def step_t_5(a_base, B, p1):
if p1 <= int(root(B, 5)):
### Посчет времени работы
start_time = time.time()
###
n_list = []
l = 5
if p1 % 4 == 3:
n_list = [p1]
q_3k4 = readfile("primes/4k+3.txt")
sign_p1 = []
for a in a_base:
sign_p1.append(numth.jacobi(a, p1))
for q in q_3k4:
if q % 24 == p1 % 24:
sign_q = []
for a in a_base:
sign_q.append(numth.jacobi(a, q))
if sign_q == sign_p1:
n_list.append(q)
# else:
# for p in primes:
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
return np.array(n_list)
else:
print(f"Value Error: p1 > {int(root(B, 5))}")
def verify(pubkey, signature, message_hash):
'''Verify a Schnorr signature, returning True if valid.
May raise a ValueError or return False on failure.
`pubkey` should be the the raw public key bytes (as you would get from
bitcoin.pubic_key_from_private_key, after hex decoding, etc).
`signature` should be the 64 byte schnorr signature as would be returned
from `sign` above.
`message_hash` should be the 32 byte sha256d hash of the tx message to be
verified'''
if not isinstance(pubkey, bytes) or len(pubkey) not in (33, 65):
raise ValueError('pubkey must be a bytes object of either length 33 or 65')
if not isinstance(signature, bytes) or len(signature) != 64:
raise ValueError('signature must be a bytes object of length 64')
if not isinstance(message_hash, bytes) or len(message_hash) != 32:
raise ValueError('message_hash must be a bytes object of length 32')
G = ecdsa.SECP256k1.generator
order = G.order()
fieldsize = G.curve().p()
try:
pubpoint = ser_to_point(pubkey)
except:
# off-curve points, failed decompression, bad format,
# point at infinity:
raise ValueError('pubkey could not be parsed')
rbytes = signature[:32]
## these unnecessary since below we do bytes comparison and
## R.x() is always < fieldsize.
# r = int.from_bytes(rbytes, 'big')
# if r >= fieldsize:
# return False
sbytes = signature[32:]
s = int.from_bytes(sbytes, 'big')
if s >= order:
return False
# compressed format, regardless of whether pubkey was compressed or not:
pubbytes = point_to_ser(pubpoint, comp=True)
ebytes = hashlib.sha256(rbytes + pubbytes + message_hash).digest()
e = int.from_bytes(ebytes, 'big')
R = s*G + (- e)*pubpoint
if R == ecdsa.ellipticcurve.INFINITY:
return False
if jacobi(R.y(), fieldsize) != 1:
return False
return (R.x().to_bytes(32, 'big') == rbytes)
def _calc_initial_fast(self):
# Fast version of _calc_initial, using libsecp256k1. About 2.4x faster.
ctx = seclib.ctx
abytes = int(self.a).to_bytes(32, 'big')
bbytes = int(self.b).to_bytes(32, 'big')
R_buf = create_string_buffer(64)
res = seclib.secp256k1_ec_pubkey_parse(ctx, R_buf, self.R,
c_size_t(len(self.R)))
if not res:
raise ValueError('R could not be parsed by the secp256k1 library')
pubkey_buf = create_string_buffer(64)
res = seclib.secp256k1_ec_pubkey_parse(ctx, pubkey_buf, self.pubkey,
c_size_t(len(self.pubkey)))
if not res:
raise ValueError(
'pubkey could not be parsed by the secp256k1 library')
