def produce_results():
test_AF, test_LD = loadPriorKnowledge(
"E:/Lab/LCA1/honeygenes/dat/hg_allele_freqs_chr22_CEU.txt",
"E:/Lab/LCA1/honeygenes/dat/hg_ld_chr22_CEU.txt")
SNPRefList = []
dataset = []
datFile = open("E:/Lab/LCA1/honeygenes/dat/new_genotypes_chr22_CEU.txt")
for line in datFile.readlines():
attrArray = line.split()
SNPRefList.append(attrArray[0])
dataset.append(attrArray[1:])
# SNPRefList = SNPRefList[0:100]
dataset = np.array(dataset, dtype=int)
# bitLen1 = int(math.ceil(len(SNPRefList)*math.log(3,2)))
maxNaiveSeed = 3**len(SNPRefList) - 1
bitLen2 = int(math.ceil(len(SNPRefList) * 3))
for i in range(len(SNPRefList)):
powOfThree.append(mpz(3)**mpz(i))
sec_exp_result = open('sec_exp_result_large.txt', 'w')
pInd = 16
while pInd < 17:
pInd += 1
correctSize = gmpy2.log2(
intervalSize(list(dataset[:, pInd]), SNPRefList, test_AF, test_LD,
bitLen2))
numOfExps = 1000
sizes1 = [0] * numOfExps
for i in range(numOfExps):
randomSeed1 = random.randint(0, maxNaiveSeed)
randomSeq1 = naiveDecode(randomSeed1, SNPRefList, test_AF, test_LD,
maxNaiveSeed)
sizes1[i] = gmpy2.log2(
intervalSize(randomSeq1, SNPRefList, test_AF, test_LD,
bitLen2))
print sizes1[i]
print ', '.join(map(str, sizes1))
sizes2 = [0] * numOfExps
for i in range(numOfExps):
randomSeed2 = random.randint(0, 2**bitLen2 - 1)
sizes2[i] = gmpy2.log2(
intervalSize2(randomSeed2, SNPRefList, test_AF, test_LD,
bitLen2))
print ', '.join(map(str, sizes2))
sec_exp_result.write(str(correctSize) + '\n')
sec_exp_result.write('\t'.join(map(str, sizes1)) + '\n')
sec_exp_result.write('\t'.join(map(str, sizes2)) + '\n')
sec_exp_result.close()
def aks_test(n):
"""
Implement the AKS primality test.
"""
get_context().precision = bit_length(n)
# Check if n is a perfect power. If so, return composite.
if is_power(n):
return "composite"
# Find the smallest r such that the multiplicative order of n modulo r
# is greater than log(n, 2)^2
r = get_r(n)
# If 1 < gcd(a, n) < n for some a <= r, return composite
for a in range(1, r):
if gcd(a, n) > 1 and gcd(a, n) < n:
return "composite"
# If n <= r, return prime
if n <= r:
return "prime"
# Check if (x + a)^n mod (x^r - 1, n) != (x^n + a) mod (x^r - 1, n)
if False in ray.get([
is_congruent.remote(a, n, r)
for a in range(1, mpz(floor(sqrt(phi(r)) * log2(n))))
]):
return "composite"
return "prime"
def good_pair(p, q):
"""Returns p*q if p and q are a good pair, else 0."""
n = p * q
k = gmpy2.ceil(gmpy2.log2(n))
if abs(p - q) > 2**(k / 2 - 100):
return n
return 0
def check_pair(p: int, q: int) -> Tuple[int, int]:
"""Returns the encryption modulus and totient for the given primes."""
n = p*q
k = ceil(log2(n))
if abs(p - q) > 2**(k/2 - 100):
return n, n - (p + q - 1)
return 0, 0
def solve(*lines):
P, Q = lines
Q = mpz(Q)
P = mpz(P)
_gcd = gcd(P, Q)
if gcd > 1:
P = c_div(P, _gcd)
Q = c_div(Q, _gcd)
if not log2(Q).is_integer():
return 'impossible'
res = log2(P)
res = mpz(floor(res))
res, rem = c_divmod(Q, 2**res)
if rem:
return 'impossible'
return int(log2(res))
def bits_in_number(number):
"""
Returns number of bits in the given number
:param number: long number
"""
if number == 0:
return 0
return gmpy2.mpz(gmpy2.floor(gmpy2.log2(number)) + 1)
def p_to_entropy(p01, p10, bitwidth):
smp = mpfr('0.0')
mcv_prob, mcv = symbol_max_probability(p01, p10, bitwidth)
ent = -gmpy2.log2(mcv_prob)
#printf("XXX entropy = %f p01=%f, p10=%f\n",ent,p01,p10);
return ent / bitwidth, mcv_prob, mcv
def p_to_entropy(p01, p10, bitwidth, verbose=False):
smp = mpfr('0.0')
mcv_prob, mcv = symbol_max_probability(p01, p10, bitwidth)
ent = -gmpy2.log2(mcv_prob)
#printf("XXX entropy = %f p01=%f, p10=%f",ent,p01,p10,file=sys.stderr)
