0xgame2022复现

0xgame
赛题
发布日期:   2025-07-14

misc

看不见的字符

零宽隐写

赛博厨子一把梭

最后flag为

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0xGame{Inv1sible_W0rds}

旅游照片

图片属性中可以找到拍摄的日期和时间

网上找B-7631号在这段时间的航班信息即可

垃圾邮件

拿到key.txt先进行解密

AAencode解密

brainfuck解密

一把梭

垃圾邮件解密

最后flag为

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0xGame{KFC_CRAZY_THURSDAY_V_ME_50!!!!}

EzPcap

过滤http，搜索关键字0xGame

最后flag为

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0xGame{85dad2d8-55f0-4f05-a420-3c3b3cb6e86f}

奇怪的符号

下载附件

塞尔达语言

《塞尔达传说荒野之息》席卡、海利亚及格鲁德文字标识解读_席卡古文篇-初始台地-游民星空 GamerSky.com

好多压缩包

爆破压缩包密码

伪加密破解

掩码爆破

明文攻击

得到flag

最后flag为

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0xGame{7f42e75d-e769-40a1-a46c-43dac55f2d54}

booooom

crc爆破

4字节

5字节

得到密码

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You_Know_CRC32

查看

emojiaes解密

最后flag为

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0xGame{8d815cfe-851c-4c8c-b283-858d3f3e8c91}

BabyRe

uncompyle6反编译得到py文件

加密函数就是将原flag的每一位与上一位异或的结果再加30最后整体base64加密

exp：

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import base64


enc = "MGZdRComPDglIHsrICVzZzwkcSJtN296eW0yLCQlOWoedylvb3QfcCwnbjo="


s_bytes = base64.b64decode(enc)
s = [b for b in s_bytes] 


flag_chars = [ord('0')]


for i in range(1, len(s)):
    b = s[i]
    orig_xor = (b - 30) % 256  
    next_char = orig_xor ^ flag_chars[i-1] 
    flag_chars.append(next_char)


flag = ''.join(chr(c) for c in flag_chars)
print(flag)

运行得到

最后flag为

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0xGame{afd9461d-35fb-4e9b-9716-aa83b3ed681a}

哥们在这给你说唱

静默隐写

deepsound隐写

最后flag为

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0xGame{5d4d7df0-6de7-4897-adee-e4b3828978f8}

不太普通的图片

stegsolve查看通道

cloacked-pixel隐写

最后flag为

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0xGame{Hidd3n_1n_Pic}

隔空取物

bkcrack爆破

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echo 89504E470D0A1A0A0000000D49484452 | xxd -r -ps > png_header
bkcrack -C flag.zip -c flag.png -p png_header

提取文件

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bkcrack -C flag.zip -k ab7d8bcd 6ce75578 4de51c12 -U gkqw.zip 123

宽高一把梭

最后flag为

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0xGame{D0_Y0u_L1k3_89504E47?}

BabyUSB

第一部分

第二部分

得到压缩包密码

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P@33w0rD_1s_Here

解压压缩包

最后flag为

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0xGame{E43y_Traff1c_Analy3i3}

螺旋升天

密码

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pass
a@Yw
:*7o
sidr
螺旋密码为passwordis:a@Y7*

螺旋矩阵还原压缩包

exp：

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def function(n):
    matrix = [[0] * n for _ in range(n)]

    number = 1
    left, right, up, down = 0, n - 1, 0, n - 1
    while left < right and up < down:
        # 从左到右
        for i in range(left, right):
            matrix[up][i] = number
            number += 1

        # 从上到下
        for i in range(up, down):
            matrix[i][right] = number
            number += 1

        # 从右向左
        for i in range(right, left, -1):
            matrix[down][i] = number
            number += 1

        for i in range(down, up, -1):
            matrix[i][left] = number
            number += 1
        left += 1
        right -= 1
        up += 1
        down -= 1
    # n 为奇数的时候，正方形中间会有个单独的空格需要单独填充
    if n % 2 != 0:
        matrix[n // 2][n // 2] = number
    return matrix

import struct
s = function(17)
s = sum(s,[])
f = open('D:\\tmp\\flag.zip','rb').read()
arr = [0]*289
for i in range(len(s)):
    arr[s[i]-1] = f[i]
with open('D:\\tmp\\flag1.zip', 'wb')as fp:
    for x in arr:
        b = struct.pack('B', x)
        fp.write(b)

运行得到

根据给的密码解压压缩包得到flag

最后flag为

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0xGame{6e93c04c-5478-4d34-9dd2-c46742d551bb}

证取单简

查看计算机密码

查看编辑框

reverse

AES解密

最后flag为

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0xGame{F1rst_St3p_0f_Forens1cs}

Time To Live

把所有数字转2进制之后可以发现后4位全是1，取前两位即可解密

exp：

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from Crypto.Util.number import long_to_bytes

def process_ttl_file(file_path):
    # 一次性读取所有行并处理
    with open(file_path, 'r') as f:
        binary_data = ''.join(
            bin(int(line.strip()))[2:].zfill(8)[:4] 
            for line in f if line.strip()
        )
    
    # 处理空文件情况
    if not binary_data:
        return b''
    
    # 计算需要填充的位数（使总长度为8的倍数）
    pad_bits = (8 - len(binary_data) % 8) % 8
    padded_binary = binary_data + '0' * pad_bits
    
    # 直接转换为字节
    return long_to_bytes(int(padded_binary, 2))

# 使用示例
result = process_ttl_file(r"D:\\tmp\\Time To Live.txt")
print(result)

运行得到

base转图片

盲水印

最后flag为

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0xGame{2ade442e-2b56-4794-9d58-cff8eb88b2bf}

我也很异或呢

xortool

xor文件，key是0xGame

保存并解压压缩包

按键精灵

最后flag为

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0xGame{4e09d99d-f1f5-4287-a6ca-7467d2ed6ec0}

听首音乐？

midi文件编译

运行exe文件

long_to_bytes

最后flag为

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0xGame{StRAnGe_eSOL4N9}

ColorfulDisk

diskgennius打开文件

vc挂载

导出所有rgb值并写入文件

exp：

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from PIL import Image, ImageDraw
import struct
width = 1042
height = 1042
img=Image.open("D:\\tmp\\1.png")
a=[]
for i in range(height):
	for j in range(width):
		pi=img.getpixel((j,i))
		for k in range(3):
			a.append(pi[k])
with open('D:\\tmp\\flag', 'wb')as fp:
    for x in a:
        b = struct.pack('B', x)
        fp.write(b)

分析文件是wav文件

加上后缀.wav，听音频听到无线声音

sstv隐写

解压压缩包得到flag

最后flag为

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0xGame{RGB_Co1or_Pix3l}

SIMPLEQR(旧)

二维码处理

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反相--曲线--缩小图像三种操作

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0xGame{ed4a6398-9360-????

binwalk分离图片

赛博厨子

如果把这段数据想成是二维码的数据的话，根据阅读标准，那么前四位就是模式标识符，这里是0100也
就是字节模式。模式标识符后八位代表所承载数据的长度，所以可以读出数据长度为19。同时在字节模
式下，数据是按照每个字节八位二进制的方式存储的。
最后，直接删掉4位的模式标识符和8位的长度标识符，就可以读出这段长度为19的数据了，也就是flag

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00101101001110010110001100111000001110010010110100111000001100100011001000110111001100100110011000110011011000110011011000110010001100010110010101111101001011101100001100101110011000100010111000101110001011100010111001100110011000100010111000101110010100100010111001000011011100100010111000110110011000100010111000100011

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-9c89-82272f3c621e}

binwalk分离出2个zlib图片

寻找png文件尾

添加

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89 50 4E 47 0D 0A 1A 0A 00 00 00 0D 49 48 44 52

保存文件为1.png是二维码，扫描二维码

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41ff

最后flag为

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0xGame{ed4a6398-9360-41ff-9c89-82272f3c621e}

SIMPLEQR(新)

第一部分和上一题思路一样，使用ps处理得到

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0xGame{ed4a6398-9360-????

binwalk分离得到

01转二维码

扫描二维码得到

得到

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-9c89-82272f3c621e}

第三部分和上面那题思路一样，添加png文件头16字节，加上文件尾得到二维码，扫描二维码得到

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41ff

最后flag为

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0xGame{ed4a6398-9360-41ff-9c89-82272f3c621e}

crypto

ext_Affine

下载附件

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from secret import flag
import random
import gmpy2


def gen_key():
    while True:
        x = random.randint(1, 128)
        if gmpy2.gcd(x, 128) == 1:
            break
    y = random.randint(1, 128)
    return x, y


cipher = ""
a, b = gen_key()
for i in flag:
    tmp = (ord(i) * a + b) % 128
    cipher += chr(tmp)

with open("cipher.txt", "w") as f:
    f.write(cipher)

with open("key.txt", "w") as f:
    f.write("a = {}".format(str(a)))
    f.write("\n")
    f.write("b = {}".format(str(b)))

key.txt

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a = 27
b = 121

仿射密码

exp:

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from Crypto.Util.number import *

a = 27
b = 121

f = open("D:\\tmp\\cipher.txt", "rb")
s = f.read()
flag = ""
a_ = inverse(a, 128)
for i in s:
    tmp = (i - b) * a_ % 128
    flag += chr(tmp)

print(flag)

运行得到

最后flag为

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0xGame{U_kn0w|@^1ot_4bout~Pyth0n}

Factor

下载附件

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

m = bytes_to_long(flag)
n = 177726843226591634556244030635816071333
assert m < n
e = 0x10001
c = pow(m, e, n)

print(c)

# 49549088434190402681586345733724247189

一把梭

最后flag为

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0xGame{we1come_t0_rs4}

simpleBabyEasyRSA

下载附件

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p = 59
q = 97
e = 37
c = 3738

请在求出私钥d，明文m后将连接值的md5值（32位小写）包上flag提交

如求出d = 12，m = 34，则flag为0xGame{md5(1234)}

一把梭

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0xGame{md5(3015499)}

md5加密

最后flag为

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0xGame{d42b66fc047f9e80922f1a2b11e589c0}

Vigenère

下载附件

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Yqbtxvla IFEr gew wygzkrl vgyufmkq lq yqquk nk ct qctinlkuzzk kkwtiurd zb ykbq ozxgaeobzmzf wzvqqhkaug oz rdihjkts z lgpzktq, zr crdn ge bntqmezumf gav tkmbsoay vu fgd ybjv ur zsznumy rnttq ap ztd qknd yudkc (o.r., twm nnttgq rxafqgzk kt bqnlrkuoamzr fwvzumfy). Cjqsumdtg svzmbj/jrxgted BZSk ktoktjr VGL ONM'y, bxvkz bntfafkddc zuw "hozzky" bx vnq bnscwvofhnt patighs gav jkxc roaug 1996[4] gf sgk ystmqrs nnumkd bntswtkzbd, gav vnq MXA-PKCC (Oxake Kgigqhzl Sygddmkfk Ykqj), snr dcxsdrz flwjqms iltgx-edbaeave onmzrkv.Ixzryvu EZR zbzvnkzudr oaunapd qkiwtyq-dmmvfgkdhmm, cseqqs rtvxhozf, oxblqiak ztndayur, reflgs mcloaauzdzsobf, rxafqgzekts, bqeclqgzzkefau, gzc vxvlkts dwvygkze, zluay qztdqy.[9] Vf ct mssgpc/fkrdmyr kvexd buzhgzushua, wcit sdgz au muudt n ecithmk (bj c yyzkr awvcaqj) zb vglqmc—zlhkimkke bf ct urnrnlgj onlvrlkzunm trlyudj. Skneu gdd ribjgj am augz vnqhq yhueker ht qwhkzchtt ljkuq zyfaitqc lgpzktq(r) ztq gp ztdhx fmeiqrr oa svzmbjoay vnq nsnrj vkml'r snujozdr.[10] G istomshua xtuy bkgfkki rkzm-flggxhmm vk vu "bkztg" gyt rkzmf gp ubontrfv'y yzbnvfgy.Tzqjjstk ogzrywpmqr tyhsnrk hmbbdxk sdszvfi gz tmqagyt bhdir gh nmqccnjg gzc ggiapm fn eotmtk ats nbo vu nxogfk rgds nl gzg yqbtxvla sqzraewu, k.s. troay fkntfmvfi vaqsy bj wyumf g fafk-ogztawn gfszix.[ukzmshua fgkpdc] Prgrgdcx-ygqnk onlvrlkzunmy njg ixnrke lq vdnfxneoozf buzhgzushuak: vkmlr jb fqz phqkplne mssgpc ggog nzuwt, hgs qggzgx enkbr ujgxkdttwu vardj oq vnq nqmnfkfqqr. Zveg oe fdtrjcrxx mug s hgosnx vf uiaqhtt ljked buzhgzushuak, daf "ehxfl dranc" hbfwy bnhtgk cxq nezrf iohdm zb ljk rhqyg kqrhdq.[ivlczunm trwfkp] Hm Qvfi ur sgk Uanr–esxrr ujgxkdttwu, vxzxkek igum ouvfvy nx qkysvohd qgackts. Bkgfkkimkke, bfne fgd zbh vkml fgvfu vahmzf. 0pIgyd{U19kawTk_Q4rx}Cuwp gznsnrj vkml akflu ztd baejgtf bggzhkuz (d.f., hl ycozhmm nueker su gzg ytzqkq "lcxsds" snujozd snnl vnq bggzhkuz vzy qwhkzchtt), ljkk adibeg ztd mkj ujgyohuak ctp rgosl vu pdekavkts sgkvj qcz onyvlkuz zfgvfuz asgkek.

