GDOUCTF 2023

由于当时比赛那天参加学校活动比较忙错过了比赛，那就看看题吧。

Absolute_Baby_Encrytpion

题目给了一段密文和js代码：

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+}!q")hiim)#}-nvm)i-$#mvn#0mnbm)im#n+}!qnm8)i-$#mvnoc#0nz<$9inm!>-n1:1-nm8)i-$~c58n!}qhij#0[noic##m8nc8n?!8c}w!n]>&
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let messagetoEncrypt = prompt("Enter a string: ").toLowerCase();
let charArray = messagetoEncrypt.split("");
let encryptedString = "";
let hasInvalidCharacter = false;

for (let i = 0; i < charArray.length; i++) {
    switch (charArray[i]) {
        case 'a':
            encryptedString = encryptedString.concat('!')
            break;
        case 'b':
            encryptedString = encryptedString.concat('1')
            break;
        case 'c':
            encryptedString = encryptedString.concat(')')
            break;
        case 'd':
            encryptedString = encryptedString.concat('v')
            break;
        case 'e':
            encryptedString = encryptedString.concat('m')
            break;
        case 'f':
            encryptedString = encryptedString.concat('+')
            break;
        case 'g':
            encryptedString = encryptedString.concat('q')
            break;
        case 'h':
            encryptedString = encryptedString.concat('0')
            break;
        case 'i':
            encryptedString = encryptedString.concat('c')
            break;
        case 'j':
            encryptedString = encryptedString.concat(']')
            break;
        case 'k':
            encryptedString = encryptedString.concat('(')
            break;
        case 'l':
            encryptedString = encryptedString.concat('}')
            break;
        case 'm':
            encryptedString = encryptedString.concat('[')
            break;
        case 'n':
            encryptedString = encryptedString.concat('8')
            break;
        case 'o':
            encryptedString = encryptedString.concat('5')
            break;
        case 'p':
            encryptedString = encryptedString.concat('$')
            break;
        case 'q':
            encryptedString = encryptedString.concat('*')
            break;
        case 'r':
            encryptedString = encryptedString.concat('i')
            break;
        case 's':
            encryptedString = encryptedString.concat('>')
            break;
        case 't':
            encryptedString = encryptedString.concat('#')
            break;
        case 'u':
            encryptedString = encryptedString.concat('<')
            break;
        case 'v':
            encryptedString = encryptedString.concat('?')
            break;
        case 'w':
            encryptedString = encryptedString.concat('o')
            break;
        case 'x':
            encryptedString = encryptedString.concat('^')
            break;
        case 'y':
            encryptedString = encryptedString.concat('-')
            break;
        case 'z':
            encryptedString = encryptedString.concat('_')
            break;
        case '0':
            encryptedString = encryptedString.concat('h')
            break;
        case '1':
            encryptedString = encryptedString.concat('w')
            break;
        case '2':
            encryptedString = encryptedString.concat('e')
            break;
        case '3':
            encryptedString = encryptedString.concat('9')
            break;
        case '4':
            encryptedString = encryptedString.concat('g')
            break;
        case '5':
            encryptedString = encryptedString.concat('z')
            break;
        case '6':
            encryptedString = encryptedString.concat('d')
            break;
        case '7':
            encryptedString = encryptedString.concat('~')
            break;
        case '8':
            encryptedString = encryptedString.concat('=')
            break;
        case '9':
            encryptedString = encryptedString.concat('x')
            break;
        case '!':
            encryptedString = encryptedString.concat('j')
            break;
        case '@':
            encryptedString = encryptedString.concat(':')
            break;
        case '#':
            encryptedString = encryptedString.concat('4')
            break;
        case '$':
            encryptedString = encryptedString.concat('b')
            break;
        case '%':
            encryptedString = encryptedString.concat('`')
            break;
        case '^':
            encryptedString = encryptedString.concat('l')
            break;
        case '&':
            encryptedString = encryptedString.concat('3')
            break;
        case '*':
            encryptedString = encryptedString.concat('t')
            break;
        case '(':
            encryptedString = encryptedString.concat('6')
            break;
        case ')':
            encryptedString = encryptedString.concat('s')
            break;
        case '_':
            encryptedString = encryptedString.concat('n')
            break;
        case '+':
            encryptedString = encryptedString.concat(';')
            break;