return ent / bitwidth, mcv_prob, mcv
def ecm(N: int):
"""
Elliptic-curve factorization method
Args:
N (int): target
Returns:
int: factor
"""
L = int(gmpy2.log2(N)**2 + gmpy2.log2(N) * 0.25)
iter_count = 0
while True:
a = gmpy2.mpz(random.randint(0, N))
x = gmpy2.mpz(random.randint(0, N))
y = gmpy2.mpz(random.randint(0, N))
ECMPoint.init(a, N)
P = ECMPoint(x, y)
prime = gmpy2.mpz(2)
while prime <= L:
base = copy.copy(P)
exponent = gmpy2.mpz(logn(L, prime))
M = pow(prime, exponent)
prime = next_prime(prime)
M -= 1
while M > 0:
if M % 2 == 1:
add_rslt = P.add(base)
if not add_rslt:
return ecm_calc_factor(P, base, N)
add_rslt = base.add(base)
if not add_rslt:
return ecm_calc_factor(base, base, N)
M //= 2
iter_count += 1
def compute_parameters(self, orwell_file):
data_prob = 0.0
total_count = 0
for token_list in self.data_parser.iterate_line(orwell_file):
total_count += 1
sent_len = len(token_list) - 1
sent_prob = self.sent_prob(sent_len)
data_prob += gmpy2.log2(sent_prob)
log_data = (data_prob / total_count)
perplexity = math.pow(2, (-1.0 * log_data))
cross_entropy = math.log(perplexity, 2)
return cross_entropy, perplexity
def check_modulus_size(n):
# type: (int) -> RE
"""
Checks if the modulus has good RSA sizes
:n The RSA modulus
"""
# TODO: Research exact size
if gmpy2.log2(n) < 1023:
return RSAResult.SMALL_MODULUS
return RSAResult.OK
def find_composite():
"""
Historically the mersenne.org manual results didn't mark as complete
ranges that included a composite result.
e.g. https://www.mersenne.org/report_exponent/?exp_lo=113644673&full=1
Search for any result that contained 1 or more composite factor and save
<factor>
<factor>
found <x> factor for M<z> from 2^72 to 2^73 [mfaktc 0.21 barrett76_mul32_gs]
"""
# results[exp][bitlevel] = []
results = defaultdict(lambda: defaultdict(list))
# set of (exp, bitlevels) that will need to be resubmitted
composite = set()
assert os.path.isfile(RESULTS_FILE), RESULTS_FILE
with open(RESULTS_FILE) as results_file:
for result in results_file:
match = re.match("M([0-9]*) has a factor: ([0-9]*).*TF:..:([0-9]{2})", result)
if match:
M, factor, upper_tf = map(int, match.groups())
# Wonky factor, see https://www.mersenneforum.org/showthread.php?p=585014#post585014
if factor == 147602823780943516039:
continue
# Composite factor
if not gmpy2.is_prime(factor):
results[M][upper_tf].append(result)
log2 = gmpy2.log2(factor)
assert (upper_tf - 1) < log2 < upper_tf, (factor, log2, upper_tf)
composite.add( (M, upper_tf) )
match = re.match("found [1-9]+ factors? for M([0-9]+) from 2\^([0-9]+) to 2\^([0-9]+)", result)
if match:
# Assumes that mfaktc was run with StopAfterFactor=0 (which is was
M, low, high = map(int, match.groups())
results[M][high].append(result)
print ()
print ("{} compsite factors found, {} exponents {} bit levels".format(
len(composite), len(results), sum(map(len, results.values()))))
print ()
for M, high in sorted(composite):
if high <= 68:
continue
#print (f"\t# M{M} 2^{high-1} to 2^{high}")
for result in results[M][high]:
print (result.strip())
def is_good_pair(p: int, q: int) -> Optional[Tuple[int, int]]:
"""Returns the encryption modulus and totient for the given primes.
:param p: One of the two primes to be used for encryption.
:type p: int
:param q: The other prime used for encryption.
:type q: int
:returns: Either the encryption modulus and the totient, or None.
:rtype: Optional[Tuple[int, int]]"""
n = p*q
k = gmpy2.ceil(gmpy2.log2(n))
if abs(p - q) > 2**(k/2 - 100):
return n, n - (p + q - 1)
return None
def get_r(n):
"""
Find the smallest r such that the multiplicative order of n modulo r
is greater than log(n, 2)^2. If r and n are not coprime, skip this r.