维吉尼亚无密钥解密

最后flag为

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0xGame{V19eneRe_E4sy}

简单套娃

核心价值观解密

阴阳怪气解密

摩斯解密

摩斯解密

注意%u7b代表”{“，%u7d代表”}”，即得到：

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0W_1QIN4WN_D_FR{DL1C_JYLPDNA3GCY}X1S3J

W型栅栏解密

凯撒解密

最后flag为

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0XGame{CL4SS1CAL_C1PH3R_1S_V3RY_FUNNY}

linearEquation

下载附件

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import random

x = [random.getrandbits(32) for _ in range(32)]

# flag为0xGame{md5(sum(x))}

for i in range(32):
    ans = 0
    rand = [random.getrandbits(32) for _ in range(32)]
    for j in range(31):
        ans += x[j] * rand[j]
        print("x{} * {} + ".format(j, rand[j]), end="")
    ans += x[31] * rand[31]
    print("x{} * {} = ".format(31, rand[31]), end="")
    print(ans)
    #x0 * 2905774839 + x1 * 937692645 + x2 * 2277996359 + x3 * 1574938713 + x4 * 825047075 + x5 * 1179013397 + x6 * 2366890081 + x7 * 3219529440 + x8 * 2414190453 + x9 * 3590757506 + x10 * 3909323650 + x11 * 2183139299 + x12 * 1579902159 + x13 * 3343902869 + x14 * 896068862 + x15 * 309758299 + x16 * 901531607 + x17 * 291291156 + x18 * 2546709881 + x19 * 4221036639 + x20 * 3505720382 + x21 * 3684857351 + x22 * 2022652786 + x23 * 451227475 + x24 * 3741251238 + x25 * 3997408590 + x26 * 2256908756 + x27 * 1334843411 + x28 * 4020591098 + x29 * 2114708609 + x30 * 79808585 + x31 * 2974805697 == 153629905098136685045,
x0 * 633779458 + x1 * 760323050 + x2 * 3524136923 + x3 * 3404961172 + x4 * 3497719477 + x5 * 2036024833 + x6 * 2807481062 + x7 * 3579571169 + x8 * 1182247335 + x9 * 1473703468 + x10 * 1485764830 + x11 * 2344149245 + x12 * 2230867977 + x13 * 451381281 + x14 * 2729949187 + x15 * 1329480928 + x16 * 3036372799 + x17 * 1916707506 + x18 * 1408308101 + x19 * 3414819940 + x20 * 54157456 + x21 * 4081087004 + x22 * 81644901 + x23 * 1046457653 + x24 * 2786986628 + x25 * 3293369990 + x26 * 2547544255 + x27 * 1408426127 + x28 * 1700843152 + x29 * 4028585224 + x30 * 3882199080 + x31 * 4040732992 == 145118376676814378151,
x0 * 1158359552 + x1 * 952473112 + x2 * 2469876874 + x3 * 1877922146 + x4 * 2681754384 + x5 * 441645489 + x6 * 1451082555 + x7 * 1282675826 + x8 * 3628741269 + x9 * 1538367477 + x10 * 4256030398 + x11 * 1551122815 + x12 * 2403304542 + x13 * 1198458285 + x14 * 2596160415 + x15 * 3952532206 + x16 * 1372310735 + x17 * 3735073437 + x18 * 686367724 + x19 * 158982013 + x20 * 1901981688 + x21 * 2045511526 + x22 * 1553141146 + x23 * 574875471 + x24 * 3881193717 + x25 * 281974061 + x26 * 3401680368 + x27 * 1071341816 + x28 * 3856818199 + x29 * 1543037830 + x30 * 2600897676 + x31 * 886793613 == 125136025093969380235,
x0 * 3369804515 + x1 * 1388562875 + x2 * 2620029184 + x3 * 3424874122 + x4 * 2155070368 + x5 * 515581101 + x6 * 3448760104 + x7 * 1571958247 + x8 * 1344632695 + x9 * 3418066835 + x10 * 1055412931 + x11 * 2599736936 + x12 * 1682298601 + x13 * 3888231955 + x14 * 869443630 + x15 * 46802084 + x16 * 1434071143 + x17 * 537999569 + x18 * 3062214567 + x19 * 638588405 + x20 * 1418519591 + x21 * 921851625 + x22 * 1349011403 + x23 * 2504652024 + x24 * 1128409974 + x25 * 825642445 + x26 * 2980848614 + x27 * 3181702547 + x28 * 1665015471 + x29 * 1655900518 + x30 * 1737483004 + x31 * 4058968130 == 123888756483831750489,
x0 * 2992139966 + x1 * 3421209457 + x2 * 1518056473 + x3 * 2934632866 + x4 * 474750728 + x5 * 1888643463 + x6 * 715133241 + x7 * 270269278 + x8 * 3453364309 + x9 * 2375169043 + x10 * 475758667 + x11 * 1550808440 + x12 * 870004412 + x13 * 2502311422 + x14 * 2802347419 + x15 * 3316934713 + x16 * 3072815429 + x17 * 1955447632 + x18 * 957468873 + x19 * 2003306503 + x20 * 2991846576 + x21 * 1052908526 + x22 * 852939089 + x23 * 2001031122 + x24 * 1763364759 + x25 * 318730434 + x26 * 2271963088 + x27 * 3167595340 + x28 * 186065313 + x29 * 3124233301 + x30 * 1558676638 + x31 * 229698311 == 136466432408823062440,
x0 * 880826917 + x1 * 2298353220 + x2 * 13972845 + x3 * 2112342331 + x4 * 520363735 + x5 * 1669676202 + x6 * 2365942382 + x7 * 2454166357 + x8 * 86684296 + x9 * 4180997737 + x10 * 2651800933 + x11 * 3387852337 + x12 * 3569081096 + x13 * 412248780 + x14 * 2622374412 + x15 * 4004737267 + x16 * 3937062327 + x17 * 2122230024 + x18 * 508412261 + x19 * 925290104 + x20 * 2297262392 + x21 * 2615036583 + x22 * 956831662 + x23 * 2377853219 + x24 * 2129964002 + x25 * 711861720 + x26 * 1072575240 + x27 * 290600530 + x28 * 3557322638 + x29 * 1937025602 + x30 * 3942606369 + x31 * 848634526 == 135520634374716138253,
x0 * 1667423245 + x1 * 3205256744 + x2 * 4218058651 + x3 * 4247786171 + x4 * 2902884888 + x5 * 1776716207 + x6 * 57317883 + x7 * 2810845945 + x8 * 4056618058 + x9 * 2442806270 + x10 * 189251210 + x11 * 175454169 + x12 * 1563217423 + x13 * 1584552187 + x14 * 4066113642 + x15 * 2678017765 + x16 * 1370397535 + x17 * 1796075905 + x18 * 3507132543 + x19 * 2375242245 + x20 * 1599167786 + x21 * 3353660587 + x22 * 2792999728 + x23 * 2513875102 + x24 * 3349313992 + x25 * 561973312 + x26 * 131599779 + x27 * 1780045940 + x28 * 181893476 + x29 * 1515423140 + x30 * 1695557088 + x31 * 1103274089 == 140870834889282733787,
x0 * 2924743894 + x1 * 2747685610 + x2 * 703249631 + x3 * 2970835309 + x4 * 1709917538 + x5 * 2326038184 + x6 * 3850628518 + x7 * 1598044999 + x8 * 1230534089 + x9 * 2628050448 + x10 * 560260479 + x11 * 2827469192 + x12 * 1261659178 + x13 * 3473946812 + x14 * 2627319447 + x15 * 2783861426 + x16 * 1814833846 + x17 * 3969833864 + x18 * 4048131215 + x19 * 3849752757 + x20 * 3942527132 + x21 * 3218422785 + x22 * 1568409347 + x23 * 3959466355 + x24 * 2784582743 + x25 * 2996021365 + x26 * 1058302993 + x27 * 360568252 + x28 * 4120475817 + x29 * 612600724 + x30 * 3312442340 + x31 * 2780876242 == 162850348028726438719,
x0 * 1616016662 + x1 * 3654249690 + x2 * 137386530 + x3 * 1430840003 + x4 * 413249034 + x5 * 512756864 + x6 * 4178200879 + x7 * 2530110366 + x8 * 2920225584 + x9 * 3182457452 + x10 * 1705355659 + x11 * 2866496197 + x12 * 4233807177 + x13 * 1885804809 + x14 * 1332101007 + x15 * 511987054 + x16 * 3709126878 + x17 * 1639834513 + x18 * 2331999251 + x19 * 3942139119 + x20 * 3452087731 + x21 * 3059112759 + x22 * 3445769324 + x23 * 128282305 + x24 * 895514710 + x25 * 3973866022 + x26 * 3074206386 + x27 * 2793860989 + x28 * 4208156768 + x29 * 1868752777 + x30 * 1128655300 + x31 * 4224750762 == 173549152139361191182,
x0 * 1507751682 + x1 * 1846572164 + x2 * 2041260497 + x3 * 1124204604 + x4 * 803283004 + x5 * 2783064398 + x6 * 3894553701 + x7 * 1968388652 + x8 * 4001422379 + x9 * 3448449208 + x10 * 3520475047 + x11 * 2550138883 + x12 * 2389210163 + x13 * 126106238 + x14 * 2662172629 + x15 * 4261498421 + x16 * 3044233456 + x17 * 3644778899 + x18 * 870298634 + x19 * 2695223165 + x20 * 1650836877 + x21 * 1258482236 + x22 * 1063099544 + x23 * 3764404492 + x24 * 3967617774 + x25 * 1965577715 + x26 * 2446428246 + x27 * 1505068720 + x28 * 3981692241 + x29 * 3408565448 + x30 * 2781597153 + x31 * 3092390689 == 180393478529485883021,
x0 * 351479342 + x1 * 503524980 + x2 * 1716292026 + x3 * 938189610 + x4 * 3362208287 + x5 * 280354280 + x6 * 2300444836 + x7 * 1468215142 + x8 * 3180887405 + x9 * 2532072979 + x10 * 1652875734 + x11 * 2254901041 + x12 * 259860786 + x13 * 3263784945 + x14 * 483273054 + x15 * 3166504792 + x16 * 914039776 + x17 * 4266192190 + x18 * 1042961273 + x19 * 181336626 + x20 * 669694284 + x21 * 2453653976 + x22 * 1389685958 + x23 * 2284711690 + x24 * 3317847597 + x25 * 2440906291 + x26 * 3042784363 + x27 * 1482188614 + x28 * 2369361990 + x29 * 324426473 + x30 * 1763743995 + x31 * 3934897747 == 117888147215252945859,
x0 * 725022521 + x1 * 938746075 + x2 * 3633113215 + x3 * 4185273958 + x4 * 2800996696 + x5 * 2631729929 + x6 * 2692051893 + x7 * 3433724886 + x8 * 1616354254 + x9 * 3607913532 + x10 * 529812087 + x11 * 2791241832 + x12 * 1737462722 + x13 * 3641411598 + x14 * 1924632655 + x15 * 1616473457 + x16 * 3637886658 + x17 * 1858291856 + x18 * 1078390594 + x19 * 1887741658 + x20 * 2265350830 + x21 * 2676979191 + x22 * 1970124470 + x23 * 664078020 + x24 * 1808737559 + x25 * 2298779415 + x26 * 1388943648 + x27 * 4204667059 + x28 * 1073622448 + x29 * 3443318903 + x30 * 2171824304 + x31 * 1868209557 == 158683608359654647072,
x0 * 650341618 + x1 * 2935581294 + x2 * 2644385881 + x3 * 1535307611 + x4 * 1016591324 + x5 * 815158333 + x6 * 1448798160 + x7 * 2641332727 + x8 * 270686394 + x9 * 2219311183 + x10 * 2967122700 + x11 * 3770872278 + x12 * 3541712142 + x13 * 3868017641 + x14 * 3555690826 + x15 * 802632927 + x16 * 3680835829 + x17 * 682966028 + x18 * 1194680003 + x19 * 894072837 + x20 * 1878364070 + x21 * 1331140614 + x22 * 965880101 + x23 * 1138566143 + x24 * 701720887 + x25 * 2742737986 + x26 * 3045938774 + x27 * 147247760 + x28 * 4094028215 + x29 * 204167974 + x30 * 3200135673 + x31 * 27026610 == 119553298425410260470,
x0 * 3264996808 + x1 * 2331472878 + x2 * 2992654618 + x3 * 1337387837 + x4 * 3068330431 + x5 * 1897134387 + x6 * 2124686830 + x7 * 433732986 + x8 * 560852756 + x9 * 569523526 + x10 * 1635729292 + x11 * 3899076223 + x12 * 2599433468 + x13 * 2525044550 + x14 * 3233393817 + x15 * 1990368374 + x16 * 8003701 + x17 * 1649870439 + x18 * 429808458 + x19 * 2788914187 + x20 * 3183669167 + x21 * 4029467918 + x22 * 1823857717 + x23 * 3493646301 + x24 * 1619264007 + x25 * 1485689524 + x26 * 1136226577 + x27 * 2403749534 + x28 * 4188551850 + x29 * 19971766 + x30 * 3514606027 + x31 * 2659730746 == 129283893341689770873,
x0 * 3179913872 + x1 * 1590442647 + x2 * 16192345 + x3 * 2330075242 + x4 * 655160953 + x5 * 4052746453 + x6 * 3225345308 + x7 * 3362725382 + x8 * 350986883 + x9 * 2257032841 + x10 * 203422664 + x11 * 1211339833 + x12 * 1005356492 + x13 * 3016854180 + x14 * 3052361161 + x15 * 667363442 + x16 * 1711948350 + x17 * 674085815 + x18 * 386890144 + x19 * 3422048832 + x20 * 127837425 + x21 * 1178013843 + x22 * 642733070 + x23 * 3317927971 + x24 * 470770850 + x25 * 1793530046 + x26 * 3190738311 + x27 * 1437576481 + x28 * 273211936 + x29 * 3162727862 + x30 * 172486187 + x31 * 3154971774 == 122131281329452040239,