        case '-':
            encryptedString = encryptedString.concat('\'')
            break;
        case '=':
            encryptedString = encryptedString.concat('r')
            break;
        case '`':
            encryptedString = encryptedString.concat('k')
            break;
        case '~':
            encryptedString = encryptedString.concat('p')
            break;
        case '{':
            encryptedString = encryptedString.concat('\"')
            break;
        case '}':
            encryptedString = encryptedString.concat('&')
            break;
        case '[':
            encryptedString = encryptedString.concat('/')
            break;
        case ']':
            encryptedString = encryptedString.concat('\\')
            break;
        case '|':
            encryptedString = encryptedString.concat('2')
            break;
        case ':':
            encryptedString = encryptedString.concat('.')
            break;
        case ';':
            encryptedString = encryptedString.concat('%')
            break;
        case '\"':
            encryptedString = encryptedString.concat('|')
            break;
        case '\'':
            encryptedString = encryptedString.concat(',')
            break;
        case '<':
            encryptedString = encryptedString.concat('@')
            break;
        case '>':
            encryptedString = encryptedString.concat('{')
            break;
        case ',':
            encryptedString = encryptedString.concat('u')
            break;
        case '.':
            encryptedString = encryptedString.concat('7')
            break;
        case '?':
            encryptedString = encryptedString.concat('y')
            break;
        case '/':
            encryptedString = encryptedString.concat('a')
            break;

        default:
            hasInvalidCharacter = true;
    }
}

if (hasInvalidCharacter) {
    encryptedString = "Invalid String!";
} else {
    console.log(`Your encoded string is ${encryptedString}`);
}

简单的单表代换，写个python脚本就能得到flag：

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str='+}!q")hiim)#}-nvm)i-$#mvn#0mnbm)im#n+}!qnm8)i-$#mvnoc#0nz<$9inm!>-n1:1-nm8)i-$~c58n!}qhij#0[noic##m8nc8n?!8c}w!n]>&'
book1='abcdefghijklmnopqrstuvwxyz0123456789!@#$%^&*()_+=`~{}[]|:;\<>,.?/'
book2='!1)vm+q0c](}[85$*i>#<?o^-_hwe9gzd~=xj:4b`13t6sn;rkp"&/\2.%|,@{u7ya'
print(''.join(book1[book2.index(i)]for i in str))

Magic of Encoding

题目给了一大堆base64编码，先用cyberchef解码一下试试：

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flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canflag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}flag{Xd_fake_flag_xD}find_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canflag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}
flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}flag{not_the_correct_flag_lol}find_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}find_me_if_you_canPK.........T.V.........¥¹.}µ.}¥.}å½Õ}..¹.±..ía.}....}.±..}á.õ.±..ía.}....}.±..}á.õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±ô).±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±ô).±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±ô).±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..
.....

可以看到一大群flag，后面还跟着生成了非常多的乱码，而且一眼望过去几乎全是重复句段，只是有的是假flag有的是乱码，在确定了并没有藏flag在这里面之后，我发现了：

1
find_me_if_you_canfind_me_if_you_canflag{Xd_fake_flag_xD}find_me_if_you_canPK.........T.V.........¥¹.}µ.}¥.}å½Õ}..¹.±..ía.}....}.±..}á.õ.±..ía.}....}.±..}á.õ.±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±ô).±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..}±½±ô).±..í¹½Ñ}Ñ¡.}.½ÉÉ..Ñ}.±..

在第一块这里正常句段转到乱码的地方出现了一个PK，这就代表可能藏了压缩包（这不是misc题吗……），通过比较乱码字段和假flag段的base64源码发现其实是一样的，所以题目中所有解码出的文本几乎都为假flag段。我猜测这里这些乱码的出现是因为PK压缩包base64加密的问题导致原来的假flag码加密错位导致出现了乱码，不过它们的base64码是一样的，可以用假flag直接去掉这些码，保留pk压缩包：

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from base64 import *

with open('Magic_Of_Encoding.txt') as f:
    f=f.read()
    list = ["flag{Xd_fake_flag_xD}","find_me_if_you_can","flag{not_the_correct_flag_lol}","\nflag{not_the_correct_flag_lol}\nflag{not_the_correct_flag_lol}\n"]
    base64_flag_list = [b64encode(i.encode()).decode() for i in list]
    for i in base64_flag_list:
        f = f.replace(i,"")
with open('2.txt','wb') as t:
    t.write(b64decode(f))