"""
r = 2
while True:
if gcd(r, n) != 1:
r += 1
elif ord(n, r) > pow(log2(n), 2):
break
else:
r += 1
return r
def produce_results():
test_AF, test_LD = loadPriorKnowledge(
"E:/Lab/LCA1/honeygenes/dat/hg_allele_freqs_chr22_CEU.txt",
"E:/Lab/LCA1/honeygenes/dat/hg_ld_chr22_CEU.txt")
SNPRefList = []
dataset = []
datFile = open("E:/Lab/LCA1/honeygenes/dat/new_genotypes_chr22_CEU.txt")
for line in datFile.readlines():
attrArray = line.split()
SNPRefList.append(attrArray[0])
dataset.append(attrArray[1:])
# SNPRefList = SNPRefList[0:100]
dataset = np.array(dataset, dtype=int)
# bitLen1 = int(math.ceil(len(SNPRefList)*math.log(3,2)))
maxNaiveSeed = 3**len(SNPRefList) - 1
bitLen2 = int(math.ceil(len(SNPRefList) * 3))
for i in range(len(SNPRefList)):
powOfThree.append(mpz(3)**mpz(i))
for i in range(50):
print gmpy2.log2(
intervalSize(list(dataset[:, i]), SNPRefList, test_AF, test_LD,
bitLen2))
def compute_cross_entropy_perplexity(obj_model, data_file):
obj_model.logger.info("Started analysing data file %s to compute cross entropy" % data_file)
data_prob = 0.0
word_count = 0
for token_list in obj_model.data_parser.iterate_line(data_file):
word_count += len(token_list)
sent_prob = obj_model.sentence_probability(token_list)
if sent_prob is None:
return None
data_prob += gmpy2.log2(sent_prob)
obj_model.logger.info("Data Probability : %.10f" % data_prob)
log_data = (data_prob / word_count)
obj_model.logger.info("Log Data : %.10f" % log_data)
perplexity = math.pow(2, (-1.0 * log_data))
obj_model.logger.info("Perplexity : %.10f" % perplexity)
cross_entropy = math.log(perplexity, 2)
obj_model.logger.info("Cross Entropy : %.10f" % cross_entropy)
return cross_entropy, perplexity
def checkPQDistance(self, keys):
if not isinstance(keys, (tuple, list)):
keys = [keys]
ctx = gmpy2.get_context()
ctx.precision = 5000
ctx.round = gmpy2.RoundDown
ctx.real_round = gmpy2.RoundDown
gmpy2.set_context(ctx)
for key in keys:
gmpy_key = gmpy2.mpfr(key)
skey = int(gmpy2.sqrt(gmpy_key))
skey2 = skey ** 2
if (skey2 > key) or (((skey + 1) ** 2) < key):
print skey2
print (skey+1)**2
raise Exception("WTF")
bits = int(gmpy2.log2(key - skey2))
if bits < 480:
print '%d Has p, q distance of %d bits' % (key, bits)
def checkPQDistance(self, keys):
if not isinstance(keys, (tuple, list)):
keys = [keys]
ctx = gmpy2.get_context()
ctx.precision = 5000
ctx.round = gmpy2.RoundDown
ctx.real_round = gmpy2.RoundDown
gmpy2.set_context(ctx)
for key in keys:
gmpy_key = gmpy2.mpfr(key)
skey = int(gmpy2.sqrt(gmpy_key))
skey2 = skey**2
if (skey2 > key) or (((skey + 1)**2) < key):
print skey2
print(skey + 1)**2
raise Exception("WTF")
bits = int(gmpy2.log2(key - skey2))
if bits < 480:
print '%d Has p, q distance of %d bits' % (key, bits)
def to_bin(num, working_base=WORKING_BASE):
"""
to_bin(num) -> int(bin_num)
Calculates the binary of num.
@param num(int) -> A number.
@param working_base(int) -> num's base.
@return bin_num(int) -> num's binary value.
"""
# Initialize.
bin_num = 0
# Finding the closest power of 2 to num. Then summerizing
# the binary value of num and decreasing num until it's zero.
while num > 0:
bin_digit = int(gmpy2.log2(num))
bin_num += working_base**bin_digit
num -= BINARY**bin_digit
return bin_num
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
# Parse command line arguments
parser = argparse.ArgumentParser(description="Generate BBS parameters.")
parser.add_argument("input_file", help="""JSON file containing the seed used for generating the pseudo strong
strong prime (the name is "seed"). The required
quantity of entropy it should contain depends on bitsize. As a rule of
thumb the seed should contain at least 4*bitsize bits of entropy.""")
parser.add_argument("output_file", help="""Output JSON file where this script will write the two generated strong
strong primes "p" and "q". The output file should not exist already.""")
parser.add_argument("min_prime_bitsize", type=int, help="minimum strong strong prime bit size (e.g. 2048).")
args = parser.parse_args()
# Check arguments
output_file = args.output_file
if os.path.exists(output_file):
utils.exit_error("The output file '%s' already exists. Exiting."%(output_file))
# Declare a few important variables
min_prime_bitsize = args.min_prime_bitsize
input_file = args.input_file
with open(input_file, "r") as f:
data = json.load(f)
seed = int(data["seed"])
seed_upper_bound = int(data["seed_upper_bound"])
approx_seed_entropy = math.floor(gmpy2.log2(seed_upper_bound))
utils.colprint("Minimum strong strong prime size:", str(min_prime_bitsize))
utils.colprint("Approximate seed entropy:", str(approx_seed_entropy))
# Precomputations
first_primes = [2] # List of the first primes
PI = 2 # Product of the primes in "first_primes"
strong_strong_integers = [[1]] # strong_strong_integers[i] is the list of all strong strong integers modulo
# first_primes[i]
number_of_strong_strong_integers = [1] # number_of_strong_strong_integers[i] is the number of elements of the list
# strong_strong_integers[i]
C = 1 # Product of the elements of "number_of_strong_strong_integers"
while not 2**(min_prime_bitsize-2) < PI:
p = int(gmpy2.next_prime(first_primes[-1]))
first_primes.append(p)
PI *= p
ssi = [c for c in range(p) if is_strong_strong_basis(c, p)]
strong_strong_integers.append(ssi)
number_of_strong_strong_integers.append(len(ssi))
C *= len(ssi)
utils.colprint("Number of primes considered:", str(len(first_primes)))
utils.colprint("Number of strong strong integers to choose from:", "about 2^%f"%(gmpy2.log2(C)))
# Check that the seed is long enough
if seed_upper_bound < C**2 * (1 << (2 * min_prime_bitsize)):
utils.exit_error("The seed does not contain the required entropy.")