x0 * 1984698529 + x1 * 1445752975 + x2 * 556628780 + x3 * 1388438884 + x4 * 1249287957 + x5 * 355916806 + x6 * 317389095 + x7 * 3161347497 + x8 * 3059986980 + x9 * 3375424603 + x10 * 2501724356 + x11 * 3520286932 + x12 * 2650494784 + x13 * 3031688124 + x14 * 777396084 + x15 * 3712283044 + x16 * 2001084449 + x17 * 2179194542 + x18 * 330859108 + x19 * 4245370419 + x20 * 1597774590 + x21 * 279816529 + x22 * 2461029032 + x23 * 4024610466 + x24 * 2111027579 + x25 * 1607579079 + x26 * 2097268956 + x27 * 2069066877 + x28 * 2186433547 + x29 * 922721930 + x30 * 1292267441 + x31 * 2955441028 == 144038024275757774857,
x0 * 1241308871 + x1 * 1393662036 + x2 * 4198993351 + x3 * 91138693 + x4 * 525807852 + x5 * 2577403449 + x6 * 86644570 + x7 * 1732667838 + x8 * 2939702570 + x9 * 2284810186 + x10 * 208700933 + x11 * 2215740017 + x12 * 3214773041 + x13 * 870729362 + x14 * 65832640 + x15 * 3610432908 + x16 * 522601813 + x17 * 175075843 + x18 * 1282298391 + x19 * 36747212 + x20 * 2587821571 + x21 * 4181954474 + x22 * 1445029272 + x23 * 153408069 + x24 * 3576784077 + x25 * 3813757427 + x26 * 3320262816 + x27 * 3551464465 + x28 * 3353985098 + x29 * 2447602934 + x30 * 3490733926 + x31 * 3993341361 == 123274418600692000659,
x0 * 893304126 + x1 * 3166857574 + x2 * 2441202939 + x3 * 3327570642 + x4 * 3669549855 + x5 * 780027614 + x6 * 180713694 + x7 * 2647145856 + x8 * 2319909284 + x9 * 1561031212 + x10 * 4202799781 + x11 * 573281460 + x12 * 3493520432 + x13 * 3956590471 + x14 * 3037423252 + x15 * 3483144817 + x16 * 275082166 + x17 * 708813902 + x18 * 4034706302 + x19 * 2451646427 + x20 * 1709043422 + x21 * 3508904880 + x22 * 3914395210 + x23 * 1390932539 + x24 * 724980967 + x25 * 3605577362 + x26 * 523257167 + x27 * 869314102 + x28 * 921376992 + x29 * 3327052711 + x30 * 513275795 + x31 * 3636241417 == 157486161096751655213,
x0 * 2312777622 + x1 * 1817334395 + x2 * 1138529684 + x3 * 3773604428 + x4 * 1935211151 + x5 * 2213289840 + x6 * 377676625 + x7 * 1196080510 + x8 * 1199201227 + x9 * 2631999064 + x10 * 2323693808 + x11 * 3341119621 + x12 * 4082235941 + x13 * 1108916057 + x14 * 4084043198 + x15 * 3777740051 + x16 * 625149649 + x17 * 2152448475 + x18 * 2880243061 + x19 * 2428704446 + x20 * 747636324 + x21 * 3509162185 + x22 * 2883831894 + x23 * 414518377 + x24 * 3814902119 + x25 * 2824636355 + x26 * 247901663 + x27 * 386586108 + x28 * 1765102390 + x29 * 18084913 + x30 * 3764887142 + x31 * 1394818146 == 123317982529357675593,
x0 * 2391932865 + x1 * 1997583865 + x2 * 3809734451 + x3 * 92863853 + x4 * 252092837 + x5 * 4213171834 + x6 * 935980948 + x7 * 2427304675 + x8 * 2544835044 + x9 * 1740512234 + x10 * 2320698790 + x11 * 1671324494 + x12 * 3667386361 + x13 * 4067418541 + x14 * 157438085 + x15 * 2118582852 + x16 * 1441120116 + x17 * 2280200848 + x18 * 4208695179 + x19 * 1106492516 + x20 * 2587300334 + x21 * 3381272823 + x22 * 372050960 + x23 * 428062772 + x24 * 1286515897 + x25 * 22829630 + x26 * 1687635288 + x27 * 148405470 + x28 * 1814450870 + x29 * 1463318313 + x30 * 3619227493 + x31 * 3925731221 == 126768559219496596529,
x0 * 2347575350 + x1 * 1308889115 + x2 * 816706 + x3 * 170180207 + x4 * 685204177 + x5 * 288117352 + x6 * 1596053028 + x7 * 4247787399 + x8 * 31917025 + x9 * 2353281381 + x10 * 3185744134 + x11 * 2003614228 + x12 * 1662365886 + x13 * 2980988429 + x14 * 1627703790 + x15 * 611495148 + x16 * 1131728868 + x17 * 1957109115 + x18 * 384617144 + x19 * 1191742837 + x20 * 2946660792 + x21 * 3628902190 + x22 * 1497475406 + x23 * 3239518215 + x24 * 3998343997 + x25 * 2046453265 + x26 * 4212348310 + x27 * 1965589374 + x28 * 1828186543 + x29 * 1017928266 + x30 * 1620042354 + x31 * 727553879 == 127606112624935498339,
x0 * 832094402 + x1 * 3314572044 + x2 * 488868442 + x3 * 1841935151 + x4 * 1171324799 + x5 * 3471299188 + x6 * 2551569670 + x7 * 2706142177 + x8 * 1413270141 + x9 * 2799345217 + x10 * 1736078138 + x11 * 2640026379 + x12 * 3309523775 + x13 * 708228019 + x14 * 187736002 + x15 * 104108754 + x16 * 2004810 + x17 * 3509194834 + x18 * 1101418726 + x19 * 3213850540 + x20 * 3057147817 + x21 * 2872087805 + x22 * 2543533871 + x23 * 1405445933 + x24 * 3453063846 + x25 * 4186228310 + x26 * 2620809382 + x27 * 2719800494 + x28 * 2919918455 + x29 * 216899503 + x30 * 2182290754 + x31 * 674368800 == 146513328826081369964,
x0 * 3379659353 + x1 * 31185134 + x2 * 2705610804 + x3 * 1311536103 + x4 * 660262997 + x5 * 1502856668 + x6 * 826236852 + x7 * 1397745099 + x8 * 2502632519 + x9 * 3208481979 + x10 * 2304290531 + x11 * 315497265 + x12 * 997141305 + x13 * 1495605164 + x14 * 1363724399 + x15 * 228866868 + x16 * 2175251957 + x17 * 3389971630 + x18 * 3635887769 + x19 * 1257419666 + x20 * 1525795938 + x21 * 3607149798 + x22 * 3014126932 + x23 * 3279147474 + x24 * 298781431 + x25 * 459143014 + x26 * 219295357 + x27 * 1281424290 + x28 * 57884126 + x29 * 3878979772 + x30 * 2624360304 + x31 * 2540908447 == 125780026597502848309,
x0 * 4141491113 + x1 * 388348346 + x2 * 2889238267 + x3 * 3733701272 + x4 * 1601705709 + x5 * 1456475651 + x6 * 948577705 + x7 * 697474119 + x8 * 3725363803 + x9 * 3494425037 + x10 * 2404375304 + x11 * 1395091741 + x12 * 2014936811 + x13 * 3226479938 + x14 * 97991957 + x15 * 2571009732 + x16 * 2169251700 + x17 * 445613394 + x18 * 3338254578 + x19 * 3100217642 + x20 * 450233404 + x21 * 1452263534 + x22 * 3323263008 + x23 * 1281259019 + x24 * 2881501240 + x25 * 3853647762 + x26 * 3872612425 + x27 * 3625904675 + x28 * 28491161 + x29 * 837865088 + x30 * 3019749606 + x31 * 3755559168 == 145685276087861502602,
x0 * 868978565 + x1 * 1880902698 + x2 * 2147687639 + x3 * 3919867658 + x4 * 1156685196 + x5 * 1258174623 + x6 * 985400361 + x7 * 2158611251 + x8 * 1736758238 + x9 * 1949766062 + x10 * 2648425083 + x11 * 675668374 + x12 * 1793502003 + x13 * 1336203958 + x14 * 915529071 + x15 * 1122262796 + x16 * 4218938706 + x17 * 3220340687 + x18 * 36734 + x19 * 3241657248 + x20 * 2771578913 + x21 * 29182553 + x22 * 50755641 + x23 * 1762070976 + x24 * 3306888932 + x25 * 2636754670 + x26 * 3631173493 + x27 * 1644653937 + x28 * 2618008158 + x29 * 4191824826 + x30 * 3192806718 + x31 * 2190278270 == 144549374105911908218,
x0 * 136541182 + x1 * 2398358896 + x2 * 2797311504 + x3 * 2901208986 + x4 * 2703442703 + x5 * 2774784461 + x6 * 2896299321 + x7 * 3629629347 + x8 * 2661198340 + x9 * 2375796526 + x10 * 2881309577 + x11 * 3914693638 + x12 * 2474743366 + x13 * 1451731319 + x14 * 2469518941 + x15 * 585788456 + x16 * 1081804477 + x17 * 533018429 + x18 * 1414204985 + x19 * 3497925490 + x20 * 3647335419 + x21 * 1664992968 + x22 * 1447923481 + x23 * 3405490146 + x24 * 249505201 + x25 * 2233596994 + x26 * 1410924969 + x27 * 2337291136 + x28 * 1379480160 + x29 * 744913417 + x30 * 2626213460 + x31 * 433230044 == 152842832971821875727,
x0 * 1014008577 + x1 * 39181748 + x2 * 1609902830 + x3 * 63541537 + x4 * 1956421427 + x5 * 2909152377 + x6 * 3644591420 + x7 * 2245163593 + x8 * 4286399149 + x9 * 1403326636 + x10 * 2505241388 + x11 * 3866291259 + x12 * 2191815293 + x13 * 3790086170 + x14 * 3670225237 + x15 * 4242912516 + x16 * 3946904107 + x17 * 1837747940 + x18 * 3855688508 + x19 * 562956386 + x20 * 890540326 + x21 * 3159132292 + x22 * 2704578526 + x23 * 2105117563 + x24 * 3103140980 + x25 * 1827417523 + x26 * 483250618 + x27 * 3611418104 + x28 * 876993421 + x29 * 1524092496 + x30 * 1409341189 + x31 * 3793036452 == 171784010999187327978,
x0 * 766382107 + x1 * 1796925795 + x2 * 2252539335 + x3 * 349697888 + x4 * 2128341206 + x5 * 237551020 + x6 * 3435605863 + x7 * 3509292666 + x8 * 2464261299 + x9 * 3708905227 + x10 * 306252195 + x11 * 1348134057 + x12 * 872885862 + x13 * 3230301891 + x14 * 4223976431 + x15 * 2129576385 + x16 * 184274380 + x17 * 1339568775 + x18 * 240471204 + x19 * 4208060501 + x20 * 3866337301 + x21 * 1736393059 + x22 * 4084431732 + x23 * 3779198617 + x24 * 3474528562 + x25 * 3227302577 + x26 * 1764448184 + x27 * 1745641228 + x28 * 3436861592 + x29 * 3395770976 + x30 * 3381022139 + x31 * 297539769 == 159926095018550107875,
x0 * 2905996883 + x1 * 3368852349 + x2 * 2813356621 + x3 * 482055211 + x4 * 1197172847 + x5 * 731391015 + x6 * 2945886565 + x7 * 3467015148 + x8 * 537949256 + x9 * 2535535996 + x10 * 1176357138 + x11 * 3396182730 + x12 * 2858025536 + x13 * 3563590525 + x14 * 4141138247 + x15 * 3391692063 + x16 * 2595437915 + x17 * 234965395 + x18 * 1117742031 + x19 * 3427440116 + x20 * 3558609028 + x21 * 112305692 + x22 * 238895413 + x23 * 2820696874 + x24 * 1930124190 + x25 * 2904137135 + x26 * 3600773562 + x27 * 54663135 + x28 * 968260380 + x29 * 2500702039 + x30 * 3005295995 + x31 * 4136599497 == 147261348508848582047,
x0 * 3421877383 + x1 * 444332646 + x2 * 3066582397 + x3 * 410262930 + x4 * 2799546449 + x5 * 2190731430 + x6 * 3607309350 + x7 * 2329930437 + x8 * 2678982918 + x9 * 2797446341 + x10 * 3884979666 + x11 * 757321735 + x12 * 272692453 + x13 * 1039573000 + x14 * 1106227562 + x15 * 1967995121 + x16 * 3818641657 + x17 * 2958463100 + x18 * 693634090 + x19 * 4116131146 + x20 * 3604001650 + x21 * 1238373233 + x22 * 3200266845 + x23 * 3957996712 + x24 * 3653451723 + x25 * 2961370342 + x26 * 3043337802 + x27 * 1398445668 + x28 * 3133330721 + x29 * 679074840 + x30 * 3563156569 + x31 * 176796959 == 167538035640995956562,
x0 * 3407463393 + x1 * 2954388381 + x2 * 3398321376 + x3 * 703750584 + x4 * 719140271 + x5 * 4255500079 + x6 * 683637205 + x7 * 3659297114 + x8 * 618688496 + x9 * 2469121759 + x10 * 3644135823 + x11 * 1311631006 + x12 * 3732181084 + x13 * 2946211492 + x14 * 3723132383 + x15 * 1325756630 + x16 * 568937023 + x17 * 3359219977 + x18 * 2395244206 + x19 * 4246808660 + x20 * 2956191019 + x21 * 494313100 + x22 * 3493565032 + x23 * 2125356358 + x24 * 293383341 + x25 * 2881003778 + x26 * 1563660838 + x27 * 2562578871 + x28 * 4144554067 + x29 * 22718298 + x30 * 2390441161 + x31 * 3851902251 == 149364132975709163594,
x0 * 3700867328 + x1 * 162482258 + x2 * 172681360 + x3 * 673608768 + x4 * 3896952374 + x5 * 1606330254 + x6 * 2557779118 + x7 * 2839188805 + x8 * 789655247 + x9 * 3424210560 + x10 * 100545829 + x11 * 3936538736 + x12 * 1653944730 + x13 * 2102833767 + x14 * 3306727712 + x15 * 599821842 + x16 * 2700883336 + x17 * 2593372272 + x18 * 4217672760 + x19 * 1547041783 + x20 * 3434126938 + x21 * 356726724 + x22 * 3095721683 + x23 * 2932731911 + x24 * 4136374907 + x25 * 730165508 + x26 * 3627218359 + x27 * 2518974159 + x28 * 3248668960 + x29 * 1495203249 + x30 * 2284224748 + x31 * 1790575076 == 139010541840838007430

