print 'q = ' + str(mpz(gmpy2.add(A, x)))
else:
print 'x is not square, must be wrong...'
# ------------------------------------------------
### IMPORTS ###
from gmpy2 import context, set_context
from gmpy2 import mpfr, sqrt, const_pi, exp, sin, cos, polar, norm
import matplotlib.pyplot as plt
from seaborn import set_style
# ------------------------------------------------
### DEFINITIONS ###
set_style('darkgrid')
bits = 64
set_context(context(precision=bits, allow_complex=True))
I = sqrt(-1)
pi = const_pi(bits)
# ------------------------------------------------
### FUNCTIONS ###
def backf(val, digits=8):
return [backf(v, digits)
for v in val] if isinstance(val,
(list, tuple, map,
zip)) else float(round(val, digits))
out = partial(print, sep='\n', end='\n\n')
if __name__ == '__main__':
# Reales de precisión arbitraria
# En el siguiente ejemplo se muestra con la precisión normal
out ('Raíz de dos: ', gmpy2.sqrt(2))
# Obtenemos la precisión máxima teórica de la computadora
out ('Precisión máxima: ', gmpy2.get_max_precision())
# ¿Cuál es la precisión por defecto?
out ('Precisión por defecto', gmpy2.get_context().precision)
# Cambiamos la precisión de la biblioteca
gmpy2.get_context().precision=100
# Otra vez la raíz de dos, con precisión aumentada
out ('Raíz de dos: ', gmpy2.sqrt(2))
# De hecho es la precisión de cualquier número
out ('Un flotante: ', mpfr('1.2'))
# Ahora creamos un contexto para manejar la precisión
with gmpy2.local_context(gmpy2.context(), precision=200) as ctx:
out ('Precisión alterada en contexto', gmpy2.sqrt(2))
ctx.precision += 100
out ('Aún mejor precision', gmpy2.sqrt(2))
# De regreso al contexto original, precision normal
out ('Raíz de dos', gmpy2.sqrt(2))
def mp(num):
return mpfr(str(num))
def backf(num, digits=5):
return float(round(num, digits))
def listf( l ):
return list(map(backf, l))
# ------------------------------------------------
### TESTS ###
gmpy2.set_context(gmpy2.context(precision=32))
# for the 1st order Euler EDO method
dy_dt = lambda t, y: 4*t - (2/t)*y
t_0 = mp(1)
y_0 = mp(2)
dt = 8*mp(10)**-3
interv = [mp(0.2), mp(1.8)]
sol1_t = arange( *interv, dt)
sol1_y = list(map(lambda t: t**2 + 1/(t**2), sol1_t))
[apr1_t , apr1_y] = [listf(l) for l in edo1(dy_dt, t_0, y_0, dt, interv)]
import uuid
import gmpy2
import os.path
import traceback
import __builtin__
from glob import glob
from HALapi import get_main_dir, module_filter, HALcannotHandle
# Some version of gmpy2 doesn't have pow()
try:
gmpy2.pow(2, 10)
except (AttributeError, TypeError):
gmpy2.pow = lambda x, y: x**y
gmpy2.context().precision = 256
math_list = ['acos', 'asin', 'atan', 'atan2', 'ceil', 'cos', 'cosh', 'exp', 'floor', 'fmod', 'hypot', 'modf', 'pow', 'sin', 'sinh', 'sqrt', 'tan', 'tanh']
builtin_list = ['abs']
funcs = dict((name, getattr(gmpy2, name)) for name in math_list)
funcs.update(dict((name, getattr(__builtin__, name)) for name in builtin_list))
funcs.update(fact=math.factorial, mpfr=gmpy2.mpfr, arctan=gmpy2.atan, arccos=gmpy2.acos, arcsin=gmpy2.asin, log=gmpy2.log10,
ln=gmpy2.log)
const = dict(e =gmpy2.mpfr('2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274'),
pi=gmpy2.mpfr('3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679'))
filters = {
'^': '**',
re.compile(r'([0-9]+)!'): lambda m: 'fact(%s)'%m.group(1),
}
import gmpy2
import binascii
ctx = gmpy2.context(precision=10000000,round=gmpy2.RoundUp)
gmpy2.set_context(ctx)
def FermatFactor(N):
A = gmpy2.mpz( gmpy2.ceil( gmpy2.sqrt(N) ) )
B2 = gmpy2.sub( gmpy2.square(A), N )
while not gmpy2.is_square(B2):
A = gmpy2.add( A, gmpy2.mpz("1") )
B2 = gmpy2.sub( gmpy2.square(A), N )
B = gmpy2.sqrt(B2)
P = gmpy2.mpz( gmpy2.sub( A, B ) )
Q = gmpy2.mpz( gmpy2.add( A, B ) )
if not checkFactors(P,Q,N):
raise Exception("Bad factors generated")
return ( P, Q )
def checkFactors(p,q,N):
x = gmpy2.f_mod( N, p )
y = gmpy2.f_mod( N, q )
zero = gmpy2.mpz('0')
if g.is_prime(p) and g.is_prime(q):
return N == g.mul(p,q) and x == zero and y == zero
return False
def checkD(e,d,phi):
import gmpy2 as g
import binascii
import sys
ctx = g.context(precision=10000000,round=g.RoundUp)
g.set_context(ctx)
def bruteSmall(N):
zero = g.mpz(0)
two = g.mpz(2)
if g.f_mod(N, two) == zero:
return two, g.mpz(g.div(N, two))
i = g.mpz(3)
while True:
if g.f_mod(N, i) == zero:
p = g.mpz(i)
q = g.mpz( g.div(N,i) )
if checkFactors(p,q,N) :
return p,q
i = g.add(i, two)
def checkFactors(p,q,N):
x = g.f_mod( N, p )
y = g.f_mod( N, q )
zero = g.mpz('0')
if g.is_prime(p) and g.is_prime(q):
return N == g.mul(p,q) and x == zero and y == zero
return False
def checkD(e,d,phi):