# Precomputations for the CRT
mu = [gmpy2.divexact(PI,p) for p in first_primes]
delta = [gmpy2.invert(x,y) for x,y in zip(mu,first_primes)]
gamma = [gmpy2.mul(x,y) for x,y in zip(mu,delta)]
# Generate the first strong prime
print("Generating the first strong strong prime...")
(p,seed) = generate_strong_strong_prime(seed,
min_prime_bitsize,
strong_strong_integers,
number_of_strong_strong_integers,
gamma,
PI)
utils.colprint("\tThis is the first strong strong prime:", str(p))
# Generate the second strong prime
print("Generating the second strong strong prime...")
(q,seed) = generate_strong_strong_prime(seed,
min_prime_bitsize,
strong_strong_integers,
number_of_strong_strong_integers,
gamma,
PI)
utils.colprint("\tThis is the second strong strong prime:", str(q))
# Generate the BBS start
print("Generating the BBS starting point...")
n = p*q
s = seed % n
while s == 0 or s == 1 or s == p or s == q:
s = (s+1) % n
s0 = (s**2) % n
utils.colprint("\tThis is the starting point s0 of BBS:", str(s0))
# Save p,q, and s to the output_file
print("Saving p,q, and s0 to %s"%(output_file))
with open(output_file, "w") as f:
json.dump({"bbs_p": int(p),
"bbs_q": int(q),
"bbs_s": int(s0)},
f,
sort_keys=True)
def parse_and_print(filenames):
# For polyfit of composite, prime
timings = defaultdict(list)
for fn in filenames:
base, ext = os.path.splitext(fn)
if ext == ".txt":
pfgw_fn = min([
fn2
for fn2 in filenames if fn2.startswith(base) and '.pfgw' in fn2
],
default="")
gmp_fn = min([
fn2
for fn2 in filenames if fn2.startswith(base) and '.gmp' in fn2
],
default="")
print()
print(f"{fn:25} | pfgw: {pfgw_fn:33} gmp: {gmp_fn}")
if gmp_fn and pfgw_fn:
with open(fn) as bf:
blines = list(map(str.strip, bf.readlines()))
with open(gmp_fn) as gf:
glines = list(map(str.strip, gf.readlines()))
with open(pfgw_fn) as pf:
plines = list(map(str.strip, pf.readlines()))
rows = []
for line in blines:
if not line: continue
match = POWER_RE.search(line)
match = match or PRIMORIAL_RE.search(line)
assert match, line
number, part, add = match.groups()
alt_number = number.replace("# +", "# + ").replace(
"# -", "# + -")
g_line = min(
[g for g in glines if number in g or alt_number in g],
default="")
p_line = min([p for p in plines if number in p],
default="")
if not g_line or not p_line:
print(number, "NOT FOUND")
break
g_s = TIME_RE.search(g_line).group(0)
p_s = TIME_RE.search(p_line).group(0)
status = "prime" if "prime" in g_line else "composite"
#print (number)
#print (g_line)
#print (p_line)
#print (g_s, p_s)
bits = round(
gmpy2.log2(10**int(part) if '10^' in
number else gmpy2.primorial(int(part))))
ratio = round(float(g_s) / (float(p_s) + 1e-4), 1)
rows.append((number, bits, status, p_s, g_s, ratio))
timings["gmp_" + status].append(
(float(bits * math.log(2)), float(g_s)))
timings["pfgw_" + status].append(
(float(bits * math.log(2)), float(p_s)))
print()
print(header)
print(seperator)
for row in rows:
print(columns.format(*row))
print()
return timings
def _ilog2_gmpy(n): return int(gmpy.log2(n))
#import matplotlib.pyplot as plt
import os
import bisect
from numpy import linspace
# gmpy2 precision initialization
BITS = (1 << 10)
BYTES = BITS/8
gmpy2.get_context().precision = BITS # a whole lotta bits
def random():
seed = int(os.urandom(BYTES).encode('hex'), 16)
return gmpy2.mpfr_random(gmpy2.random_state(seed))
# Useful constants as mpfr
PI = gmpy2.acos(-1)
LOG2E = gmpy2.log2(gmpy2.exp(1))
LN2 = gmpy2.log(2)
# Same, as 192.64 fixedpoint
FX_PI = int(PI * 2**64)
FX_LOG2E = int(LOG2E * 2**64)
FX_LN2 = int(LN2 * 2**64)
FX_ONE = 1 << 64
## The index of a poly is the power of x,
## the val at the index is the coefficient.
##
## An nth degree poly is a list of len n + 1.
##
## The vals in a poly must all be floating point
## numbers.
def poly_add(p1, p2):
def good_pair(p: int, q: int) -> int:
n = p * q
k = gmpy2.ceil(gmpy2.log2(n))
if abs(p - q) > 2**(k / 2 - 100):
return n
return 0
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
# Parse command line arguments
parser = argparse.ArgumentParser(description="From a table of draws, output a seed of appropriate length.")