将得到的二进制文本写入压缩包，解压得到flag。

Math Problem

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#!/usr/bin/env sage
import secret
from Crypto.Util.number import *

p, q = getPrime(512), getPrime(512)
e, n = 0x10001, p * q
c = pow(bytes_to_long(secret.flag), e, n)

a, b = getPrime(512), getPrime(512)
E = EllipticCurve(GF(p), [a, b])
G = E.lift_x(ZZ(getPrime(64)))
print(f"{a = }\n{b = }\ny = {G.xy()[1]}")

'''
e = 65537
n = 79239019133008902130006198964639844798771408211660544649405418249108104979283858140199725213927656792578582828912684320882248828512464244641351915288069266378046829511827542801945752252863425605946379775869602719406340271702260307900825314967696531175183205977973427572862807386846990514994510850414958255877
c = 45457869965165575324534408050513326739799864850578881475341543330291990558135968254698676312246850389922318827771380881195754151389802803398367341521544667542828862543407738361578535730524976113729406101764290984943061582342991118766322793847422471903811686775249409300301726906738475446634950949059180072008
a = 9303981927028382051386918702900550228062240363697933771286553052631411452412621158116514735706670764224584958899184294505751247393129887316131576567242619
b = 9007779281398842447745292673398186664639261529076471011805234554666556577498532370235883716552696783469143334088312327338274844469338982242193952226631913
y = 970090448249525757357772770885678889252473675418473052487452323704761315577270362842929142427322075233537587085124672615901229826477368779145818623466854
'''

G = E.lift_x(ZZ(getPrime(64)))这段代码是为椭圆曲线创建一个点。具体来说，它接受一个x坐标作为输入，返回一个对应的点。这个点的纵坐标y是根据椭圆曲线上的方程计算得出的。

一道数学题，用了ECC算法。

题目把a和b都给了，已知方程参数和生成点y，x位数比较小，尝试使用coppersmith求x：

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from Crypto.Util.number import *
import gmpy2

e = 65537
n = 79239019133008902130006198964639844798771408211660544649405418249108104979283858140199725213927656792578582828912684320882248828512464244641351915288069266378046829511827542801945752252863425605946379775869602719406340271702260307900825314967696531175183205977973427572862807386846990514994510850414958255877
c = 45457869965165575324534408050513326739799864850578881475341543330291990558135968254698676312246850389922318827771380881195754151389802803398367341521544667542828862543407738361578535730524976113729406101764290984943061582342991118766322793847422471903811686775249409300301726906738475446634950949059180072008

a = 9303981927028382051386918702900550228062240363697933771286553052631411452412621158116514735706670764224584958899184294505751247393129887316131576567242619
b = 9007779281398842447745292673398186664639261529076471011805234554666556577498532370235883716552696783469143334088312327338274844469338982242193952226631913
y = 970090448249525757357772770885678889252473675418473052487452323704761315577270362842929142427322075233537587085124672615901229826477368779145818623466854

p.<x>=PolynomialRing(Zmod(n))
f=x^3+a*x+b-y^2
f=f.monic()
x0=f.small_roots(X=2^64,beta=0.4,epsilon=0.01)[0]

这里再详细的回顾一下f.small_roots()这个函数，这行代码的含义是在多项式f中找到一个小于$2^{64}$的根。参数beta表示多项式模的次数系数上限，epsilon表示找到可接受的根的概率，这两个参数都控制了算法的时间复杂度和准确率。由于多项式模问题是一个NP难问题，因此在实际运行中，可能需要多次运行算法才能找到一个合适的解。

NP难问题指的是一类NP问题，这些问题非常困难，目前没有已知的多项式算法能够在多项式时间内解决它们。因此不能保证在多项式时间内求解这些问题，但是可以在多项式时间内验证一个给定的解是否正确。——取自ChatGPT