解方程

exp：

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34
#Sage
x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31 = var('x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31')
solve([x0 * 2905774839 + x1 * 937692645 + x2 * 2277996359 + x3 * 1574938713 + x4 * 825047075 + x5 * 1179013397 + x6 * 2366890081 + x7 * 3219529440 + x8 * 2414190453 + x9 * 3590757506 + x10 * 3909323650 + x11 * 2183139299 + x12 * 1579902159 + x13 * 3343902869 + x14 * 896068862 + x15 * 309758299 + x16 * 901531607 + x17 * 291291156 + x18 * 2546709881 + x19 * 4221036639 + x20 * 3505720382 + x21 * 3684857351 + x22 * 2022652786 + x23 * 451227475 + x24 * 3741251238 + x25 * 3997408590 + x26 * 2256908756 + x27 * 1334843411 + x28 * 4020591098 + x29 * 2114708609 + x30 * 79808585 + x31 * 2974805697 == 153629905098136685045,
x0 * 633779458 + x1 * 760323050 + x2 * 3524136923 + x3 * 3404961172 + x4 * 3497719477 + x5 * 2036024833 + x6 * 2807481062 + x7 * 3579571169 + x8 * 1182247335 + x9 * 1473703468 + x10 * 1485764830 + x11 * 2344149245 + x12 * 2230867977 + x13 * 451381281 + x14 * 2729949187 + x15 * 1329480928 + x16 * 3036372799 + x17 * 1916707506 + x18 * 1408308101 + x19 * 3414819940 + x20 * 54157456 + x21 * 4081087004 + x22 * 81644901 + x23 * 1046457653 + x24 * 2786986628 + x25 * 3293369990 + x26 * 2547544255 + x27 * 1408426127 + x28 * 1700843152 + x29 * 4028585224 + x30 * 3882199080 + x31 * 4040732992 == 145118376676814378151,
x0 * 1158359552 + x1 * 952473112 + x2 * 2469876874 + x3 * 1877922146 + x4 * 2681754384 + x5 * 441645489 + x6 * 1451082555 + x7 * 1282675826 + x8 * 3628741269 + x9 * 1538367477 + x10 * 4256030398 + x11 * 1551122815 + x12 * 2403304542 + x13 * 1198458285 + x14 * 2596160415 + x15 * 3952532206 + x16 * 1372310735 + x17 * 3735073437 + x18 * 686367724 + x19 * 158982013 + x20 * 1901981688 + x21 * 2045511526 + x22 * 1553141146 + x23 * 574875471 + x24 * 3881193717 + x25 * 281974061 + x26 * 3401680368 + x27 * 1071341816 + x28 * 3856818199 + x29 * 1543037830 + x30 * 2600897676 + x31 * 886793613 == 125136025093969380235,
x0 * 3369804515 + x1 * 1388562875 + x2 * 2620029184 + x3 * 3424874122 + x4 * 2155070368 + x5 * 515581101 + x6 * 3448760104 + x7 * 1571958247 + x8 * 1344632695 + x9 * 3418066835 + x10 * 1055412931 + x11 * 2599736936 + x12 * 1682298601 + x13 * 3888231955 + x14 * 869443630 + x15 * 46802084 + x16 * 1434071143 + x17 * 537999569 + x18 * 3062214567 + x19 * 638588405 + x20 * 1418519591 + x21 * 921851625 + x22 * 1349011403 + x23 * 2504652024 + x24 * 1128409974 + x25 * 825642445 + x26 * 2980848614 + x27 * 3181702547 + x28 * 1665015471 + x29 * 1655900518 + x30 * 1737483004 + x31 * 4058968130 == 123888756483831750489,
x0 * 2992139966 + x1 * 3421209457 + x2 * 1518056473 + x3 * 2934632866 + x4 * 474750728 + x5 * 1888643463 + x6 * 715133241 + x7 * 270269278 + x8 * 3453364309 + x9 * 2375169043 + x10 * 475758667 + x11 * 1550808440 + x12 * 870004412 + x13 * 2502311422 + x14 * 2802347419 + x15 * 3316934713 + x16 * 3072815429 + x17 * 1955447632 + x18 * 957468873 + x19 * 2003306503 + x20 * 2991846576 + x21 * 1052908526 + x22 * 852939089 + x23 * 2001031122 + x24 * 1763364759 + x25 * 318730434 + x26 * 2271963088 + x27 * 3167595340 + x28 * 186065313 + x29 * 3124233301 + x30 * 1558676638 + x31 * 229698311 == 136466432408823062440,
x0 * 880826917 + x1 * 2298353220 + x2 * 13972845 + x3 * 2112342331 + x4 * 520363735 + x5 * 1669676202 + x6 * 2365942382 + x7 * 2454166357 + x8 * 86684296 + x9 * 4180997737 + x10 * 2651800933 + x11 * 3387852337 + x12 * 3569081096 + x13 * 412248780 + x14 * 2622374412 + x15 * 4004737267 + x16 * 3937062327 + x17 * 2122230024 + x18 * 508412261 + x19 * 925290104 + x20 * 2297262392 + x21 * 2615036583 + x22 * 956831662 + x23 * 2377853219 + x24 * 2129964002 + x25 * 711861720 + x26 * 1072575240 + x27 * 290600530 + x28 * 3557322638 + x29 * 1937025602 + x30 * 3942606369 + x31 * 848634526 == 135520634374716138253,
x0 * 1667423245 + x1 * 3205256744 + x2 * 4218058651 + x3 * 4247786171 + x4 * 2902884888 + x5 * 1776716207 + x6 * 57317883 + x7 * 2810845945 + x8 * 4056618058 + x9 * 2442806270 + x10 * 189251210 + x11 * 175454169 + x12 * 1563217423 + x13 * 1584552187 + x14 * 4066113642 + x15 * 2678017765 + x16 * 1370397535 + x17 * 1796075905 + x18 * 3507132543 + x19 * 2375242245 + x20 * 1599167786 + x21 * 3353660587 + x22 * 2792999728 + x23 * 2513875102 + x24 * 3349313992 + x25 * 561973312 + x26 * 131599779 + x27 * 1780045940 + x28 * 181893476 + x29 * 1515423140 + x30 * 1695557088 + x31 * 1103274089 == 140870834889282733787,
x0 * 2924743894 + x1 * 2747685610 + x2 * 703249631 + x3 * 2970835309 + x4 * 1709917538 + x5 * 2326038184 + x6 * 3850628518 + x7 * 1598044999 + x8 * 1230534089 + x9 * 2628050448 + x10 * 560260479 + x11 * 2827469192 + x12 * 1261659178 + x13 * 3473946812 + x14 * 2627319447 + x15 * 2783861426 + x16 * 1814833846 + x17 * 3969833864 + x18 * 4048131215 + x19 * 3849752757 + x20 * 3942527132 + x21 * 3218422785 + x22 * 1568409347 + x23 * 3959466355 + x24 * 2784582743 + x25 * 2996021365 + x26 * 1058302993 + x27 * 360568252 + x28 * 4120475817 + x29 * 612600724 + x30 * 3312442340 + x31 * 2780876242 == 162850348028726438719,
x0 * 1616016662 + x1 * 3654249690 + x2 * 137386530 + x3 * 1430840003 + x4 * 413249034 + x5 * 512756864 + x6 * 4178200879 + x7 * 2530110366 + x8 * 2920225584 + x9 * 3182457452 + x10 * 1705355659 + x11 * 2866496197 + x12 * 4233807177 + x13 * 1885804809 + x14 * 1332101007 + x15 * 511987054 + x16 * 3709126878 + x17 * 1639834513 + x18 * 2331999251 + x19 * 3942139119 + x20 * 3452087731 + x21 * 3059112759 + x22 * 3445769324 + x23 * 128282305 + x24 * 895514710 + x25 * 3973866022 + x26 * 3074206386 + x27 * 2793860989 + x28 * 4208156768 + x29 * 1868752777 + x30 * 1128655300 + x31 * 4224750762 == 173549152139361191182,
x0 * 1507751682 + x1 * 1846572164 + x2 * 2041260497 + x3 * 1124204604 + x4 * 803283004 + x5 * 2783064398 + x6 * 3894553701 + x7 * 1968388652 + x8 * 4001422379 + x9 * 3448449208 + x10 * 3520475047 + x11 * 2550138883 + x12 * 2389210163 + x13 * 126106238 + x14 * 2662172629 + x15 * 4261498421 + x16 * 3044233456 + x17 * 3644778899 + x18 * 870298634 + x19 * 2695223165 + x20 * 1650836877 + x21 * 1258482236 + x22 * 1063099544 + x23 * 3764404492 + x24 * 3967617774 + x25 * 1965577715 + x26 * 2446428246 + x27 * 1505068720 + x28 * 3981692241 + x29 * 3408565448 + x30 * 2781597153 + x31 * 3092390689 == 180393478529485883021,
x0 * 351479342 + x1 * 503524980 + x2 * 1716292026 + x3 * 938189610 + x4 * 3362208287 + x5 * 280354280 + x6 * 2300444836 + x7 * 1468215142 + x8 * 3180887405 + x9 * 2532072979 + x10 * 1652875734 + x11 * 2254901041 + x12 * 259860786 + x13 * 3263784945 + x14 * 483273054 + x15 * 3166504792 + x16 * 914039776 + x17 * 4266192190 + x18 * 1042961273 + x19 * 181336626 + x20 * 669694284 + x21 * 2453653976 + x22 * 1389685958 + x23 * 2284711690 + x24 * 3317847597 + x25 * 2440906291 + x26 * 3042784363 + x27 * 1482188614 + x28 * 2369361990 + x29 * 324426473 + x30 * 1763743995 + x31 * 3934897747 == 117888147215252945859,
x0 * 725022521 + x1 * 938746075 + x2 * 3633113215 + x3 * 4185273958 + x4 * 2800996696 + x5 * 2631729929 + x6 * 2692051893 + x7 * 3433724886 + x8 * 1616354254 + x9 * 3607913532 + x10 * 529812087 + x11 * 2791241832 + x12 * 1737462722 + x13 * 3641411598 + x14 * 1924632655 + x15 * 1616473457 + x16 * 3637886658 + x17 * 1858291856 + x18 * 1078390594 + x19 * 1887741658 + x20 * 2265350830 + x21 * 2676979191 + x22 * 1970124470 + x23 * 664078020 + x24 * 1808737559 + x25 * 2298779415 + x26 * 1388943648 + x27 * 4204667059 + x28 * 1073622448 + x29 * 3443318903 + x30 * 2171824304 + x31 * 1868209557 == 158683608359654647072,
x0 * 650341618 + x1 * 2935581294 + x2 * 2644385881 + x3 * 1535307611 + x4 * 1016591324 + x5 * 815158333 + x6 * 1448798160 + x7 * 2641332727 + x8 * 270686394 + x9 * 2219311183 + x10 * 2967122700 + x11 * 3770872278 + x12 * 3541712142 + x13 * 3868017641 + x14 * 3555690826 + x15 * 802632927 + x16 * 3680835829 + x17 * 682966028 + x18 * 1194680003 + x19 * 894072837 + x20 * 1878364070 + x21 * 1331140614 + x22 * 965880101 + x23 * 1138566143 + x24 * 701720887 + x25 * 2742737986 + x26 * 3045938774 + x27 * 147247760 + x28 * 4094028215 + x29 * 204167974 + x30 * 3200135673 + x31 * 27026610 == 119553298425410260470,
x0 * 3264996808 + x1 * 2331472878 + x2 * 2992654618 + x3 * 1337387837 + x4 * 3068330431 + x5 * 1897134387 + x6 * 2124686830 + x7 * 433732986 + x8 * 560852756 + x9 * 569523526 + x10 * 1635729292 + x11 * 3899076223 + x12 * 2599433468 + x13 * 2525044550 + x14 * 3233393817 + x15 * 1990368374 + x16 * 8003701 + x17 * 1649870439 + x18 * 429808458 + x19 * 2788914187 + x20 * 3183669167 + x21 * 4029467918 + x22 * 1823857717 + x23 * 3493646301 + x24 * 1619264007 + x25 * 1485689524 + x26 * 1136226577 + x27 * 2403749534 + x28 * 4188551850 + x29 * 19971766 + x30 * 3514606027 + x31 * 2659730746 == 129283893341689770873,
x0 * 3179913872 + x1 * 1590442647 + x2 * 16192345 + x3 * 2330075242 + x4 * 655160953 + x5 * 4052746453 + x6 * 3225345308 + x7 * 3362725382 + x8 * 350986883 + x9 * 2257032841 + x10 * 203422664 + x11 * 1211339833 + x12 * 1005356492 + x13 * 3016854180 + x14 * 3052361161 + x15 * 667363442 + x16 * 1711948350 + x17 * 674085815 + x18 * 386890144 + x19 * 3422048832 + x20 * 127837425 + x21 * 1178013843 + x22 * 642733070 + x23 * 3317927971 + x24 * 470770850 + x25 * 1793530046 + x26 * 3190738311 + x27 * 1437576481 + x28 * 273211936 + x29 * 3162727862 + x30 * 172486187 + x31 * 3154971774 == 122131281329452040239,
x0 * 1984698529 + x1 * 1445752975 + x2 * 556628780 + x3 * 1388438884 + x4 * 1249287957 + x5 * 355916806 + x6 * 317389095 + x7 * 3161347497 + x8 * 3059986980 + x9 * 3375424603 + x10 * 2501724356 + x11 * 3520286932 + x12 * 2650494784 + x13 * 3031688124 + x14 * 777396084 + x15 * 3712283044 + x16 * 2001084449 + x17 * 2179194542 + x18 * 330859108 + x19 * 4245370419 + x20 * 1597774590 + x21 * 279816529 + x22 * 2461029032 + x23 * 4024610466 + x24 * 2111027579 + x25 * 1607579079 + x26 * 2097268956 + x27 * 2069066877 + x28 * 2186433547 + x29 * 922721930 + x30 * 1292267441 + x31 * 2955441028 == 144038024275757774857,
