def test(self):
"""
def hermite(n,y):
if n == 1: return 2*y
if n == 0: return 1
return expand(2*y*hermite(n-1,y) - 2*(n-1)*hermite(n-2,y))
time hermite(15,var('y'))
"""
from sage.all_cmdline import Integer, sqrt, real, var, expand
for _ in xrange(self.rounds):
_sage_const_2 = Integer(2)
_sage_const_1 = Integer(1)
_sage_const_0 = Integer(0)
_sage_const_15 = Integer(18)
def hermite(n, y):
if n == _sage_const_1: return _sage_const_2 * y
if n == _sage_const_0: return _sage_const_1
return expand(
_sage_const_2 * y * hermite(n - _sage_const_1, y) -
_sage_const_2 *
(n - _sage_const_1) * hermite(n - _sage_const_2, y))
hermite(_sage_const_15, var('y'))
def calibrate(self):
from sage.all_cmdline import Integer, var
for i in xrange(self.rounds):
_sage_const_1 = Integer(1)
_sage_const_7 = Integer(10)
var('x,y,z')
f = (x+y+z+_sage_const_1 )**_sage_const_7
def test(self):
from sage.all_cmdline import Integer, var, sin, cos, taylor
for i in xrange(self.rounds):
_sage_const_0 = Integer(0)
_sage_const_1000 = Integer(350)
x=var('x')
w = (sin(x)*cos(x)).taylor(x,_sage_const_0 ,_sage_const_1000 )
def test(self):
from sage.all_cmdline import Integer, ellipsis_range, pi
for _ in xrange(self.rounds):
_sage_const_1 = Integer(1)
_sage_const_10 = Integer(40000)
v = (ellipsis_range(-pi, -pi + _sage_const_1 / _sage_const_10,
Ellipsis, pi))
def test(self):
from sage.all_cmdline import Integer, expand, var
for i in xrange(self.rounds):
_sage_const_1 = Integer(1)
_sage_const_7 = Integer(10)
var('x,y,z')
f = (x+y+z+_sage_const_1 )**_sage_const_7
g = expand(f*(f+_sage_const_1 ));
def test(self):
from sage.all_cmdline import Integer, random, ellipsis_range, I
for _ in xrange(self.rounds):
_sage_const_0 = Integer(0)
_sage_const_1000 = Integer(2000)
a = [
random() + random() * I for w in (
ellipsis_range(_sage_const_0, Ellipsis, _sage_const_1000))
]
def calibrate(self):
from sage.all_cmdline import Integer, sqrt, i
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_2 = Integer(2)
_sage_const_1 = Integer(1)
def f(z):
return sqrt(_sage_const_1 / _sage_const_3
) * z**_sage_const_2 + i / _sage_const_3
def test(self):
"""
u = [e, pi, sqrt(2)]
time Tuples(u,3).cardinality()
"""
from sage.all_cmdline import Integer, sqrt, e, pi, Tuples
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_2 = Integer(2)
u = [e, pi, sqrt(_sage_const_2)]
Tuples(u, _sage_const_3).cardinality()
def test(self):
from sage.all_cmdline import Integer, sqrt, real, i
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_2 = Integer(2)
_sage_const_1 = Integer(1)
def f(z):
return sqrt(_sage_const_1 / _sage_const_3
) * z**_sage_const_2 + i / _sage_const_3
real(f(f(f(f(f(i / _sage_const_2))))))
def calibrate(self):
from sage.all_cmdline import Integer, real, expand
for _ in xrange(self.rounds):
_sage_const_2 = Integer(2)
_sage_const_1 = Integer(1)
_sage_const_0 = Integer(0)
_sage_const_15 = Integer(15)
def hermite(n, y):
if n == _sage_const_1: return _sage_const_2 * y
if n == _sage_const_0: return _sage_const_1
return expand(
_sage_const_2 * y * hermite(n - _sage_const_1, y) -
_sage_const_2 *
(n - _sage_const_1) * hermite(n - _sage_const_2, y))
def calibrate(self):
from sage.all_cmdline import Integer, var, expand
for i in xrange(self.rounds):
_sage_const_50 = Integer(55)
x=var('x')
y=var('y')
z=var('z')
f=expand((x**y+y**z+z**x)**_sage_const_50)
def inverse(el):
ret = el.parent().zero()
ORDER = el.parent().nilpotency_order
for i in range(0,ORDER+1):
add = (el-1)**i
add *= Integer( (-1)**(i) )
ret += add
return ret
def test(self):
from sage.all_cmdline import Integer, expand, var, diff
for i in xrange(self.rounds):
_sage_const_50 = Integer(110)
x=var('x')
y=var('y')
z=var('z')
f=expand((x**y+y**z+z**x)**_sage_const_50)
g = f.diff(x)
def calibrate(self):
from sage.all_cmdline import Integer, var
for _ in xrange(self.rounds):
_sage_const_2 = Integer(2)
_sage_const_10 = Integer(10)
_sage_const_0 = Integer(0)
_sage_const_5 = Integer(5)
_sage_const_4 = Integer(4)
def right(f, a, b, n):
Deltax = (b - a) / n
c = a
est = _sage_const_0
for _ in range(n):
c += Deltax
est += f(x=c)
return est * Deltax
x = var('x')
def calibrate(self):
from sage.all_cmdline import Integer, var
for _ in xrange(self.rounds):
_sage_const_10 = Integer(10)
l = []
for j in xrange(1, 10):
l.append("q" + str(j))
s = reduce(lambda a, b: a + "," + b, l)
sp = reduce(lambda a, b: a + "+" + b, l)
var(s)
f = eval(sp)
def get_flag():
# Recover message
_, u, v = xgcd(e1, e2)
m = pow(ct1, u, modulus) * pow(ct2, v, modulus)
# Get binary representation and pad
bin = Integer(m).binary()
