文章 - PH | NSSCTF

Problem: [领航杯江苏省赛 2021]ECC
思路

解题大致思路
EXP


p = 64464091191308356774703439660771627086045800299627641179047457478059588557461
a = 31926335967105564755113987930261069322507794703287741857397622356704769886356
b = 34835808070187351680507689900273321615070127680320357724483770400791707112940
Gx = 2053202552422630348010474635096983783565667661786369125783579647572276572403
Gy = 51320753844844801021362329076409450910659564359017581255542897537756778371539
GF = IntegerModRing(p)
curve = EllipticCurve(GF,[a,b])
P = curve.point((Gx,Gy))
n = curve.order()
Q = curve.point((31981799071949968743482831587417174146463993877255771340814476669214408840460,15144025062588325012239455117890516531350002058200271280110877844265896081387))
# 分解出来的因子
primes = [4, 3, 1246057, 2357351, 435374689]
dlogs = []
for fac in primes:
    t = int(n)//int(fac)
    dlog = discrete_log(t*Q,t*P,operation="+")
    dlogs += [dlog]
    print("factor:"+str(fac)+",Discrete Log,"+str(dlog))
d = crt(dlogs, primes)
q = 4 * 3 * 1246057 * 2357351 * 435374689
print("\nresult:")
for k in range(2^21,0,-1):
    flag = d + k*n
    K = flag * P
    if K ==Q :
        print(b"NSSCTF{" + long_to_bytes(flag) + b"}")
        break
总结

对该题的考点总结