parser.add_argument("input_draw_file", help="""Text file with draws.""")
parser.add_argument("output_seed_file", help="""JSON file where we can store the seed computed from the draws.""")
parser.add_argument("entropy_to_gather", help="""Minimum entropy to extract before drawing lone bits.""")
parser.add_argument("--nbr_lone_bits", type=int, help="""Number of lone bits to extract.""", default=0)
args = parser.parse_args()
# Check arguments
output_seed_file = args.output_seed_file
if os.path.exists(output_seed_file):
utils.exit_error("The output file '%s' already exists. Exiting."%(output_seed_file))
# Declare a few important variables
two_pow_entropy_to_gather = (1<<int(args.entropy_to_gather))
seed = 0
L = 1 # before lone bits are drawn, seed lies in [0,L - 1]
lone_bits_part = 0
nbr_lone_bits = args.nbr_lone_bits
# Scan the input file, construct the seed
with open(args.input_draw_file, "r") as f:
for line in f:
if not line or line.strip() == "" or line.startswith("#"):
continue
(draw_id, m, n, draw) = re.split("\s+", line.strip(), maxsplit=3)
if draw == "None":
continue
m = int(m)
n = int(n)
draw = [ int(x) for x in draw.split(",") ]
index = index_from_draw(draw,m)
if L < two_pow_entropy_to_gather:
print("Draw %s used to extract entropy"%(draw_id))
seed = gmpy2.bincoef(n,m)*seed + index
L *= gmpy2.bincoef(n,m)
else:
print("Draw %s used to extract a lone bit"%(draw_id))
b = index & 1
seed += L * (b << (args.nbr_lone_bits - nbr_lone_bits))
nbr_lone_bits -= 1
if L >= two_pow_entropy_to_gather and nbr_lone_bits == 0:
break
if nbr_lone_bits > 0 or L < two_pow_entropy_to_gather:
utils.exit_error("There wasn't enough draws to collect to request quantity of entropy and lone bits.")
seed_upper_bound = L * 2**(args.nbr_lone_bits)
seed_entropy = math.floor(gmpy2.log2(seed_upper_bound))
print("The seed contains more than %d bits of entropy (including the %s lone bits)."%(seed_entropy,args.nbr_lone_bits))
print("The seed is %d"%(seed))
print("Saving the seed to %s"%(output_seed_file))
with open(output_seed_file, "w") as f:
json.dump({"seed": int(seed),
"seed_upper_bound": int(seed_upper_bound),
"approx_seed_entropy": int(seed_entropy),
"lone_bits": int(args.nbr_lone_bits)},
f,
sort_keys=True)
def is_prime_by_AKS(n):
"""
使用AKS算法确定n是否是一个素数
True:n是素数
False:n是合数
"""
def __is_integer__(n):
"""
判断一个数是否是整数
"""
i = gmpy2.mpz(n)
f = n - i
return not f
def __phi__(n):
"""
欧拉函数，测试小于n并与n互素的个数
"""
res = gmpy2.mpz(n)
a = gmpy2.mpz(n)
for i in range(2, a + 1):
if a % i == 0:
res = res // i * (i - 1)
while a % i == 0:
a //= i
if a > 1:
res = res // a * (a - 1)
return res
def __gcd__(a, b):
"""
计算a b的最大公约数
"""
if b == 0:
return a
return __gcd__(gmpy2.mpz(b), gmpy2.mpz(a) % gmpy2.mpz(b))
print("步骤1, 确定%d是否是纯次幂" % n)
for b in range(2, gmpy2.mpz(gmpy2.floor(gmpy2.log2(n))) + 1):
a = n**(1 / b)
if __is_integer__(a):
return False
print("步骤2，找到一个最小的r，符合o_r(%d) > (log%d)^2" % (n, n))
maxk = gmpy2.mpz(gmpy2.floor(gmpy2.log2(n)**2))
maxr = max(3, gmpy2.mpz(gmpy2.ceil(gmpy2.log2(n)**5)))
nextR = True
r = 0
for r in range(2, maxr):
if nextR == False:
break
nextR = False
for k in range(1, maxk + 1):
if nextR == True:
break
nextR = (gmpy2.mpz(n**k % r) == 0) or (gmpy2.mpz(n**k % r) == 1)
r = r - 1 # 循环多增加了一层
print("r = %d" % r)
print("步骤3，如果 1 < gcd(a, %d) < %d，对于一些 a <= %d, 输出合数" % (n, n, r))
for a in range(r, 1, -1):
g = __gcd__(a, n)
if g > 1 and g < n:
return False
print("步骤4，如果n=%d <= r=%d，输出素数" % (n, r))
if n <= r:
return True
print("步骤5")
print("遍历a从1到\sqrt{\phi(r=%d)}logn=%d" % (r, n))
print("如果(X+a)^%d != X^%d+a mod {X^%d-1, %d}$输出合数" % (n, n, r, n))
# 构造P = (X+a)^n mod (X^r-1)
print("构造多项式(X+a)^%d,并且进行二项式展开" % n)
X = multi_ysymbols('X')
a = multi_ysymbols('a')
X_a_n_expand = binomial_expand(ypolynomial1(X, a), n)
print(X_a_n_expand)