while (len(bin) % 8 != 0):
bin = '0' + bin
# Return ASCII string
print(bin_to_ascii(bin))
def log(el):
"""
TESTS:
sage: from word_algebras import *
sage: NFA = NilpotentFreeAlgebra(QQ,2,'x',3)
sage: x0,x1 = NFA.gens()
sage: assert x0 == log(exp(x0))
"""
ret = 0
ORDER = el.parent().nilpotency_order
for i in range(1,ORDER+1):
add = (el-1)**i
add *= Integer( (-1)**(i+1) ) / i
ret += add
return ret
def test(self):
"""
sage: time v = [-pi,-pi+1/10..,pi]
"""
from sage.all_cmdline import Integer, var
for _ in xrange(self.rounds):
_sage_const_10 = Integer(500)
l = []
for j in xrange(1, 1000):
l.append("q" + str(j))
s = reduce(lambda a, b: a + "," + b, l)
sp = reduce(lambda a, b: a + "+" + b, l)
var(s)
f = eval(sp)
a = [bool(f == f) for _ in range(_sage_const_10)]
def test(self):
from sage.all_cmdline import Integer, random, var
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_32 = Integer(32)
_sage_const_45 = Integer(45)
_sage_const_4 = Integer(4)
_sage_const_9 = Integer(9)
_sage_const_12 = Integer(12)
_sage_const_10 = Integer(9)
_sage_const_18 = Integer(18)
_sage_const_21 = Integer(21)
_sage_const_34 = Integer(34)
_sage_const_24 = Integer(24)
x = var('x')
f = x**_sage_const_24 + _sage_const_34 * x**_sage_const_12 + _sage_const_45 * x**_sage_const_3 + _sage_const_9 * x**_sage_const_18 + _sage_const_34 * x**_sage_const_10 + _sage_const_32 * x**_sage_const_21
a = [f(x=random()) for _ in xrange(_sage_const_10**_sage_const_4)]
def calibrate(self):
from sage.all_cmdline import Integer
for _ in xrange(self.rounds):
_sage_const_1 = Integer(1)
_sage_const_10 = Integer(1000)
def calibrate(self):
from sage.all_cmdline import Integer, var
for i in xrange(self.rounds):
_sage_const_100 = Integer(120)
x,y,z=var('x,y,z')
def test(self):
from sage.all_cmdline import Integer, expand, sin, cos, var
for i in xrange(self.rounds):
_sage_const_100 = Integer(200)
x,y,z=var('x,y,z')
a = expand((x**sin(x) + y**cos(y) - z**(x+y))**_sage_const_100 );
def test(self):
from sage.all_cmdline import Integer, sin
for _ in xrange(self.rounds):
_sage_const_100 = Integer(1400)
sum(((x + sin(i)) / x + (x - sin(i)) / x)
for i in xrange(_sage_const_100))
def calibrate(self):
from sage.all_cmdline import Integer, var
for i in xrange(self.rounds):
_sage_const_0 = Integer(0)
_sage_const_1000 = Integer(200)
x=var('x')
def calibrate(self):
from sage.all_cmdline import Integer, sqrt, e, pi, Tuples
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_2 = Integer(2)
u = [e, pi, sqrt(_sage_const_2)]
# This file was *autogenerated* from the file ./flag.sage
from sage.all_cmdline import Integer, xgcd # import sage library
from sage.crypto.util import bin_to_ascii
# Given values
ct1 = Integer(
13981765388145083997703333682243956434148306954774120760845671024723583618341148528952063316653588928138430524040717841543528568326674293677228449651281422762216853098529425814740156575513620513245005576508982103360592761380293006244528169193632346512170599896471850340765607466109228426538780591853882736654
)
ct2 = Integer(
79459949016924442856959059325390894723232586275925931898929445938338123216278271333902062872565058205136627757713051954083968874644581902371182266588247653857616029881453100387797111559677392017415298580136496204898016797180386402171968931958365160589774450964944023720256848731202333789801071962338635072065
)
e1 = Integer(13)
e2 = Integer(15)
modulus = Integer(
103109065902334620226101162008793963504256027939117020091876799039690801944735604259018655534860183205031069083254290258577291605287053538752280231959857465853228851714786887294961873006234153079187216285516823832102424110934062954272346111907571393964363630079343598511602013316604641904852018969178919051627
)
def get_flag():
# Recover message
_, u, v = xgcd(e1, e2)
m = pow(ct1, u, modulus) * pow(ct2, v, modulus)
# Get binary representation and pad
bin = Integer(m).binary()
while (len(bin) % 8 != 0):
bin = '0' + bin
# Return ASCII string
print(bin_to_ascii(bin))
def calibrate(self):
from sage.all_cmdline import Integer, var
for _ in xrange(self.rounds):
_sage_const_3 = Integer(3)
_sage_const_32 = Integer(32)
_sage_const_45 = Integer(45)
_sage_const_4 = Integer(4)
_sage_const_9 = Integer(9)
_sage_const_12 = Integer(12)
_sage_const_10 = Integer(10)
_sage_const_18 = Integer(18)
_sage_const_21 = Integer(21)
_sage_const_34 = Integer(34)
_sage_const_24 = Integer(24)
x = var('x')
f = x**_sage_const_24 + _sage_const_34 * x**_sage_const_12 + _sage_const_45 * x**_sage_const_3 + _sage_const_9 * x**_sage_const_18 + _sage_const_34 * x**_sage_const_10 + _sage_const_32 * x**_sage_const_21