超递增背包问题(较清晰)

from Crypto.Util.number import *
from secret import flag

def encrypt(m):
	m = str(bin(m))[2:][::-1]
	enc = 0
	for i in range(len(m)):
		enc += init[i] * int(m[i]) % n
	return enc

w = getPrime(64)
n = getPrime(512)
init = [w*pow(3, i) % n for i in range(512)]

c = encrypt(bytes_to_long(flag))

print(f'w={w}')
print(f'n={n}')
print(f'c={c}')

'''
w=16221818045491479713
n=9702074289348763131102174377899883904548584105641045150269763589431293826913348632496775173099776917930517270317586740686008539085898910110442820776001061
c=4795969289572314590787467990865205548430190921556722879891721107719262822789483863742356553249935437004378475661668768893462652103739250038700528111
'''

from Crypto.Util.number import *

w=16221818045491479713
n=9702074289348763131102174377899883904548584105641045150269763589431293826913348632496775173099776917930517270317586740686008539085898910110442820776001061
c=4795969289572314590787467990865205548430190921556722879891721107719262822789483863742356553249935437004378475661668768893462652103739250038700528111

init = [w*pow(3, i) % n for i in range(512)]

n = len(init)
L = Matrix(ZZ, n+1, n+1)

for i in range(n):
    L[i,i] = 1
    L[i,-1] = init[i]
L[-1,-1] = -c

res = L.LLL()

for i in range(n + 1):
    M = res.row(i).list()
    flag = True
    for m in M:
        if m != 0 and m != 1:
            flag = False
            break
    if flag:
        print(i, M)

m = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
for i in range(len(m)):
    m[i] = str(m[i])
m = "".join(m)[::-1]
print(long_to_bytes(int(m,2)))
#0xGame{Welc0me_2_Crypt0_G@me!#$&%}