X.pow(r)
reduce_poly = ypolynomial1(X, ysymbol(value=-1.0))
print("构造消减多项式 %s" % reduce_poly)
print("进行运算 (X+a)^%d mod (X^%d-1)" % (n, r))
r_equ = ypolynomial_mod(X_a_n_expand, reduce_poly)
print("得到余式: %s" % r_equ)
print("进行运算'余式' mod %d 得到式(A)" % n)
A = ypolynomial_reduce(r_equ, n)
print("A = %s" % A)
print("B = x^%d+a mod x^%d-1" % (n, r))
B = ypolynomial1(multi_ysymbols('X', power=31), a)
B = ypolynomial_mod(B, reduce_poly)
print("B = %s" % B)
C = ypolynomial_sub(A, B)
print("C = A - B = %s" % C)
maxa = math.floor(math.sqrt(__phi__(r)) * math.log2(n))
print("遍历a = 1 to %d" % maxa)
print("检查每个'%s = 0 (mod %d)'" % (C, n))
for a in range(1, maxa + 1):
print("检查a = %d" % a)
C.set_variables_value(a=a)
v = C.eval()
if v % n != 0:
return False
print("步骤6 输出素数")
return True
def compute_final(self, result_list, i, num_words, tag_list):
return result_list[num_words - 1][i][0] + gmpy2.log2(self.get_transition_prob(tag_list[i]))
def compute_prev(self, result_list, t, i, j, word_list, tag_list):
if t < 0:
return gmpy2.log2(self.get_transition_prob(tag_list[i], tag_list[j])) + gmpy2.log2(self.get_emission_prob(tag_list[j], word_list[t + 1]))
return result_list[t][i][0] + gmpy2.log2(self.get_transition_prob(tag_list[i], tag_list[j])) + gmpy2.log2(self.get_emission_prob(tag_list[j], word_list[t + 1]))
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
# Parse command line arguments
parser = argparse.ArgumentParser(description="Generate BBS parameters.")
parser.add_argument(
"input_file",
help=
"""JSON file containing the seed used for generating the pseudo strong
strong prime (the name is "seed"). The required
quantity of entropy it should contain depends on bitsize. As a rule of
thumb the seed should contain at least 4*bitsize bits of entropy."""
)
parser.add_argument(
"output_file",
help=
"""Output JSON file where this script will write the two generated strong
strong primes "p" and "q". The output file should not exist already."""
)
parser.add_argument(
"min_prime_bitsize",
type=int,
help="minimum strong strong prime bit size (e.g. 2048).")
args = parser.parse_args()
# Check arguments
output_file = args.output_file
if os.path.exists(output_file):
utils.exit_error("The output file '%s' already exists. Exiting." %
(output_file))
# Declare a few important variables
min_prime_bitsize = args.min_prime_bitsize
input_file = args.input_file
with open(input_file, "r") as f:
data = json.load(f)
seed = int(data["seed"])
seed_upper_bound = int(data["seed_upper_bound"])
approx_seed_entropy = math.floor(gmpy2.log2(seed_upper_bound))
utils.colprint("Minimum strong strong prime size:", str(min_prime_bitsize))
utils.colprint("Approximate seed entropy:", str(approx_seed_entropy))
# Precomputations
first_primes = [2] # List of the first primes
PI = 2 # Product of the primes in "first_primes"
strong_strong_integers = [
[1]
] # strong_strong_integers[i] is the list of all strong strong integers modulo
# first_primes[i]
number_of_strong_strong_integers = [
1
] # number_of_strong_strong_integers[i] is the number of elements of the list
# strong_strong_integers[i]
C = 1 # Product of the elements of "number_of_strong_strong_integers"
while not 2**(min_prime_bitsize - 2) < PI:
p = int(gmpy2.next_prime(first_primes[-1]))
first_primes.append(p)
PI *= p
ssi = [c for c in range(p) if is_strong_strong_basis(c, p)]
strong_strong_integers.append(ssi)
number_of_strong_strong_integers.append(len(ssi))
C *= len(ssi)
utils.colprint("Number of primes considered:", str(len(first_primes)))
utils.colprint("Number of strong strong integers to choose from:",
"about 2^%f" % (gmpy2.log2(C)))
# Check that the seed is long enough
if seed_upper_bound < C**2 * (1 << (2 * min_prime_bitsize)):
utils.exit_error("The seed does not contain the required entropy.")