x0 * 1241308871 + x1 * 1393662036 + x2 * 4198993351 + x3 * 91138693 + x4 * 525807852 + x5 * 2577403449 + x6 * 86644570 + x7 * 1732667838 + x8 * 2939702570 + x9 * 2284810186 + x10 * 208700933 + x11 * 2215740017 + x12 * 3214773041 + x13 * 870729362 + x14 * 65832640 + x15 * 3610432908 + x16 * 522601813 + x17 * 175075843 + x18 * 1282298391 + x19 * 36747212 + x20 * 2587821571 + x21 * 4181954474 + x22 * 1445029272 + x23 * 153408069 + x24 * 3576784077 + x25 * 3813757427 + x26 * 3320262816 + x27 * 3551464465 + x28 * 3353985098 + x29 * 2447602934 + x30 * 3490733926 + x31 * 3993341361 == 123274418600692000659,
x0 * 893304126 + x1 * 3166857574 + x2 * 2441202939 + x3 * 3327570642 + x4 * 3669549855 + x5 * 780027614 + x6 * 180713694 + x7 * 2647145856 + x8 * 2319909284 + x9 * 1561031212 + x10 * 4202799781 + x11 * 573281460 + x12 * 3493520432 + x13 * 3956590471 + x14 * 3037423252 + x15 * 3483144817 + x16 * 275082166 + x17 * 708813902 + x18 * 4034706302 + x19 * 2451646427 + x20 * 1709043422 + x21 * 3508904880 + x22 * 3914395210 + x23 * 1390932539 + x24 * 724980967 + x25 * 3605577362 + x26 * 523257167 + x27 * 869314102 + x28 * 921376992 + x29 * 3327052711 + x30 * 513275795 + x31 * 3636241417 == 157486161096751655213,
x0 * 2312777622 + x1 * 1817334395 + x2 * 1138529684 + x3 * 3773604428 + x4 * 1935211151 + x5 * 2213289840 + x6 * 377676625 + x7 * 1196080510 + x8 * 1199201227 + x9 * 2631999064 + x10 * 2323693808 + x11 * 3341119621 + x12 * 4082235941 + x13 * 1108916057 + x14 * 4084043198 + x15 * 3777740051 + x16 * 625149649 + x17 * 2152448475 + x18 * 2880243061 + x19 * 2428704446 + x20 * 747636324 + x21 * 3509162185 + x22 * 2883831894 + x23 * 414518377 + x24 * 3814902119 + x25 * 2824636355 + x26 * 247901663 + x27 * 386586108 + x28 * 1765102390 + x29 * 18084913 + x30 * 3764887142 + x31 * 1394818146 == 123317982529357675593,
x0 * 2391932865 + x1 * 1997583865 + x2 * 3809734451 + x3 * 92863853 + x4 * 252092837 + x5 * 4213171834 + x6 * 935980948 + x7 * 2427304675 + x8 * 2544835044 + x9 * 1740512234 + x10 * 2320698790 + x11 * 1671324494 + x12 * 3667386361 + x13 * 4067418541 + x14 * 157438085 + x15 * 2118582852 + x16 * 1441120116 + x17 * 2280200848 + x18 * 4208695179 + x19 * 1106492516 + x20 * 2587300334 + x21 * 3381272823 + x22 * 372050960 + x23 * 428062772 + x24 * 1286515897 + x25 * 22829630 + x26 * 1687635288 + x27 * 148405470 + x28 * 1814450870 + x29 * 1463318313 + x30 * 3619227493 + x31 * 3925731221 == 126768559219496596529,
x0 * 2347575350 + x1 * 1308889115 + x2 * 816706 + x3 * 170180207 + x4 * 685204177 + x5 * 288117352 + x6 * 1596053028 + x7 * 4247787399 + x8 * 31917025 + x9 * 2353281381 + x10 * 3185744134 + x11 * 2003614228 + x12 * 1662365886 + x13 * 2980988429 + x14 * 1627703790 + x15 * 611495148 + x16 * 1131728868 + x17 * 1957109115 + x18 * 384617144 + x19 * 1191742837 + x20 * 2946660792 + x21 * 3628902190 + x22 * 1497475406 + x23 * 3239518215 + x24 * 3998343997 + x25 * 2046453265 + x26 * 4212348310 + x27 * 1965589374 + x28 * 1828186543 + x29 * 1017928266 + x30 * 1620042354 + x31 * 727553879 == 127606112624935498339,
x0 * 832094402 + x1 * 3314572044 + x2 * 488868442 + x3 * 1841935151 + x4 * 1171324799 + x5 * 3471299188 + x6 * 2551569670 + x7 * 2706142177 + x8 * 1413270141 + x9 * 2799345217 + x10 * 1736078138 + x11 * 2640026379 + x12 * 3309523775 + x13 * 708228019 + x14 * 187736002 + x15 * 104108754 + x16 * 2004810 + x17 * 3509194834 + x18 * 1101418726 + x19 * 3213850540 + x20 * 3057147817 + x21 * 2872087805 + x22 * 2543533871 + x23 * 1405445933 + x24 * 3453063846 + x25 * 4186228310 + x26 * 2620809382 + x27 * 2719800494 + x28 * 2919918455 + x29 * 216899503 + x30 * 2182290754 + x31 * 674368800 == 146513328826081369964,
x0 * 3379659353 + x1 * 31185134 + x2 * 2705610804 + x3 * 1311536103 + x4 * 660262997 + x5 * 1502856668 + x6 * 826236852 + x7 * 1397745099 + x8 * 2502632519 + x9 * 3208481979 + x10 * 2304290531 + x11 * 315497265 + x12 * 997141305 + x13 * 1495605164 + x14 * 1363724399 + x15 * 228866868 + x16 * 2175251957 + x17 * 3389971630 + x18 * 3635887769 + x19 * 1257419666 + x20 * 1525795938 + x21 * 3607149798 + x22 * 3014126932 + x23 * 3279147474 + x24 * 298781431 + x25 * 459143014 + x26 * 219295357 + x27 * 1281424290 + x28 * 57884126 + x29 * 3878979772 + x30 * 2624360304 + x31 * 2540908447 == 125780026597502848309,
x0 * 4141491113 + x1 * 388348346 + x2 * 2889238267 + x3 * 3733701272 + x4 * 1601705709 + x5 * 1456475651 + x6 * 948577705 + x7 * 697474119 + x8 * 3725363803 + x9 * 3494425037 + x10 * 2404375304 + x11 * 1395091741 + x12 * 2014936811 + x13 * 3226479938 + x14 * 97991957 + x15 * 2571009732 + x16 * 2169251700 + x17 * 445613394 + x18 * 3338254578 + x19 * 3100217642 + x20 * 450233404 + x21 * 1452263534 + x22 * 3323263008 + x23 * 1281259019 + x24 * 2881501240 + x25 * 3853647762 + x26 * 3872612425 + x27 * 3625904675 + x28 * 28491161 + x29 * 837865088 + x30 * 3019749606 + x31 * 3755559168 == 145685276087861502602,
x0 * 868978565 + x1 * 1880902698 + x2 * 2147687639 + x3 * 3919867658 + x4 * 1156685196 + x5 * 1258174623 + x6 * 985400361 + x7 * 2158611251 + x8 * 1736758238 + x9 * 1949766062 + x10 * 2648425083 + x11 * 675668374 + x12 * 1793502003 + x13 * 1336203958 + x14 * 915529071 + x15 * 1122262796 + x16 * 4218938706 + x17 * 3220340687 + x18 * 36734 + x19 * 3241657248 + x20 * 2771578913 + x21 * 29182553 + x22 * 50755641 + x23 * 1762070976 + x24 * 3306888932 + x25 * 2636754670 + x26 * 3631173493 + x27 * 1644653937 + x28 * 2618008158 + x29 * 4191824826 + x30 * 3192806718 + x31 * 2190278270 == 144549374105911908218,
x0 * 136541182 + x1 * 2398358896 + x2 * 2797311504 + x3 * 2901208986 + x4 * 2703442703 + x5 * 2774784461 + x6 * 2896299321 + x7 * 3629629347 + x8 * 2661198340 + x9 * 2375796526 + x10 * 2881309577 + x11 * 3914693638 + x12 * 2474743366 + x13 * 1451731319 + x14 * 2469518941 + x15 * 585788456 + x16 * 1081804477 + x17 * 533018429 + x18 * 1414204985 + x19 * 3497925490 + x20 * 3647335419 + x21 * 1664992968 + x22 * 1447923481 + x23 * 3405490146 + x24 * 249505201 + x25 * 2233596994 + x26 * 1410924969 + x27 * 2337291136 + x28 * 1379480160 + x29 * 744913417 + x30 * 2626213460 + x31 * 433230044 == 152842832971821875727,
x0 * 1014008577 + x1 * 39181748 + x2 * 1609902830 + x3 * 63541537 + x4 * 1956421427 + x5 * 2909152377 + x6 * 3644591420 + x7 * 2245163593 + x8 * 4286399149 + x9 * 1403326636 + x10 * 2505241388 + x11 * 3866291259 + x12 * 2191815293 + x13 * 3790086170 + x14 * 3670225237 + x15 * 4242912516 + x16 * 3946904107 + x17 * 1837747940 + x18 * 3855688508 + x19 * 562956386 + x20 * 890540326 + x21 * 3159132292 + x22 * 2704578526 + x23 * 2105117563 + x24 * 3103140980 + x25 * 1827417523 + x26 * 483250618 + x27 * 3611418104 + x28 * 876993421 + x29 * 1524092496 + x30 * 1409341189 + x31 * 3793036452 == 171784010999187327978,
x0 * 766382107 + x1 * 1796925795 + x2 * 2252539335 + x3 * 349697888 + x4 * 2128341206 + x5 * 237551020 + x6 * 3435605863 + x7 * 3509292666 + x8 * 2464261299 + x9 * 3708905227 + x10 * 306252195 + x11 * 1348134057 + x12 * 872885862 + x13 * 3230301891 + x14 * 4223976431 + x15 * 2129576385 + x16 * 184274380 + x17 * 1339568775 + x18 * 240471204 + x19 * 4208060501 + x20 * 3866337301 + x21 * 1736393059 + x22 * 4084431732 + x23 * 3779198617 + x24 * 3474528562 + x25 * 3227302577 + x26 * 1764448184 + x27 * 1745641228 + x28 * 3436861592 + x29 * 3395770976 + x30 * 3381022139 + x31 * 297539769 == 159926095018550107875,
x0 * 2905996883 + x1 * 3368852349 + x2 * 2813356621 + x3 * 482055211 + x4 * 1197172847 + x5 * 731391015 + x6 * 2945886565 + x7 * 3467015148 + x8 * 537949256 + x9 * 2535535996 + x10 * 1176357138 + x11 * 3396182730 + x12 * 2858025536 + x13 * 3563590525 + x14 * 4141138247 + x15 * 3391692063 + x16 * 2595437915 + x17 * 234965395 + x18 * 1117742031 + x19 * 3427440116 + x20 * 3558609028 + x21 * 112305692 + x22 * 238895413 + x23 * 2820696874 + x24 * 1930124190 + x25 * 2904137135 + x26 * 3600773562 + x27 * 54663135 + x28 * 968260380 + x29 * 2500702039 + x30 * 3005295995 + x31 * 4136599497 == 147261348508848582047,
x0 * 3421877383 + x1 * 444332646 + x2 * 3066582397 + x3 * 410262930 + x4 * 2799546449 + x5 * 2190731430 + x6 * 3607309350 + x7 * 2329930437 + x8 * 2678982918 + x9 * 2797446341 + x10 * 3884979666 + x11 * 757321735 + x12 * 272692453 + x13 * 1039573000 + x14 * 1106227562 + x15 * 1967995121 + x16 * 3818641657 + x17 * 2958463100 + x18 * 693634090 + x19 * 4116131146 + x20 * 3604001650 + x21 * 1238373233 + x22 * 3200266845 + x23 * 3957996712 + x24 * 3653451723 + x25 * 2961370342 + x26 * 3043337802 + x27 * 1398445668 + x28 * 3133330721 + x29 * 679074840 + x30 * 3563156569 + x31 * 176796959 == 167538035640995956562,
x0 * 3407463393 + x1 * 2954388381 + x2 * 3398321376 + x3 * 703750584 + x4 * 719140271 + x5 * 4255500079 + x6 * 683637205 + x7 * 3659297114 + x8 * 618688496 + x9 * 2469121759 + x10 * 3644135823 + x11 * 1311631006 + x12 * 3732181084 + x13 * 2946211492 + x14 * 3723132383 + x15 * 1325756630 + x16 * 568937023 + x17 * 3359219977 + x18 * 2395244206 + x19 * 4246808660 + x20 * 2956191019 + x21 * 494313100 + x22 * 3493565032 + x23 * 2125356358 + x24 * 293383341 + x25 * 2881003778 + x26 * 1563660838 + x27 * 2562578871 + x28 * 4144554067 + x29 * 22718298 + x30 * 2390441161 + x31 * 3851902251 == 149364132975709163594,
x0 * 3700867328 + x1 * 162482258 + x2 * 172681360 + x3 * 673608768 + x4 * 3896952374 + x5 * 1606330254 + x6 * 2557779118 + x7 * 2839188805 + x8 * 789655247 + x9 * 3424210560 + x10 * 100545829 + x11 * 3936538736 + x12 * 1653944730 + x13 * 2102833767 + x14 * 3306727712 + x15 * 599821842 + x16 * 2700883336 + x17 * 2593372272 + x18 * 4217672760 + x19 * 1547041783 + x20 * 3434126938 + x21 * 356726724 + x22 * 3095721683 + x23 * 2932731911 + x24 * 4136374907 + x25 * 730165508 + x26 * 3627218359 + x27 * 2518974159 + x28 * 3248668960 + x29 * 1495203249 + x30 * 2284224748 + x31 * 1790575076 == 139010541840838007430],x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31)

