TSGCTF 2020 sweet-like-apple-pie

solve.sage

from Crypto.Util.number import *
R1 = RealField(998); R1
RealNumber = R1

# calculate t1 = arcsin(output)
# calculate t2 = pi - t1
# solve linear cong: 10^299 * flag  = t2 mod pi


def pi2():
    lasts, t, s, n, na, d, da = 0, R1(3), 3, 1, 0, 0, 24
    while s != lasts:
        lasts = s
        n, na = n + na, na + 8
        d, da = d + da, da + 32
        t = (t * n) / d
        s += t
    return s
pi = pi2()


def sin2(x):
    x = R(x) % pi
    p, factor = 0, x
    for n in range(10000):
        p += factor
        factor *= - (x ** 2) / ((2 * n + 2) * (2 * n + 3))
    return p

x = 0.162452474092990408037062573408259688253995107643493293584426591003988903469791005222132158897198623144937279539555347413553688190959907095952250683633029959235933436782707275021817801890433801800730214807785288112267446678747104887584191096749196212784470161670299495426679759221652356130008110761143
print(arcsin(x))

t1 = 0.16317563760274096449072206226706138969608813915823060089904696867219050674349529473699077485324166107301677400198214572696291025373771977005460699177654679173873510871281393870913102947550839826319038943469831241191164283753165280426912074533597486915007225858970132342567867947771076975765821846727
print(pi - t1)
t2 = 2.97841701598705227397192132101244149450108126021687522007589762363562589954271370389104405048887540690913131251130016092013093435581286246167075241635193432571154899398912458239642861514744055666719157499411266325402180329094399542951766241993522703999557630833375902518477564717050262384960203067400

p = 314159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914120
t1 = 16317563760274096449072206226706138969608813915823060089904696867219050674349529473699077485324166107301677400198214572696291025373771977005460699177654679173873510871281393870913102947550839826319038943469831241191164283753165280426912074533597486915007225858970132342567867947771076975765821846727
t2 = 297841701598705227397192132101244149450108126021687522007589762363562589954271370389104405048887540690913131251130016092013093435581286246167075241635193432571154899398912458239642861514744055666719157499411266325402180329094399542951766241993522703999557630833375902518477564717050262384960203067400
R.<x> = PolynomialRing(Zmod(p//40))
f = (10^299//40) * x - t2//40
print(f.monic())
flag = R(-7853981633974483096156608458198757210492923498437764552437361480769541015715522496570087063355292669955370216283205766617734611523876455579313398520320939551223521636163549493418135210571434074361754437275962215925343331417551514098569089684935495906861068132464569581158246674045381096870550298888)
print(flag)
flag = long_to_bytes(263242402188620591296809345763900985938312964200473796065223239490283903637606485897868228242508866003053284844081290367889142575152387147600323965)
print(flag)