# Precomputations for the CRT
mu = [gmpy2.divexact(PI, p) for p in first_primes]
delta = [gmpy2.invert(x, y) for x, y in zip(mu, first_primes)]
gamma = [gmpy2.mul(x, y) for x, y in zip(mu, delta)]
# Generate the first strong prime
print("Generating the first strong strong prime...")
(p, seed) = generate_strong_strong_prime(seed, min_prime_bitsize,
strong_strong_integers,
number_of_strong_strong_integers,
gamma, PI)
utils.colprint("\tThis is the first strong strong prime:", str(p))
# Generate the second strong prime
print("Generating the second strong strong prime...")
(q, seed) = generate_strong_strong_prime(seed, min_prime_bitsize,
strong_strong_integers,
number_of_strong_strong_integers,
gamma, PI)
utils.colprint("\tThis is the second strong strong prime:", str(q))
# Generate the BBS start
print("Generating the BBS starting point...")
n = p * q
s = seed % n
while s == 0 or s == 1 or s == p or s == q:
s = (s + 1) % n
s0 = (s**2) % n
utils.colprint("\tThis is the starting point s0 of BBS:", str(s0))
# Save p,q, and s to the output_file
print("Saving p,q, and s0 to %s" % (output_file))
with open(output_file, "w") as f:
json.dump({
"bbs_p": int(p),
"bbs_q": int(q),
"bbs_s": int(s0)
},
f,
sort_keys=True)
def integer_log2(i: Integer) -> int:
return int(log2(i.value))
def main():
# Test local versions of libraries
utils.test_python_version()
utils.test_gmpy2_version()
# Parse command line arguments
parser = argparse.ArgumentParser(
description=
"From a table of draws, output a seed of appropriate length.")
parser.add_argument("input_draw_file", help="""Text file with draws.""")
parser.add_argument(
"output_seed_file",
help=
"""JSON file where we can store the seed computed from the draws.""")
parser.add_argument(
"entropy_to_gather",
help="""Minimum entropy to extract before drawing lone bits.""")
parser.add_argument("--nbr_lone_bits",
type=int,
help="""Number of lone bits to extract.""",
default=0)
args = parser.parse_args()
# Check arguments
output_seed_file = args.output_seed_file
if os.path.exists(output_seed_file):
utils.exit_error("The output file '%s' already exists. Exiting." %
(output_seed_file))
# Declare a few important variables
two_pow_entropy_to_gather = (1 << int(args.entropy_to_gather))
seed = 0
L = 1 # before lone bits are drawn, seed lies in [0,L - 1]
lone_bits_part = 0
nbr_lone_bits = args.nbr_lone_bits
# Scan the input file, construct the seed
with open(args.input_draw_file, "r") as f:
for line in f:
if not line or line.strip() == "" or line.startswith("#"):
continue
(draw_id, m, n, draw) = re.split("\s+", line.strip(), maxsplit=3)
if draw == "None":
continue
m = int(m)
n = int(n)
draw = [int(x) for x in draw.split(",")]
index = index_from_draw(draw, m)
if L < two_pow_entropy_to_gather:
print("Draw %s used to extract entropy" % (draw_id))
seed = gmpy2.bincoef(n, m) * seed + index
L *= gmpy2.bincoef(n, m)
else:
print("Draw %s used to extract a lone bit" % (draw_id))
b = index & 1
seed += L * (b << (args.nbr_lone_bits - nbr_lone_bits))
nbr_lone_bits -= 1
if L >= two_pow_entropy_to_gather and nbr_lone_bits == 0:
break
if nbr_lone_bits > 0 or L < two_pow_entropy_to_gather:
utils.exit_error(
"There wasn't enough draws to collect to request quantity of entropy and lone bits."
)
seed_upper_bound = L * 2**(args.nbr_lone_bits)
seed_entropy = math.floor(gmpy2.log2(seed_upper_bound))
print(
"The seed contains more than %d bits of entropy (including the %s lone bits)."
% (seed_entropy, args.nbr_lone_bits))
print("The seed is %d" % (seed))
print("Saving the seed to %s" % (output_seed_file))
with open(output_seed_file, "w") as f:
json.dump(
{
"seed": int(seed),
"seed_upper_bound": int(seed_upper_bound),
"approx_seed_entropy": int(seed_entropy),
"lone_bits": int(args.nbr_lone_bits)
},
f,
sort_keys=True)
dEX = cuda.to_device(np_str, stream)
dHH = cuda.device_array(np_str.shape[0], dtype=np.uint64)
dRR = cuda.device_array(10, dtype=np.int32)
r_str = np_str[rdrand.rand32() % np_str.shape[0]]
h_str = c_hash0(r_str)
set_dim(np_str.shape[0])
stream.synchronize()
hash0_kernel[DIM](dEX, dHH)
search_kernel[DIM](dHH, h_str, dRR)
np_res = dRR.copy_to_host()
v1 = gmpy2.mpz(int.from_bytes(bytes(np_str[np_res[1]]), 'big'))
v2 = gmpy2.mpz(int.from_bytes(bytes(r_str), 'big'))
assert (v1 == v2)
print(
"Total GPU (64bit hash) search results:\t{0:,d} of {1:,d}\t(index {2:d})".