运行得到

解出x0-x31来，然后将他们加起来进行md5加密即可得到flag

exp：

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import hashlib
 
c = [89155365, 3795653268, 783620457, 763601920, 1653708118, 2433063826, 4217977576, 1709775682, 3519663525, 1970630923, 4089088412, 974751512, 2984323532, 2502694787, 417461604, 1806361262, 4041026542, 1690492554, 1842407621, 3241492534, 2467028824, 2258589262, 1908777079, 3977926013, 2553491708, 2361686047, 483149607, 3782713824, 42128790, 4130286729, 12709818, 75034618]
res = 0
for i in c:
    res += i
print(hashlib.md5(str(res).encode()).hexdigest())

运行得到

最后flag为

1
0xGame{d23caedc66301966094bf8968610f61f}

RSA大闯关

下载附件

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from Crypto.Util.number import *
from secret import flag, hint
 
# part1
print('part1:')
m = bytes_to_long(flag)
p = getPrime(512)
q = getPrime(512)
n = p * q
e = 5
c = pow(m, e, n)
print(f'n = {n}')
 
# part2
print('part2:')
m = c
while True:
    p = getPrime(256)
    q = 2 * p - 1
    if isPrime(q):
        break
r = getPrime(256)
n = (p ** 2) * (q ** 3) * r
q = 2 * p - 1
r = n // p // p // q // q // q
phi = p * (p - 1) * (q ** 2) * (q - 1) * (r - 1)
e = 0x10001
c = pow(m, e, n)
e = 0x10001
d = inverse(e, phi)
print(f'p = {p}')
print(f'n = {n}')
 
# part3
print('part3:')
m = c
p = getPrime(1024)
q = getPrime(1024)
n = p * q
e = 0x10001
c = pow(m, e, n)
print(f'n1 = {n}')
m_hint = bytes_to_long(hint)
p = getPrime(1024)
n = p * q
e = 0x10001
c_hint = pow(m_hint, e, n)
print(f'n2 = {n}')
print(f"c_hint = {c_hint}")
 
# part4
print('part4:')
m = c
p = getPrime(1024)
q = getPrime(1024)
n = p * q
e1 = 823
e2 = 827
c1 = pow(m, e1, n)
c2 = pow(m, e2, n)
print(f"c1 = {c1}")
print(f"c2 = {c2}")
print(f'n = {n}')

out.txt

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part1:
n = 61553578635593130900790335104330199899957479107753805370559935381319176517030435621892644394851110367233510867782247563759513582241371585326815640128560441855543132415804452658372689998329770879189234308679763515840663749100256299294925802306716380006559943335403696300844219318648209424221864526219684170323
part2:
p = 74447194261899797806331260065953660447629801256490828189012933613329970709947
n = 2041966692549961348577589156815535814894383939477573453736803458531176718024423820279431442431002038195467272680340686126482697016165252765359529302961780051654184833220756878301874978169377654737275593641180065950107522278461981853325163973125649755001647509934635714847722574876087513598188126414206128734529793608240092700267723049259261257688980084854149645269724715087902044253045061617087644418347545737251946830621974361352738393315774363456001260686286821
part3:
n1 = 15366889088720206462365176683482533771475038765899922246304161568426870328374352417380396654231031838308606185501644949132930223566330052875527300069440013396537288642394243440572453780188595977438549563350553795220825285867086201710340271331833567314282717818053503639202601281184963886414311276063351370392514246631613915966530559511182811214902930142301497062642020127200767773575622874178491764524627735580808973946630814640241598316693375333001863979963200190532552021172069905740730777328461596141791691176984619646698097163144730290275304802207549132742312305772773347199117833216411732334271813533947587335221
n2 = 20183388181244396840270604971327234348871288822322010757845683437514931959842693524118522620332345907816190233979463740070942867621461314257682562161455669676863270809215109867553547955455891544244660598280541169460595995979836132666968548336872337169229971614320624540103986072146724866807104701652693664361940168493838397000924419632475639380887065784985415455805447197724730216369636562749194600089463165474701372926961338986138771964038560621556333104655430975405632113198088493779517573588399048423998920358946322913978731589449991564968387399262236393754348689348364331583617892656413994899504317963936066746711
c_hint = 12120021785410200674936083975068492622806596845579817711207411931311673622528683733295899555542821765486413339677732337051154734922381291549341456901391897097071173557362462670207940577864049130086490199471016266752247947028119300006197925597902468232113412106835719324155978933609953160168249853647848792919491609758205614794158719549005912914647125869214028842543301994189007931419280489270222524804427348611393246242401221829752270244371023220680417679183759839375701147795748353616923267194525565792165688787118410950596647945293284284065635467684624433860537889580808687549562010274639326086182100555438472928477
part4:
c1 = 9078361566243923931453433235655548442655855925297849762834170634279782440176386162361175845447411925452440536363885489221360776073555926463975255326905638922390565414284680629357799512527773691276009031423377599372917213698291316223269863185821983356471150336545331992444135470581201015592546934895803603233714496806375582266021488376740973566067971171377376696739676668351989078245768566579430312381789763928896787230892629854943142188671250203690237420561985562568939519395990646242000804771019311031994084798126248041633375710435071152701495690196067180826646094418362227966248990190779434700525127330999576205403
c2 = 12177776162003265214893575222194987257070438203909939490896524118455743796605830818003435519762848552272241059418403518390909966083445568223047769437125388741650260643855866243844976422365885347004481452172768271389384606695863524445386834984939563686335088776216144173923094121825197018225369010379704707231069719085315847868962939479004164733530937883272062497573804335640040429427002585027258509179962910923328842082991111693056946212131251751202352180633674002081181776189622240094621381950470130292188270896292285264623566756488080661579679026084947009907677214940302660119264003701359714404829438298116109098858
n = 14030240067066681750909588505308848034761783265133340312144652793728120334984848299676691973630997860228334585084780567142583267241508872459495746147465287012511207543757701482011894061407632686585952604039659614267570771869230862091904009290811411173144016039144680108997615936869263338253711107240318817354345905789041695601640084081957736966556648022765868913061143917752122990399785349647514452618248194426911284810212654925532788132854712772334295140032083665199391450057318155421959795859937645872080008934829472830347990643737088885491045934515364200316439381396296113975664305689878031662485528015544354270191

共模攻击、模不互素、多素数相乘下φ(n)的计算、低指数小明文攻击

exp:

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from Crypto.Util.number import *
from gmpy2 import *


def ex_gcd(a, b):
    if b == 0:
        x, y = 1, 0
        return a, x, y
    else:
        d, y, x = ex_gcd(b, a % b)
        y = y - a // b * x
        return d, x, y


# part4
e1, e2 = 823, 827
c1 = 9078361566243923931453433235655548442655855925297849762834170634279782440176386162361175845447411925452440536363885489221360776073555926463975255326905638922390565414284680629357799512527773691276009031423377599372917213698291316223269863185821983356471150336545331992444135470581201015592546934895803603233714496806375582266021488376740973566067971171377376696739676668351989078245768566579430312381789763928896787230892629854943142188671250203690237420561985562568939519395990646242000804771019311031994084798126248041633375710435071152701495690196067180826646094418362227966248990190779434700525127330999576205403
c2 = 12177776162003265214893575222194987257070438203909939490896524118455743796605830818003435519762848552272241059418403518390909966083445568223047769437125388741650260643855866243844976422365885347004481452172768271389384606695863524445386834984939563686335088776216144173923094121825197018225369010379704707231069719085315847868962939479004164733530937883272062497573804335640040429427002585027258509179962910923328842082991111693056946212131251751202352180633674002081181776189622240094621381950470130292188270896292285264623566756488080661579679026084947009907677214940302660119264003701359714404829438298116109098858
n = 14030240067066681750909588505308848034761783265133340312144652793728120334984848299676691973630997860228334585084780567142583267241508872459495746147465287012511207543757701482011894061407632686585952604039659614267570771869230862091904009290811411173144016039144680108997615936869263338253711107240318817354345905789041695601640084081957736966556648022765868913061143917752122990399785349647514452618248194426911284810212654925532788132854712772334295140032083665199391450057318155421959795859937645872080008934829472830347990643737088885491045934515364200316439381396296113975664305689878031662485528015544354270191
_, s1, s2 = ex_gcd(e1, e2)
m = pow(c1, s1, n) * pow(c2, s2, n) % n

# part3
c = m
n1 = 15366889088720206462365176683482533771475038765899922246304161568426870328374352417380396654231031838308606185501644949132930223566330052875527300069440013396537288642394243440572453780188595977438549563350553795220825285867086201710340271331833567314282717818053503639202601281184963886414311276063351370392514246631613915966530559511182811214902930142301497062642020127200767773575622874178491764524627735580808973946630814640241598316693375333001863979963200190532552021172069905740730777328461596141791691176984619646698097163144730290275304802207549132742312305772773347199117833216411732334271813533947587335221
n2 = 20183388181244396840270604971327234348871288822322010757845683437514931959842693524118522620332345907816190233979463740070942867621461314257682562161455669676863270809215109867553547955455891544244660598280541169460595995979836132666968548336872337169229971614320624540103986072146724866807104701652693664361940168493838397000924419632475639380887065784985415455805447197724730216369636562749194600089463165474701372926961338986138771964038560621556333104655430975405632113198088493779517573588399048423998920358946322913978731589449991564968387399262236393754348689348364331583617892656413994899504317963936066746711
q = gcd(n1, n2)
p = n1 // q
phi = (p - 1) * (q - 1)
e = 0x10001
d = inverse(e, phi)
m = pow(c, d, n1)

# part2
c = m
p = 74447194261899797806331260065953660447629801256490828189012933613329970709947
n = 2041966692549961348577589156815535814894383939477573453736803458531176718024423820279431442431002038195467272680340686126482697016165252765359529302961780051654184833220756878301874978169377654737275593641180065950107522278461981853325163973125649755001647509934635714847722574876087513598188126414206128734529793608240092700267723049259261257688980084854149645269724715087902044253045061617087644418347545737251946830621974361352738393315774363456001260686286821
q = 2 * p - 1
r = n // p ** 2 // q ** 3
phi = p * (p - 1) * (q ** 2) * (q - 1) * (r - 1)
e = 0x10001
d = inverse(e, phi)
m = pow(c, d, n)

# part1
c = m
n = 61553578635593130900790335104330199899957479107753805370559935381319176517030435621892644394851110367233510867782247563759513582241371585326815640128560441855543132415804452658372689998329770879189234308679763515840663749100256299294925802306716380006559943335403696300844219318648209424221864526219684170323
for k in range(1000000000000000):
    if iroot(c + k * n, 5)[1]:
        m = iroot(c + k * n, 5)[0]
        print(long_to_bytes(m))
        break

运行得到

最后flag为

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0xGame{rsa-----just_so_so}

公平竞争

下载附件

playfair加密，对密文分组，2个一组，对照给的表进行解密，需要注意的是，在加密的过程中，如果成对后有两个相同字 母紧挨或最后一个字母是单个的，就插入一个字母X（或者Q），这里应该是插入的X，对照表解出：0xGame{emmxmp1ayf4irx}，去掉x即为flag

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0xGame{emmmp1ayf4ir}

B_D

下载附件

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from Crypto.Util.number import *
from random import getrandbits
from gmpy2 import iroot
from secret import flag

p = getPrime(1024)
q = getPrime(1024)
N = p * q
print(f'N = {N}')
phi = (p - 1) * (q - 1)
d = int(iroot(N, 4)[0]) ^ getrandbits(250)
e = inverse(d, phi)
print(f'e = {e}')
m = bytes_to_long(flag)
c = pow(m, e, N)
print(f'c = {c}')

