def __init__(self,
a: RingElement,
b: RingElement,
ring: Ring = None,
base_tuple: tuple = None,
cardinality: int = None,
check_singularity: bool = True):
"""
Parameters:
a (RingElement): `a` coefficient.
b (RingElement): `b` constant.
ring (Ring): Underlying ring.
base_tuple (tuple): Tuple representing the base point 'G'.
cardinality (int): Number of points on the curve.
check_singularity (bool): Check if the curve is singular (no cusps or self-intersections).
"""
from samson.math.symbols import Symbol
self.a = a
self.b = b
self.ring = ring or self.a.ring
if check_singularity:
if (4 * a**3 - 27 * b**2) == self.ring.zero():
raise ValueError("Elliptic curve can't be singular")
if base_tuple:
base_tuple = WeierstrassPoint(*base_tuple, self)
self.G_cache = base_tuple
self.PAF_cache = None
self.dpoly_cache = {}
self.cardinality_cache = cardinality
self.curve_poly_ring = self[Symbol('x'), Symbol('y')]
def parse_atkin(data: str):
x = Symbol('x')
y = Symbol('y')
P = ZZ[x, y]
p = P.zero
for line in data.strip().split('\n'):
xp, yp, c = [int(c) for c in line.strip().split()]
p += x**xp * y**yp * c
return p
def __init__(self, ring: Ring, symbol: Symbol=None):
"""
Parameters:
ring (Ring): Underlying ring.
"""
self.ring = ring
self.symbol = symbol or Symbol('x')
self.symbol.build(self)
def test_vec0(self):
seed = 0xACE1
x = Symbol('x')
_ = (ZZ / ZZ(2))[x]
poly = x**16 + x**14 + x**13 + x**11 + 1
expected_output = [
1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1,
0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,
1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0,
1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0,
0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1,
1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0,
1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1,
0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0,
1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1,
0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,
1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1,
0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0,
1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0,
1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1,
0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1,
1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0,
1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0,
0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0,
0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0,
0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1,
1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0,
1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0,
0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1,
0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1,
0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1,
1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,
1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1,
0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0,
0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1,
1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1,
1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0,
0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1,
1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0,
0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0,
0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0,
1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1,
0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1,
0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0,
0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1,
1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0,
1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
1, 0, 1, 0, 0, 0, 0, 1, 1, 1
]
self._run_test(seed, poly, expected_output)
def __init__(self,
coeffs: list,
coeff_ring: Ring = None,
symbol: object = None,
ring: Ring = None):
"""
Parameters:
coeffs (list or Expr): Coefficients of the polynomial as a list of increasing degree or an expression.
coeff_ring (Ring): Ring the coefficients are in.
symbol (Symbol): Symbol to use as the indeterminate.
ring (Ring): Parent PolynomialRing.
"""
from samson.math.symbols import Symbol
self.coeff_ring = coeff_ring or coeffs[0].ring
if type(coeffs) is list or type(coeffs) is tuple or type(
coeffs) is dict:
if type(coeffs) is dict or (len(coeffs) > 0
and type(coeffs[0]) is tuple):
vec = coeffs
else:
vec = [self.coeff_ring.coerce(coeff) for coeff in coeffs]
self.coeffs = SparseVector(vec, self.coeff_ring.zero())
elif type(coeffs) is SparseVector:
self.coeffs = coeffs
else:
raise Exception(
f"'coeffs' is not of an accepted type. Received {type(coeffs)}"
)
self.symbol = symbol or Symbol('x')
self.ring = ring or self.coeff_ring[self.symbol]
if len(self.coeffs.values) == 0:
self.coeffs = SparseVector([self.coeff_ring.zero()],
self.coeff_ring.zero())
def __init__(self, kc: list, addr: list, master_clk: list):
"""
Parameters:
kc (list): Session key derived from master key.
addr (list): Hardware address.
master_clk (list): Master clock values.
"""
Primitive.__init__(self)
x = Symbol('x')
_ = (ZZ / ZZ(2))[x]
self.lfsrs = [
FLFSR(0, x**25 + x**20 + x**12 + x**8 + 1),
FLFSR(0, x**31 + x**24 + x**16 + x**12 + 1),
FLFSR(0, x**33 + x**28 + x**24 + x**4 + 1),
FLFSR(0, x**39 + x**36 + x**28 + x**4 + 1)
]
self.kc = kc
self.addr = addr
self.master_clk = master_clk
self.state = 0
self.key = 0
self.key_schedule()
from samson.math.algebra.all import FF, ZZ, QQ, P256
from samson.math.symbols import Symbol, oo
from samson.math.general import random_int, find_prime, factor
from samson.utilities.exceptions import NotInvertibleException
from functools import reduce
import unittest
x = Symbol('x')
y = Symbol('y')
F = FF(2, 8)
F23 = F / F[23]
FX2 = F[x] / (x**2)
Z_star = ZZ.mul_group()
Zp_star = (ZZ / ZZ(find_prime(128))).mul_group()
Zn_star = (ZZ / ZZ(random_int(2**32))).mul_group()
Z_2 = ZZ / ZZ(2)
P = Z_2[x]
P_q = P / (x**8 + x**4 + x**3 + x + 1)
R = ZZ[x] / (x**167 - 1)
P256C = P256[x, y]
ALGEBRAS = [ZZ, QQ, F, F23, P, Z_star, Z_2, P_q, P256, P256C]
class AlgebraTestCase(unittest.TestCase):
def test_random(self):
for algebra in ALGEBRAS:
try:
max_elem = algebra[11]
except NotImplementedError:
from samson.math.algebra.rings.integer_ring import ZZ
from samson.math.symbols import Symbol
from samson.public_key.ntru import NTRU
from samson.utilities.bytes import Bytes
import unittest
x = Symbol('x')
_ = ZZ[x]
# https://en.wikipedia.org/wiki/NTRUEncrypt
PARAM_SETS = [(167, 128, 3), (251, 128, 3), (347, 128, 3), (503, 128, 3)]
class NTRUTestCase(unittest.TestCase):
def test_gauntlet(self):
for N, q, p in PARAM_SETS:
print(N, q, p)
for _ in range(3):
ntru = NTRU(N=N, p=p, q=q)
plaintext = Bytes.random(8)
ciphertext = ntru.encrypt(plaintext)
self.assertEqual(ntru.decrypt(ciphertext).zfill(8), plaintext)
# Tests generated manually using https://github.com/jkrauze/ntru
# Commands generally of the form:
# ./ntru.py gen N p q test_priv test_pub
# echo -ne "<plaintext>" > test_msg
# ./ntru.py -o enc test_pub.npz test_msg
# ./ntru.py enc test_pub.npz test_msg > test_enc
# ./ntru.py dec test_priv.npz test_enc