这里如果不加epsilon参数会求不出来，测试设为0.01能求出小值根。

得到根之后代入回原方程组得到f值，由于是在模n多项式环下为0，f值小于n，和n有公共因子p，得到因式分解：

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from Crypto.Util.number import *
import gmpy2

e = 65537
n = 79239019133008902130006198964639844798771408211660544649405418249108104979283858140199725213927656792578582828912684320882248828512464244641351915288069266378046829511827542801945752252863425605946379775869602719406340271702260307900825314967696531175183205977973427572862807386846990514994510850414958255877
c = 45457869965165575324534408050513326739799864850578881475341543330291990558135968254698676312246850389922318827771380881195754151389802803398367341521544667542828862543407738361578535730524976113729406101764290984943061582342991118766322793847422471903811686775249409300301726906738475446634950949059180072008

x = 9757458594430450711
f = x**3+a*x+b-y**2
p = gmpy2.gcd(f, n)
q = n//p
phi = (p-1)*(q-1)
d = gmpy2.invert(e, phi)
m = pow(c, d, n)
print(long_to_bytes(m))

babylua

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local flag = '' --这里是你要逆推出的flag
local md5 = require("md5")

math.randomseed(os.time())

local function randomStr(len)
    local rankStr = ""
    local randNum = 0
    for i = 1, len do
        randNum = math.random(1, 2)
        if randNum == 1 then
            rankStr = rankStr .. string.char(math.random(65, 90))
        elseif randNum == 2 then
            rankStr = rankStr .. string.char(math.random(97, 122))
        end
    end
    return rankStr
end

local seed = randomStr(4)
local key = md5.sumhexa(md5.sumhexa(seed))
print(key:sub(1,10))

secret = {}

for i = 1, #flag do
    secret[i] = string.byte(flag:sub(i,i)) + string.byte(key:sub(i,i))
end

for i, v in ipairs(secret) do
    io.write(v, ' ')
end

print()

--程序运行输出结果：
--b5e62abe84
--200 161 198 157 173 169 199 150 105 163 193 175 173 194 135 131 135 225
--请你分析代码，逆向推出flag

题目给了一种我没见过的语言，简单认识一下：

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local flag = '' --这里是你要逆推出的flag
local md5 = require("md5")

-- 根据当前系统时间设置随机数生成器的种子
math.randomseed(os.time())

-- 生成指定长度的随机字符串
local function randomStr(len)
    local result = ""
    local randNum = 0
    for i = 1, len do
        -- 随机生成一个数字，1表示大写字母，2表示小写字母
        randNum = math.random(1, 2)
        -- 根据randNum生成对应类型的随机字符
        if randNum == 1 then
            result = result .. string.char(math.random(65, 90)) -- 生成一个大写字母
        elseif randNum == 2 then
            result = result .. string.char(math.random(97, 122)) -- 生成一个小写字母
        end
    end
    return result
end

-- 生成4位的随机字符串种子seed
local seed = randomStr(4)

-- 将seed进行两次MD5加密后得到密钥key（key为32位的16进制字符串）
local key = md5.sumhexa(md5.sumhexa(seed))

-- 输出key的前10位
print(key:sub(1,10))

-- 加密flag
local secret = {}
for i = 1, #flag do
    secret[i] = string.byte(flag:sub(i,i)) + string.byte(key:sub(i,i))
end

-- 输出加密后的每一个字符
for i, v in ipairs(secret) do
    io.write(v, ' ')
end

print()

--程序运行输出结果：
--b5e62abe84
--200 161 198 157 173 169 199 150 105 163 193 175 173 194 135 131 135 225
--请你分析代码，逆向推出flag

题目给了两次md5加密后的前10位，四位的seed可以尝试爆破，用itertools库生成所有随机组合的大写小写字母：

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import string
import itertools
from hashlib import md5

chars = string.ascii_lowercase+string.ascii_uppercase
cs = itertools.product(chars, repeat=4)
for c in cs:
    s=''.join(c)
    h = md5((md5(s.encode()).hexdigest()).encode()).hexdigest()
    if h[:10]=='b5e62abe84':
        print(s,h)
        break

爆破出之后直接按照他给的算法逆回去就得到flag了：

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import string
import itertools
from hashlib import md5

chars = string.ascii_lowercase+string.ascii_uppercase
cs = itertools.product(chars, repeat=4)
for c in cs:
    s=''.join(c)
    h = md5((md5(s.encode()).hexdigest()).encode()).hexdigest()
    if h[:10]=='b5e62abe84':
        print(s,h)
        break

a = [200, 161, 198, 157, 173, 169, 199, 150, 105, 163, 193, 175, 173, 194, 135, 131, 135, 225]
for i in range(len(a)):
    num,b=a[i],ord(h[i])
    print(chr(num-b),end='')