'''
N = 13715167883327838365274013103811076297254519716291174626890031505049627611641807596962804506207157502045195781365630439474317484673473403986343702501452710346860882791228915615232698948400931145542432966628624716533536281875822030435151439206091534065530955853558251844179933228948946231934907101348856917824632780140302729089040084528299043022659493046663327556618853280458205340179780170389837210862308567364916986243860683903949615558074610280891213861381781319433048939289437463860265900778945092793308233742580280756443573234593229072279867130716077271555451455116619361480980560826274232688876999336924667363487
e = 1615862820938647108786482341931683353132461038363662791095097725090528207925144493492927418779285810993803186019668893476085410570338701324011680380009723017909177619155864350030705272863925396654868568018042490841315909498209546400543778057365091655159015236972999269615383129191650099946771227478019788434779769416560521875995741538043223514581448653783898100814268462500355130172367409153557166306640544650178710024155132465062731524785656554977071144060691933041728644548295325756367557081623679286709670138138897259434915699217267474125159279020820148982619570258333277071070481182133532212027568829026138356701
c = 5840501258024718864832142987890599173450298697953071330840633894213580157775134582366948009609464376347860855722853624706859551014578993970405414872475110788174945766031263741375838245446993873866074337521205610057099008802133355317057766130687125151837582629432432658067853766874748078066930025360520657828177656684371518932673114544966498967187329934293660732818645061628470501507505692848153374443370177624402249696242245782230674035636514120771392032684619892427019580836399492234567981411499400095809897517092318731307728822816363313767096033957040393013220969966377537175857321999311476688402271035503547204592
'''

非预期解法：

维纳攻击,直接一把梭

最后flag为

1
0xGame{b0n3h_durf33_YYDS}

预期解法：

boneh_durfee的攻击

exp：

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import time

"""
Setting debug to true will display more informations
about the lattice, the bounds, the vectors...
"""
debug = True

"""
Setting strict to true will stop the algorithm (and
return (-1, -1)) if we don't have a correct
upperbound on the determinant. Note that this
doesn't necesseraly mean that no solutions
will be found since the theoretical upperbound is
usualy far away from actual results. That is why
you should probably use `strict = False`
"""
strict = False

"""
This is experimental, but has provided remarkable results
so far. It tries to reduce the lattice as much as it can
while keeping its efficiency. I see no reason not to use
this option, but if things don't work, you should try
disabling it
"""
helpful_only = True
dimension_min = 7 # stop removing if lattice reaches that dimension

############################################
# Functions
##########################################

# display stats on helpful vectors
def helpful_vectors(BB, modulus):
    nothelpful = 0
    for ii in range(BB.dimensions()[0]):
        if BB[ii,ii] >= modulus:
            nothelpful += 1

    print (nothelpful, "/", BB.dimensions()[0], " vectors are not helpful")

# display matrix picture with 0 and X
def matrix_overview(BB, bound):
    for ii in range(BB.dimensions()[0]):
        a = ('%02d ' % ii)
        for jj in range(BB.dimensions()[1]):
            a += '0' if BB[ii,jj] == 0 else 'X'
            if BB.dimensions()[0] < 60:
                a += ' '
        if BB[ii, ii] >= bound:
            a += '~'
        print (a)

# tries to remove unhelpful vectors
# we start at current = n-1 (last vector)
def remove_unhelpful(BB, monomials, bound, current):
    # end of our recursive function
    if current == -1 or BB.dimensions()[0] <= dimension_min:
        return BB

    # we start by checking from the end
    for ii in range(current, -1, -1):
        # if it is unhelpful:
        if BB[ii, ii] >= bound:
            affected_vectors = 0
            affected_vector_index = 0
            # let's check if it affects other vectors
            for jj in range(ii + 1, BB.dimensions()[0]):
                # if another vector is affected:
                # we increase the count
                if BB[jj, ii] != 0:
                    affected_vectors += 1
                    affected_vector_index = jj

            # level:0
            # if no other vectors end up affected
            # we remove it
            if affected_vectors == 0:
                print ("* removing unhelpful vector", ii)
                BB = BB.delete_columns([ii])
                BB = BB.delete_rows([ii])
                monomials.pop(ii)
                BB = remove_unhelpful(BB, monomials, bound, ii-1)
                return BB

            # level:1
            # if just one was affected we check
            # if it is affecting someone else
            elif affected_vectors == 1:
                affected_deeper = True
                for kk in range(affected_vector_index + 1, BB.dimensions()[0]):
                    # if it is affecting even one vector
                    # we give up on this one
                    if BB[kk, affected_vector_index] != 0:
                        affected_deeper = False
                # remove both it if no other vector was affected and
                # this helpful vector is not helpful enough
                # compared to our unhelpful one
                if affected_deeper and abs(bound - BB[affected_vector_index, affected_vector_index]) < abs(bound - BB[ii, ii]):
                    print ("* removing unhelpful vectors", ii, "and", affected_vector_index)
                    BB = BB.delete_columns([affected_vector_index, ii])
                    BB = BB.delete_rows([affected_vector_index, ii])
                    monomials.pop(affected_vector_index)
                    monomials.pop(ii)
                    BB = remove_unhelpful(BB, monomials, bound, ii-1)
                    return BB
    # nothing happened
    return BB

"""
Returns:
* 0,0   if it fails
* -1,-1 if `strict=true`, and determinant doesn't bound
* x0,y0 the solutions of `pol`
"""
def boneh_durfee(pol, modulus, mm, tt, XX, YY):
    """
    Boneh and Durfee revisited by Herrmann and May

    finds a solution if:
    * d < N^delta
    * |x| < e^delta
    * |y| < e^0.5
    whenever delta < 1 - sqrt(2)/2 ~ 0.292
    """

    # substitution (Herrman and May)
    PR.<u, x, y> = PolynomialRing(ZZ)
    Q = PR.quotient(x*y + 1 - u) # u = xy + 1
    polZ = Q(pol).lift()

    UU = XX*YY + 1

    # x-shifts
    gg = []
    for kk in range(mm + 1):
        for ii in range(mm - kk + 1):
            xshift = x^ii * modulus^(mm - kk) * polZ(u, x, y)^kk
            gg.append(xshift)
    gg.sort()

    # x-shifts list of monomials
    monomials = []
    for polynomial in gg:
        for monomial in polynomial.monomials():
            if monomial not in monomials:
                monomials.append(monomial)
    monomials.sort()

    # y-shifts (selected by Herrman and May)
    for jj in range(1, tt + 1):
        for kk in range(floor(mm/tt) * jj, mm + 1):
            yshift = y^jj * polZ(u, x, y)^kk * modulus^(mm - kk)
            yshift = Q(yshift).lift()
            gg.append(yshift) # substitution

    # y-shifts list of monomials
    for jj in range(1, tt + 1):
        for kk in range(floor(mm/tt) * jj, mm + 1):
            monomials.append(u^kk * y^jj)

    # construct lattice B
    nn = len(monomials)
    BB = Matrix(ZZ, nn)
    for ii in range(nn):
        BB[ii, 0] = gg[ii](0, 0, 0)
        for jj in range(1, ii + 1):
            if monomials[jj] in gg[ii].monomials():
                BB[ii, jj] = gg[ii].monomial_coefficient(monomials[jj]) * monomials[jj](UU,XX,YY)

    # Prototype to reduce the lattice
    if helpful_only:
        # automatically remove
        BB = remove_unhelpful(BB, monomials, modulus^mm, nn-1)
        # reset dimension
        nn = BB.dimensions()[0]
        if nn == 0:
            print ("failure")
            return 0,0

    # check if vectors are helpful
    if debug:
        helpful_vectors(BB, modulus^mm)

    # check if determinant is correctly bounded
    det = BB.det()
    bound = modulus^(mm*nn)
    if det >= bound:
        print ("We do not have det < bound. Solutions might not be found.")
        print ("Try with highers m and t.")
        if debug:
            diff = (log(det) - log(bound)) / log(2)
            print ("size det(L) - size e^(m*n) = ", floor(diff))
        if strict:
            return -1, -1
    else:
        print ("det(L) < e^(m*n) (good! If a solution exists < N^delta, it will be found)")

    # display the lattice basis
    if debug:
        matrix_overview(BB, modulus^mm)

    # LLL
    if debug:
        print ("optimizing basis of the lattice via LLL, this can take a long time")

    BB = BB.LLL()

    if debug:
        print ("LLL is done!")

    # transform vector i & j -> polynomials 1 & 2
    if debug:
        print ("looking for independent vectors in the lattice")
    found_polynomials = False

    for pol1_idx in range(nn - 1):
        for pol2_idx in range(pol1_idx + 1, nn):
            # for i and j, create the two polynomials
            PR.<w,z> = PolynomialRing(ZZ)
            pol1 = pol2 = 0
            for jj in range(nn):
                pol1 += monomials[jj](w*z+1,w,z) * BB[pol1_idx, jj] / monomials[jj](UU,XX,YY)
                pol2 += monomials[jj](w*z+1,w,z) * BB[pol2_idx, jj] / monomials[jj](UU,XX,YY)

            # resultant
            PR.<q> = PolynomialRing(ZZ)
            rr = pol1.resultant(pol2)

            # are these good polynomials?
            if rr.is_zero() or rr.monomials() == [1]:
                continue
            else:
                print ("found them, using vectors", pol1_idx, "and", pol2_idx)
                found_polynomials = True
                break
        if found_polynomials:
            break

    if not found_polynomials:
        print ("no independant vectors could be found. This should very rarely happen...")
        return 0, 0

    rr = rr(q, q)

    # solutions
    soly = rr.roots()

    if len(soly) == 0:
        print ("Your prediction (delta) is too small")
        return 0, 0

    soly = soly[0][0]
    ss = pol1(q, soly)
    solx = ss.roots()[0][0]

    #
    return solx, soly

def example():
    ############################################
    # How To Use This Script
    ##########################################

    #
    # The problem to solve (edit the following values)
    #

    # the modulus
    N = 13715167883327838365274013103811076297254519716291174626890031505049627611641807596962804506207157502045195781365630439474317484673473403986343702501452710346860882791228915615232698948400931145542432966628624716533536281875822030435151439206091534065530955853558251844179933228948946231934907101348856917824632780140302729089040084528299043022659493046663327556618853280458205340179780170389837210862308567364916986243860683903949615558074610280891213861381781319433048939289437463860265900778945092793308233742580280756443573234593229072279867130716077271555451455116619361480980560826274232688876999336924667363487
    # the public exponent
    e = 1615862820938647108786482341931683353132461038363662791095097725090528207925144493492927418779285810993803186019668893476085410570338701324011680380009723017909177619155864350030705272863925396654868568018042490841315909498209546400543778057365091655159015236972999269615383129191650099946771227478019788434779769416560521875995741538043223514581448653783898100814268462500355130172367409153557166306640544650178710024155132465062731524785656554977071144060691933041728644548295325756367557081623679286709670138138897259434915699217267474125159279020820148982619570258333277071070481182133532212027568829026138356701

    # the hypothesis on the private exponent (the theoretical maximum is 0.292)
    delta = 0.251 # this means that d < N^delta

    #
    # Lattice (tweak those values)
    #

    # you should tweak this (after a first run), (e.g. increment it until a solution is found)
    m = 4 # size of the lattice (bigger the better/slower)

    # you need to be a lattice master to tweak these
    t = int((1-2*delta) * m)  # optimization from Herrmann and May
    X = 2*floor(N^delta)  # this _might_ be too much
    Y = floor(N^(1/2))    # correct if p, q are ~ same size

    #
    # Don't touch anything below
    #

    # Problem put in equation
    P.<x,y> = PolynomialRing(ZZ)
    A = int((N+1)/2)
    pol = 1 + x * (A + y)

    #
    # Find the solutions!
    #

    # Checking bounds
    if debug:
        print ("=== checking values ===")
        print ("* delta:", delta)
        print ("* delta < 0.292", delta < 0.292)
        print ("* size of e:", int(log(e)/log(2)))
        print ("* size of N:", int(log(N)/log(2)))
        print ("* m:", m, ", t:", t)

    # boneh_durfee
    if debug:
        print ("=== running algorithm ===")
        start_time = time.time()

    solx, soly = boneh_durfee(pol, e, m, t, X, Y)

    # found a solution?
    if solx > 0:
        print ("=== solution found ===")
        if False:
            print ("x:", solx)
            print ("y:", soly)

        d = int(pol(solx, soly) / e)
        print ("private key found:", d)
    else:
        print ("=== no solution was found ===")

    if debug:
        print("=== %s seconds ===" % (time.time() - start_time))

if __name__ == "__main__":
    example()

blocker

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

a = random.getrandbits(32)
b = random.getrandbits(32)


def circular_shift_left(int_value, k, bit=32):
    bin_value = bin(int_value)[2:].zfill(32)
    bin_value = bin_value[k:] + bin_value[:k]
    int_value = int(bin_value, 2)
    return int_value


def enc_block(block):
    block = bytes_to_long(block)
    block ^= a
    block = circular_shift_left(block, 11)
    block ^= b
    return block


def enc_msg(msg):
    block_length = 4
    msg = msg + ((block_length - len(msg) % block_length) % block_length) * b'\x00'
    plain_block = [msg[block_length * i: block_length * (i + 1)] for i in range(len(msg) // block_length)]
    cipher = b""
    IV = bytes_to_long(b"0xgm")
    for block in plain_block:
        c = enc_block(block) ^ IV
        IV = c
        cipher += long_to_bytes(c)
    return cipher


print("a =", a)
print("b =", b)
print("cipher =", enc_msg(flag))