# resave pubkey as compressed.
P_compressed = create_string_buffer(33)
P_size = c_size_t(33)
res = seclib.secp256k1_ec_pubkey_serialize(
ctx, P_compressed, byref(P_size), pubkey_buf,
secp256k1.SECP256K1_EC_COMPRESSED)
self.pubkey_compressed = P_compressed.raw
A_buf = create_string_buffer(64)
# calculate a*G. ~24 microsec
res = seclib.secp256k1_ec_pubkey_create(ctx, A_buf, abytes)
assert res == 1, "should never fail since 0 < a < order"
# in-place tweak the pubkey by multiplying with scalar b. ~33 microsec
res = seclib.secp256k1_ec_pubkey_tweak_mul(ctx, pubkey_buf, bbytes)
assert res == 1, "should never fail since 0 < b < order"
# add the three points together. ~6 microsec
Rnew_buf = create_string_buffer(64)
publist = (c_void_p * 3)(*(cast(x, c_void_p)
for x in (R_buf, A_buf, pubkey_buf)))
res = seclib.secp256k1_ec_pubkey_combine(ctx, Rnew_buf, publist, 3)
assert res == 1, "fails with 2^-256 chance (if sum is point at infinity), in which case we have cracked the key"
# serialize the new R point
Rnew_serialized = create_string_buffer(65)
Rnew_size = c_size_t(65)
res = seclib.secp256k1_ec_pubkey_serialize(
ctx, Rnew_serialized, byref(Rnew_size), Rnew_buf,
secp256k1.SECP256K1_EC_UNCOMPRESSED)
assert res == 1, "defined to never fail"
assert Rnew_size.value == 65, "should fill buffer as uncompressed"
self.Rxnew = Rnew_serialized[1:33]
y = int.from_bytes(Rnew_serialized[33:], byteorder="big")
# calculate the jacobi symbol (+1 or -1). ~30 microsec, because pure python :(
self.c = jacobi(y, self.fieldsize)
def sign(privkey, message_hash):
'''Create a Schnorr signature.
Returns a 64-long bytes object (the signature), or raise ValueError
on failure. Failure can occur due to an invalid private key.
`privkey` should be the 32 byte raw private key (as you would get from
bitcoin.deserialize_privkey, etc).
`message_hash` should be the 32 byte sha256d hash of the tx input (or
message) you want to sign
'''
if not isinstance(privkey, bytes) or len(privkey) != 32:
raise ValueError('privkey must be a bytes object of length 32')
if not isinstance(message_hash, bytes) or len(message_hash) != 32:
raise ValueError('message_hash must be a bytes object of length 32')
if _secp256k1_schnorr_sign:
sig = create_string_buffer(64)
res = _secp256k1_schnorr_sign(secp256k1.secp256k1.ctx, sig,
message_hash, privkey, None, None)
if not res:
# Looking at the libsecp256k1 code, we can see that this will
# only occur if privkey is == 0 or >= order, i.e., if it has
# no associated pubkey. But as it's not specified in API we'll
# just leave it as a vague exception.
raise ValueError('could not sign')
return bytes(sig)
else:
# pure python fallback:
G = ecdsa.SECP256k1.generator
order = G.order()
fieldsize = G.curve().p()
secexp = int.from_bytes(privkey, 'big')
if not 0 < secexp < order:
raise ValueError('could not sign')
pubpoint = secexp * G
pubbytes = point_to_ser(pubpoint, comp=True)
k = nonce_function_rfc6979(order,
privkey,
message_hash,
algo16=b'Schnorr+SHA256\x20\x20')
R = k * G
if jacobi(R.y(), fieldsize) == -1:
k = order - k
rbytes = int(R.x()).to_bytes(32, 'big')
ebytes = hashlib.sha256(rbytes + pubbytes + message_hash).digest()
e = int.from_bytes(ebytes, 'big')
s = (k + e * secexp) % order
return rbytes + int(s).to_bytes(32, 'big')
def psp_2(a_base, pq):
p, q = pq[0], pq[1]
if p % 4 == 1: # Remark for psp(2,n). Так как ищем для нескольких баз, то учитываем сразу
for a in a_base[1:]:
if numth.jacobi(q, a) != 1:
return False
else:
continue
else:
return False
return True
def Sign(v, p):
if p % 4 == 3:
sgm_v_p = []
for a in v:
if numth.jacobi(a, p) == 1:
sgm_v_p.append(0)
elif numth.jacobi(a, p) == -1:
sgm_v_p.append(1)
return sgm_v_p
elif p % 4 == 1:
sgm_v_p = []
for a in v:
if numth.jacobi(a, p) == -1:
val = Val(2, p - 1)
sgm_v_p.append(val)
else:
# print(f'a_base item {a},{p}')
ord = Ord(p, a)
val = Val(2, ord)
sgm_v_p.append(val)
return sgm_v_p
def sign(privkey, message_hash):
'''Create a Schnorr signature.
Returns a 64-long bytes object (the signature), or raise ValueError
on failure. Failure can occur due to an invalid private key.