format(np_res[0], np_str.shape[0], np_res[1]))
print("\t\t###\trdrand.seed_bytes({:d})\t###".format(SEED))
print("{0}\tlength {1:d}".format(v1.digits(2), v1.bit_length()))
print("int\t{0:d}\t(log2 ~ {1:.9f})".format(v1, gmpy2.log2(v1)))
assert (np.unique(np_str, axis=0).shape[0] == np_str.shape[0])
np_h = dHH.copy_to_host()
assert (np.unique(np_h).shape[0] == np_h.shape[0])
def __init__(self, n):
self.n = n
self.n_sq = n * n
self.g = n + 1
self.bits = mpz(rint_round(log2(self.n)))
def _get_max_prime(start, gap, max_prime):
if max_prime is None or max_prime <= 1:
log2 = float(gmpy2.log2(start + gap))
max_prime = verify.sieve_limit(log2, gap)
return max_prime
#!/usr/bin/python2
import sys
import multiprocessing
import gmpy2
import scipy
import scipy.interpolate
import numpy
import random
import itertools
import time
gmpy2.get_context().precision = 256
LOG2E = int(gmpy2.log2(gmpy2.exp(1))*2**64)
def fxp_ilog2(x):
y = x >> 64
lo = 0
hi = 191
mid = (lo + hi) >> 1
while lo < hi:
if (1 << mid) > y:
hi = mid - 1
else:
lo = mid + 1
mid = (lo + hi) >> 1
return lo
def fxp_lagrange(x, coeffs):
result = 0
xpow = 1 << 64
def random_from_interval(random_state, low, high, m=32):
M = int(g.ceil(g.log2(high)))
random = g.mpz_urandomb(random_state, M + m)
c = g.add(g.f_mod(random, g.add(g.sub(high, low), 1)), low)
return c
from SecMult_Sub import Sub
from Client_Server import *
import timeit
import time
import numpy as np
from sympy.polys.domains import ZZ
from sympy.polys.galoistools import gf_neg
from sympy.polys.galoistools import *
from sympy import *
import gmpy2
from gmpy2 import mpz, mpfr, log2
from sklearn import linear_model
from sklearn.metrics import mean_squared_error
a = 12345678901234567890
gmpy2.get_context().precision = 70
mpz(2**log2(a))
mpz(12345678901234567890)
N = 999999999999999999999999999999999999999999999999999999999999
M1 = 10000000000000000000000000000000000000000
Prec = 100000000000000000000
In_Pre = 1000000000000000
Lambda = 1000000000000000000000000000000
def mod(x, modulus):
numer, denom = x.as_numer_denom()
return numer * mod_inverse(denom, modulus) % modulus
def Test():
def __init__(self, n):
self.n = n
self.n_sq = n * n
self.g = n + 1
self.bits=mpz(rint_round(log2(self.n)))
#import matplotlib.pyplot as plt
import os
import bisect
from numpy import linspace
# gmpy2 precision initialization
BITS = (1 << 10)
BYTES = BITS/8
gmpy2.get_context().precision = BITS # a whole lotta bits
def random():
seed = int(os.urandom(BYTES).encode('hex'), 16)
return gmpy2.mpfr_random(gmpy2.random_state(seed))
# Useful constants as mpfr
PI = gmpy2.acos(-1)
LOG2E = gmpy2.log2(gmpy2.exp(1))
LN2 = gmpy2.log(2)
# Same, as 192.64 fixedpoint
FX_PI = int(PI * 2**64)
FX_LOG2E = int(LOG2E * 2**64)
FX_LN2 = int(LN2 * 2**64)
FX_ONE = 1 << 64
## The index of a poly is the power of x,
## the val at the index is the coefficient.
##
## An nth degree poly is a list of len n + 1.
##
## The vals in a poly must all be floating point
## numbers.
def poly_add(p1, p2):
b0c = [gmpy2.mul(b, ci) for b, ci in zip(b0, c)]
b1c = [gmpy2.mul(b, ci) for b, ci in zip(b1, c)]
s_0b = gmpy2.mpz(0)
s_1b = gmpy2.mpz(0)
for j in range(n):
if a[j] != 0:
s_0b = gmpy2.add(s_0b, b0a[j])
s_1b = gmpy2.add(s_1b, b1a[j])
else:
s_0b = gmpy2.add(s_0b, b0c[j])
s_1b = gmpy2.add(s_1b, b1c[j])
diff0 = gmpy2.sub(Ep, s_0b)
overflow0 = gmpy2.log2(diff0)
diff1 = gmpy2.sub(Ep, s_1b)
overflow1 = gmpy2.log2(diff1)
s_0b = gmpy2.digits(s_0b)
s_1b = gmpy2.digits(s_1b)
#print("\na: " + str(a))
#print("b0: " + str(b0))
#print("b1: " + str(b1))
#print("choice: " + str(choice))
#print("s_Ep: " + s_Ep)
#print("s_0b: " + s_0b)
#print("s_1b: " + s_1b)
guess = eq_digits(no_digits, s_Ep, s_1b)