'''
a = 232825750
b = 1828860569
cipher = b'\x9a]\xec\x18\xd9\x98\x1d\x85\x0b}V\xf0\xc9\x98\x8d\x85"<\xf4\x02+\xa1m\xe7\xa0\xa6dJ\x8b\x93u?\x0b\x8d\xf62'
'''

简单的块密码

exp：

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from Crypto.Util.number import *

a = 232825750
b = 1828860569
cipher = b'\x9a]\xec\x18\xd9\x98\x1d\x85\x0b}V\xf0\xc9\x98\x8d\x85"<\xf4\x02+\xa1m\xe7\xa0\xa6dJ\x8b\x93u?\x0b\x8d\xf62'
block_length = 4


def circular_shift_left(int_value, k, bit=32):
    bin_value = bin(int_value)[2:].zfill(32)
    bin_value = bin_value[k:] + bin_value[:k]
    int_value = int(bin_value, 2)
    return int_value


def dec_block(block):
    block ^= b
    block = circular_shift_left(block, 21)
    block ^= a
    block = long_to_bytes(block)
    return block


ff = []
flag = b""
plain_block = [cipher[block_length * i: block_length * (i + 1)] for i in range(len(cipher) // block_length)]

flag += (dec_block(bytes_to_long(b'0xgm') ^ bytes_to_long(plain_block[0])))
for i in range(8):
    flag += (dec_block(bytes_to_long(plain_block[i]) ^ bytes_to_long(plain_block[i + 1])))
print(flag)

运行得到

最后flag为

1
0xGame{n0w_y0u_kn0w_bl0ck|c1pher?}

Euler

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

n = 1
phi = 1
for i in range(20):
    tmp = getPrime(50)
    n *= tmp
m = bytes_to_long(flag)
e = random.getrandbits(32)
l = pow(3, pow(3, e), n)
c = l ^ m

print(e)
print(n)
print(c)
'''
231259269673028
29929378538095242599885557965311297229924523708488195903349782032363055913634371143193552305707368798772150932190898234995143081146304332830718576568862215833419088712212229994786373886002933885241338295986566059232256985357837569354103718470254246398122059607732272010616255443856829833332931407591
14115545351007949046897492137862741044898077109960419446496565606468622772683580281638816799144770994249828910260693306203880085794955034747476060153997656323523503375955659777681988740544687254199590802537529515579620119333945661254265030658518256358717772703818654480106524239143719389868004689600
'''

欧拉定理

exp：

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from functools import reduce
from Crypto.Util.number import *

n = 29929378538095242599885557965311297229924523708488195903349782032363055913634371143193552305707368798772150932190898234995143081146304332830718576568862215833419088712212229994786373886002933885241338295986566059232256985357837569354103718470254246398122059607732272010616255443856829833332931407591
factors = [1031597280836669, 831763169751037, 1047241102139227, 1121166222643673, 1106502088074143, 724280506692727,
           564473023238051, 722283223420861, 712230248080397, 995107014561889, 755979891579641, 1108754952183367,
           1002598179716267, 627339010540087, 681606630260771, 986358416636413, 771609538687643, 729341978292667,
           585469394406137, 1098486200089483]
phi = 1
for i in factors:
    phi *= i-1
c = 14115545351007949046897492137862741044898077109960419446496565606468622772683580281638816799144770994249828910260693306203880085794955034747476060153997656323523503375955659777681988740544687254199590802537529515579620119333945661254265030658518256358717772703818654480106524239143719389868004689600
e = 231259269673028
p = pow(3, e, phi)
l = pow(3, p, n)
m = l ^ c
print(long_to_bytes(m))

运行得到

最后flag为

1
0xGame{Euler_1s_v3ry|useful!}

签个名吧

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from Crypto.Util.number import *
from hashlib import *
from secret import secretkey, flag

assert flag == '0xGame{' + md5(str(secretkey).encode()).hexdigest() + '}'


class DigitalSignatureAlgorithm:
    def __init__(self):
        self.p = 11165563731567620813280603348108480503936143873639953843877402138097093301295650519258404426227037499368315956021156867415800042556171179986919811355886447
        self.q = 1427665647738374763020227949129429759446792665193
        self.g = 8385242253270806088154521306824584871033482078620830257754618478173828281256533554013845296082505886967783284208873604051466162625518031631615203713726934
        self.k = getRandomRange(1, self.q)

    def sign(self, m, x):
        z = bytes_to_long(sha256(m).digest())
        r = int(pow(self.g, self.k, self.p)) % self.q
        s = (int(inverse(self.k, self.q)) * (z + x * r)) % self.q
        return r, s


DSA = DigitalSignatureAlgorithm()
x = secretkey
y = pow(DSA.g, x, DSA.p)
print(y)

m0 = b'0xGame'
m1 = b'hack_fun'

r0, s0 = DSA.sign(m0, x)
r1, s1 = DSA.sign(m1, x)
print(r0, s0)
print(r1, s1)

'''
629561663141556350240195805457452624173044316397843833361377725186629298877124510669391999570948536274320600603150740845095742614597958058723489543231707
9569108440001628337054549116871993930089020799 1155391566683353144613828381835889947132557976718
9569108440001628337054549116871993930089020799 182166581822791423481695372664923137176789829383
'''

DSA签名

exp：

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from hashlib import *
from Crypto.Util.number import *

s0 = 1155391566683353144613828381835889947132557976718
s1 = 182166581822791423481695372664923137176789829383
q = 1427665647738374763020227949129429759446792665193
m0 = b'0xGame'
m1 = b'hack_fun'
hm0 = bytes_to_long(sha256(m0).digest())
hm1 = bytes_to_long(sha256(m1).digest())
k = (inverse(s1 - s0, q) * (hm1 - hm0)) % q
# print(k)
r0 = 9569108440001628337054549116871993930089020799
x = inverse(r0, q) * (s0 * k - hm0) % q
# print(x)
flag = '0xGame{' + md5(str(x).encode()).hexdigest() + '}'
print(flag)

运行得到

最后flag为

1
0xGame{0d49c454e403b622070f7257682fe8d6}

ECC

下载附件

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from secret import msg
flag = b'0xGame{' + msg + b'}'
p = 112495892893734483388663296402932842095997843753374438421695290988359832460051
x = bytes_to_long(msg[:8])
y = bytes_to_long(msg[8:])
a = 101981543389703054444906888236965100227902100585263327233246492901054535785571
b = 2706186933878057652676309926348143366670031701983557300942511880324524788574
E = EllipticCurve(GF(p),[a,b])
G = E(101981543389703054444906888236965100227902100585263327233246492901054535785573,91039746864447832832895531433088113132756837557011083320841009534578343965536)
m = E(x,y)
n = G.order()
k = randint(1,n)
K = k*G
r1 = randint(1, n)
r2 = randint(1, n)
c1 = m + r1 * K
c2 = r2 * G

print(k)
print(r1)
print(r2)
print(c1.xy())
print(c2.xy())

# 71945889038953341847263519104630318243817670767276069261230241683585545826661
# 17508017898353406319910889374706380553395041177439941992127017651621727142700
# 9635688439246373463146554181223462429254170330456300413235282298036335053171
# (50699670968971868104581239148265328978400022565577671265162163603182863155985, 35650116946501339414509636935589952076371147766891190369628323621304967371478)
# (24844834536235754929295699976588636674139783137334889500986181346650283652602, 103436077552626107087076436692500561168148578742541763620395982301426624422180)

exp：

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from Crypto.Util.number import *
p = 112495892893734483388663296402932842095997843753374438421695290988359832460051
a = 101981543389703054444906888236965100227902100585263327233246492901054535785571
b = 2706186933878057652676309926348143366670031701983557300942511880324524788574
k = 71945889038953341847263519104630318243817670767276069261230241683585545826661
E = EllipticCurve(GF(p),[a,b])
G = E(101981543389703054444906888236965100227902100585263327233246492901054535785573,91039746864447832832895531433088113132756837557011083320841009534578343965536)
r1 = 17508017898353406319910889374706380553395041177439941992127017651621727142700    
r2 = 9635688439246373463146554181223462429254170330456300413235282298036335053171
c1 = E(50699670968971868104581239148265328978400022565577671265162163603182863155985, 35650116946501339414509636935589952076371147766891190369628323621304967371478)
c2 = E(24844834536235754929295699976588636674139783137334889500986181346650283652602, 103436077552626107087076436692500561168148578742541763620395982301426624422180)
n = G.order()
r2m = r2 * c1 - r1 * k * c2
m = r2m * inverse(r2, n)
m = long_to_bytes(int(m.xy()[0]))+long_to_bytes(int(m.xy()[1]))
print(m)

运行得到

最后flag为

1
0xGame{Ecc:have_fun!~~~'}

我也不知道取啥名捏

下载附件

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from Crypto.Util.number import *
from gmpy2 import next_prime
from random import getrandbits
from secret import flag

p = getStrongPrime(1024)
q = next_prime(p ^ ((1 << 1024) - 1) ^ getrandbits(16))
n = p * q
e = 65537

m = bytes_to_long(flag)
assert m < n
c = pow(m, e, n)

print(hex(n))
# 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

print(hex(c))
# 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

exp：

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from gmpy2 import *
from Crypto.Util.number import *

n = 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
p = ((1 << 1024) - 1) ^ ((1 << 20) - 1)
q = 0
for i in range(1022, 20, -1):
    cur = 1 << i
    if (p ^ cur) * (q ^ cur) < n:
        p ^= cur
        q ^= cur
while n % p != 0:
    p = gmpy2.next_prime(p)
q = n // p
e = 65537
c = 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

phi = (p - 1) * (q - 1)
d = inverse(e, phi)
m = pow(c, d, n)
print(long_to_bytes(m))

运行得到

最后flag为

1
0xGame{c3c7bca98ce4dc4cce797d8197597a40}

MTP

下载附件

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from secret import flag


def str_xor(m, k):
    return ''.join([chr(m[i] ^ k[i]) for i in range(len(m))])


m = []
c = []
l = len(flag)
with open('m.txt', 'rb') as f:
    tmp = f.read(l)
    while tmp:
        m.append(tmp)
        c.append(str_xor(tmp, flag))
        tmp = f.read(l)
with open('output.txt', 'w') as f:
    for i in c:
        f.write(i.encode().hex().ljust(2 * l, 'f') + '\n')

m.txt

1
In this meaning, the term cryptosystem is used as shorthand, or as an abbreviation for "cryptographic system". A cryptographic system is any computer system that involves cryptography. Such systems include for instance, a system for secure electronic mail which might include methods for digital signatures, cryptographic hash functions, key management techniques, and so on.

output.txt

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79166715050c08490316520d1c1c5450530d1b11451918
421567021f1c0b1d01004a1001175e5c1a0a5301160819
101934411e0d141b1a1b520d115e131301591207450c13
101925031f000d000f075a0c1b5255130159511717140d
441720130c1513000d53401a0606561151575335450e0f
4908330e0a171a19061a5043060b40081614531d164d1c
5e01670202080b1c1a164143060b4008161453000d0c09
1011291702090d0c1d5350110c024713140b12040d1453
102b3202054508101d07560e06525a1210150610004d1b
5f0a670803160f080010564f5513130f0a0a0711084d1b
5f0a671208060e1b0b53560f1011470e1c171a1745001c
59146716050c18014e1e5a041d0613151d1a1f0101085d
5d1d330902010849081c4143111b541507181f5416041a
5e1933141f0008454e10411a05065c1b0118031c0c0e5d
581934094d030e070d075a0c1b011f5c181c0a54080c13
511f220c080b0f491a16500b1b1b4209160a5f54040319
100b2841020b55ffffffffffffffffffffffffffffffff

Many Time Pad

exp:

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import Crypto.Util.strxor as xo
import libnum, codecs, numpy as np

def isChr(x):
    if ord('a') <= x and x <= ord('z'): return True
    if ord('A') <= x and x <= ord('Z'): return True
    return False


def infer(index, pos):
    if msg[index, pos] != 0:
        return
    msg[index, pos] = ord(' ')
    for x in range(len(c)):
        if x != index:
            msg[x][pos] = xo.strxor(c[x], c[index])[pos] ^ ord(' ')

def know(index, pos, ch):
    msg[index, pos] = ord(ch)
    for x in range(len(c)):
        if x != index:
            msg[x][pos] = xo.strxor(c[x], c[index])[pos] ^ ord(ch)


dat = []

def getSpace():
    for index, x in enumerate(c):
        res = [xo.strxor(x, y) for y in c if x!=y]
        f = lambda pos: len(list(filter(isChr, [s[pos] for s in res])))
        cnt = [f(pos) for pos in range(len(x))]
        for pos in range(len(x)):
            dat.append((f(pos), index, pos))

c = [codecs.decode(x.strip().encode(), 'hex') for x in open('D:\\tmp\\0xGame2022-main\\0xGame2022-main\\Crypto\\week4\\MTP\\output.txt', 'r').readlines()]

msg = np.zeros([len(c), len(c[0])], dtype=int)

getSpace()

dat = sorted(dat)[::-1]
for w, index, pos in dat:
    infer(index, pos)

know(1, 6, 'p')
know(4, 1, 'o')
know(0, 10, 'a')


print('\n'.join([''.join([chr(c) for c in x]) for x in msg]))

key = xo.strxor(c[0], ''.join([chr(c) for c in msg[0]]).encode())
print(key)

运行得到

最后flag为

1
0xGame{ins3cur3|system}
文章作者: yiqing
文章链接: http://yiqing.asia/posts/7777104.html
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