`privkey` should be the 32 byte raw private key (as you would get from
bitcoin.deserialize_privkey, etc).
`message_hash` should be the 32 byte sha256d hash of the tx input (or
message) you want to sign
'''
if not isinstance(privkey, bytes) or len(privkey) != 32:
raise ValueError('privkey must be a bytes object of length 32')
if not isinstance(message_hash, bytes) or len(message_hash) != 32:
raise ValueError('message_hash must be a bytes object of length 32')
G = ecdsa.SECP256k1.generator
order = G.order()
fieldsize = G.curve().p()
secexp = int.from_bytes(privkey, 'big')
if not 0 < secexp < order:
raise ValueError('could not sign')
pubpoint = secexp * G
pubbytes = point_to_ser(pubpoint, comp=True)
k = nonce_function_rfc6979(order, privkey, message_hash,
algo16=b'Schnorr+SHA256\x20\x20')
R = k * G
if jacobi(R.y(), fieldsize) == -1:
k = order - k
rbytes = R.x().to_bytes(32,'big')
ebytes = hashlib.sha256(rbytes + pubbytes + message_hash).digest()
e = int.from_bytes(ebytes, 'big')
s = (k + e*secexp) % order
return rbytes + s.to_bytes(32, 'big')
def _calc_initial(self):
# Internal function, calculates Rxnew, c, and compressed pubkey.
try:
Rpoint = ser_to_point(self.R)
except:
# off-curve points, failed decompression, bad format,
# point at infinity:
raise ValueError('R could not be parsed')
try:
pubpoint = ser_to_point(self.pubkey)
except:
# off-curve points, failed decompression, bad format,
# point at infinity:
raise ValueError('pubkey could not be parsed')
self.pubkey_compressed = point_to_ser(pubpoint, comp=True)
# multiply & add the points -- takes ~190 microsec
Rnew = Rpoint + self.a * ecdsa.SECP256k1.generator + self.b * pubpoint
self.Rxnew = int(Rnew.x()).to_bytes(32, 'big')
y = Rnew.y()
# calculate the jacobi symbol (+1 or -1). ~30 microsec
self.c = jacobi(y, self.fieldsize)
def step_t_3(a_base, B):
clearfile(f"res/jnd/3/{a_base}/spsp_{B}.txt")
clearfile(f"res/jnd/3/{a_base}/n_list_{B}.txt")
n_list = []
### Посчет времени работы
start_time = time.time()
###
# equal_2_list = parsefile(f"res/jnd/2/{a_base}/n_list_{B}.txt")
# упорядочены по возрастанию p1, где p1<p2
# if len(equal_2_list) != 0:
# for i in range(len(equal_2_list)):
# p1 = equal_2_list[i].primes[0]
# p2 = equal_2_list[i].primes[1]
# b = int(p1 * p2)
for p1 in primes:
p1 = int(p1)
print(p1)
if p1 <= int(root(B, 3)): # and b * p2 < B:
if p1 > a_base[-1]:
print(p1)
s = ""
if len(a_base) > 6:
a_base = a_base[:6]
leg1 = []
for a in a_base:
leg1.append(numth.jacobi(a, p1))
p2_3k4 = readfile("primes/4k+3.txt")
p2_1k4 = readfile("primes/4k+1.txt")
p2_5k8 = readfile("primes/8k+5.txt")
p2_1k8 = readfile("primes/8k+1.txt")
if p1 % 4 == 3:
print(f"p1 34 {p1}")
for p2 in p2_3k4:
if p2 > p1 and p2 < B and p2 < B: # на всякий случай проверим
print(f"p2 34 {p2}")
leg2 = []
b = int(p1 * p2)
for a in a_base:
leg2.append(numth.jacobi(a, p2))
if leg1 == leg2: # Prop.2 inverse is true
if b < 2 * 10**6: # a trick
gcd_23 = int(
gcd(2**(b - 1) - 1, 3**(b - 1) - 1))
factor_list = numth.factorization(gcd_23)
for i in range(len(factor_list)):
p3 = factor_list[i][0]
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
else:
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base,
B) # ищем подходящие p3
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# continue # новый item из equal_2_list
# else:
# continue
for p2 in p2_1k4:
print(f"p2 14 to mu {p2}")
if Mu_p(a_base, p2) == 4:
pass # переход к mu=4
elif p1 % 8 == 5:
print(f"p1 58 {p1}")
for p2 in p2_5k8:
if p2 > p1 and p2 < B:
print(f"p2 58 {p2}")
if len(a_base) > 5:
a_base = a_base[:5]
leg2 = []
b = int(p1 * p2)
for a in a_base:
leg2.append(numth.jacobi(a, p2))
if leg1 == leg2:
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
print(p3_list, type(p3_list))
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# continue
# else:
# continue
for p2 in p2_1k8:
if p2 > p1 and p2 < B:
print(f"p2 18 {p2}")
if p2 % 16 == 9:
print(f"p2 916 {p2}")
leg2 = []
b = int(p1 * p2)
for a in a_base:
leg2.append(numth.jacobi(a, p2))
if np.prod(
leg2
) == 1 and p2 > p1: # если все 1, то произведение 1
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
else:
continue
else:
continue
elif p2 % 16 == 1:
print(f"p2 116 to mu {p2}")
if Mu_p(a_base, p2) == 4:
pass # переход к mu=4
for p2 in p2_3k4:
if p2 > p1 and p2 < B: # в тексте этого нет, но на всякий случай проверим
print(f"p2 34 {p2}")
b = int(p1 * p2)
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
# print(f"p3 list {p3_list}")
if isinstance(p3_list, list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# continue
elif p1 % 8 == 1:
print(f"p1 18 {p1} p2 any {p2}")
e, f = Val(2, p1 - 1), Val(2, Lambda_p(a_base, p1))
if len(a_base) > 5:
a_base = a_base[:5]
for p2 in primes:
if p2 > p1 and p2 < B and e == f:
if p2 % (2**(e + 1)) == (1 + 2**e) % (2**(
e + 1)): # !!!! СКОБКИ???
leg2 = []
b = int(p1 * p2)
for a in a_base:
leg2.append(numth.jacobi(a, p2))
if leg1 == leg2:
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
else:
continue
else:
continue
elif p2 % (2**(e + 2)) == 1:
if Mu_p(a_base, p2) == 4:
pass # переход к mu=4
elif p2 % (2**(e + 2)) != 1 and p2 % (2**(
e + 2)) == (1 + 2**(e + 1)) % 2**(
e + 2): # !!!! СКОБКИ???
leg2 = []
b = int(p1 * p2)
for a in a_base:
leg2.append(numth.jacobi(a, p2))
if np.prod(leg2) == 1:
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
else:
continue
else:
continue
elif p2 > p1 and p2 < B and f < e:
if p2 % 2**f == p1:
if f == e - 1 and Mu_p(
a_base,
p1) == 2: # это есть условие выше
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
b = int(p1 * p2)
if isinstance(p3_list,
list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(
a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1),
[p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
else:
continue
else:
continue
else:
continue
# p1 is any in primes
mu_4 = readfile(f"lib/mu/{a_base}/mu_4.txt")
for p2 in mu_4:
if p2 > p1 and p2 < B: # если p2 mu=4, то не обязательно чтобы и p1 mu=4
print(f"p2 mu4 {p2}")
p_exist = np.array([p1, p2])
p3_list = next_p(p_exist, a_base, B)
b = int(p1 * p2)
if isinstance(p3_list, list) and len(p3_list) != 0:
for p3 in p3_list:
if p3 * b <= B: # and p3 * b > B // 100:
if p3 > p2:
print(f"p3 {p3}")
signss = check_signs(a_base, [p1, p3])
if signss:
item = Signature(
Sign(a_base, p1), [p1, p2, p3])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# continue
writefile(f"res/jnd/3/{a_base}/n_list_{B}.txt", s)
else:
continue
else:
break
i = 1
spsp = []
ss = ""
for item in n_list:
prod = np.prod(item.primes)
if psp(a_base, prod):
ss += f"{i} {prod} {item.primes} {item.sign}\n"
i += 1
spsp.append(item)
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
ss += f"{total_time}\n"
writefile(f"res/jnd/3/{a_base}/spsp_{B}.txt", ss)
return np.array(spsp)
def step_t_2(a_base, B, primes_list):
clearfile(f"res/jnd/2/{a_base}/spsp_{B}.txt")
clearfile(f"res/jnd/2/{a_base}/n_list_{B}.txt")
n_list = []
### Посчет времени работы
start_time = time.time()
###
for p1 in primes_list:
p1 = int(p1)
if p1 < int(root(B, 2)):
if p1 > a_base[-1]:
s = ""
if p1 < 10**6:
gcd_23 = int(gcd(2**(p1 - 1) - 1, 3**(p1 - 1) - 1))
factors = sorted(numth.factorization(gcd_23))
for i in range(len(factors)):
p2 = factors[i][0]
if p2 * p1 <= B: # and p1 * p2 > B // 100:
if p2 > p1: # В дальнейшем для того, чтобы числа в интервалах не повторялись
signss = check_signs(a_base, [p1, p2])
if signss:
item = Signature(Sign(a_base, p1),
[p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
elif p1 > 10**8:
lmd_p = Lambda_p(a_base, p1) # lmd_p = p1-1
p2 = 1
while p2 <= p1: # and p1 * p2 > B // 100: # к условию, что p2>p1
p2 += lmd_p
while p2 * p1 <= B: # and p1 * p2 > B // 100:
signss = check_signs(a_base, [p1, p2])
if signss:
item = Signature(Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(Signature(item.sign, [p1, p2]))
p2 += lmd_p
else: # между 10**6..10**8
if len(a_base) > 6:
a_base = a_base[:6]
lmd_p = Lambda_p(a_base, p1)
leg1 = []
for a in a_base:
leg1.append(numth.jacobi(a, p1))
if p1 % 4 == 1:
p2_4k3 = readfile("primes/4k+3.txt")
p2_4k1 = readfile("primes/4k+1.txt")
for p2 in p2_4k3:
if p1 * p2 <= B: # and p1 * p2 > B // 100:
if p2 % lmd_p == 1 and p2 > p1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if leg1 == leg2 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
for p2 in p2_4k1:
if p1 * p2 <= B: # and p1 * p2 > B // 100:
if p2 % lmd_p == 1 and p2 > p1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if np.prod(
leg2
) == 1 and signss: # если все 1, то произведение 1
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
elif p1 % 8 == 5:
p2_8k5 = readfile("primes/8k+5.txt")
p2_8k1 = readfile("primes/8k+1.txt")
for p2 in p2_8k5:
if p1 * p2 <= B: # and p1 * p2 > B // 100:
if p2 % lmd_p == 5 and p2 > p1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if leg1 == leg2 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
for p2 in p2_8k1:
if p1 * p2 <= B: # and p1 * p2 > B // 100:
if p2 % lmd_p == 1 and p2 > p1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if np.prod(leg2) == 1 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
elif p1 % 8 == 1:
sign = Sign([2], p1)[0]
e, f = Val(2, p1 - 1), Val(2, sign)
for p2 in primes:
if p1 * p2 <= B: # and p1 * p2 > B // 100:
if p2 > p1 and e == f:
if p2 % (2**(e - 1)) == 2**e % (2**(
e - 1)) and p2 % lmd_p == 1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if leg1 == leg2 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
elif p2 % 2**(e +
1) == 1 and p2 % lmd_p == 1:
leg2 = []
for a in a_base:
leg2.append(numth.jacobi(a, p2))
signss = check_signs(a_base, [p1, p2])
if np.prod(leg2) == 1 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
elif p2 > p1 and f < e and p1 * p2 <= B: # and p1 * p2 > B // 100:
signss = check_signs(a_base, [p1, p2])
if p2 % lmd_p == 1 and signss:
item = Signature(
Sign(a_base, p1), [p1, p2])
s += f"{item.primes} {signss} {item.sign}\n"
n_list.append(item)
# else:
# break
writefile(f"res/jnd/2/{a_base}/n_list_{B}.txt", s)
else:
continue
i = 1
spsp = []
ss = ""
for item in n_list:
prod = np.prod(item.primes)
if psp(a_base, prod):
ss += f"{i} {prod} {item.primes} {item.sign}\n"
i += 1
spsp.append(item)
###
total_time = "--- %s seconds ---\n" % (time.time() - start_time)
###
ss += f"{total_time}\n"
writefile(f"res/jnd/2/{a_base}/spsp_{B}.txt", ss)
return np.array(spsp)