WEEK 1

[EIS 2019]rsa1

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from flag import FLAG
from Crypto.Util.number import *
import gmpy2
import random

while True:
    p = int(gmpy2.next_prime(random.randint(10**399, 10**400-1)))
    q = int(str(p)[200:]+str(p)[:200])
    if gmpy2.is_prime(q):
        break

m = bytes_to_long(FLAG)
n = p*q
e = 65537
c = pow(m,e,n)

with open("enc","wb") as f:
    f.write(str(c))
    f.write("\n")
    f.write(str(n))
'''
c=16396023285324039009558195962852040868243807971027796599580351414803675753933120024077886501736987010658812435904022750269541456641256887079780585729054681025921699044139927086676479128232499416835051090240458236280851063589059069181638802191717911599940897797235038838827322737207584188123709413077535201099325099110746196702421778588988049442604655243604852727791349351291721230577933794627015369213339150586418524473465234375420448340981330049205933291705601563283196409846408465061438001010141891397738066420524119638524908958331406698679544896351376594583883601612086738834989175070317781690217164773657939589691476539613343289431727103692899002758373929815089904574190511978680084831183328681104467553713888762965976896013404518316128288520016934828176674482545660323358594211794461624622116836
n=21173064304574950843737446409192091844410858354407853391518219828585809575546480463980354529412530785625473800210661276075473243912578032636845746866907991400822100939309254988798139819074875464612813385347487571449985243023886473371811269444618192595245380064162413031254981146354667983890607067651694310528489568882179752700069248266341927980053359911075295668342299406306747805925686573419756406095039162847475158920069325898899318222396609393685237607183668014820188522330005608037386873926432131081161531088656666402464062741934007562757339219055643198715643442608910351994872740343566582808831066736088527333762011263273533065540484105964087424030617602336598479611569611018708530024591023015267812545697478378348866840434551477126856261767535209092047810194387033643274333303926423370062572301
'''

看完代码可以发现，p为一个400位随机数，q是p的前200位和后200位互换位置得到的数，和之前做的有道hamburgerRSA比较像，已知：

把pq都分成两个部分a和b，每个都是200位，那么ab乘积也就是个400位的数。

现在，n的前200位是ab的前200位（先不考虑中间区段的进位），末200位为ab后200位（这个不会被进位卡混淆），可以得到ab的乘积，得到乘积之后，减回去稍微计算一下就能得到$a^2+b^2$：

我们先走到这里检查一下：

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c=16396023285324039009558195962852040868243807971027796599580351414803675753933120024077886501736987010658812435904022750269541456641256887079780585729054681025921699044139927086676479128232499416835051090240458236280851063589059069181638802191717911599940897797235038838827322737207584188123709413077535201099325099110746196702421778588988049442604655243604852727791349351291721230577933794627015369213339150586418524473465234375420448340981330049205933291705601563283196409846408465061438001010141891397738066420524119638524908958331406698679544896351376594583883601612086738834989175070317781690217164773657939589691476539613343289431727103692899002758373929815089904574190511978680084831183328681104467553713888762965976896013404518316128288520016934828176674482545660323358594211794461624622116836
n=21173064304574950843737446409192091844410858354407853391518219828585809575546480463980354529412530785625473800210661276075473243912578032636845746866907991400822100939309254988798139819074875464612813385347487571449985243023886473371811269444618192595245380064162413031254981146354667983890607067651694310528489568882179752700069248266341927980053359911075295668342299406306747805925686573419756406095039162847475158920069325898899318222396609393685237607183668014820188522330005608037386873926432131081161531088656666402464062741934007562757339219055643198715643442608910351994872740343566582808831066736088527333762011263273533065540484105964087424030617602336598479611569611018708530024591023015267812545697478378348866840434551477126856261767535209092047810194387033643274333303926423370062572301
e = 65537
N=str(n)
ab=int(N[:200]+N[600:])
a2b2=(n-ab*pow(10,400)-ab)//pow(10,200)

输出发现$a^2+b^2$是负数，这肯定是不对的，问题出在哪里呢，可以看看之前的公式：

我们还有中间四百位没有考虑，$a^2+b^2$的位数是未知的。类比一下，对于一个两位数，$a^2+b^2$最小就是$10^2+10^2=200$，三位；最大有$99^2+99^2=19602$，五位。相应的，$a^2+b^2$的位数应该在399,400,401三个值上，如果出现401位，首位只能为1。

所以出现负数的结果，一定是$a^2+b^2$位数为401导致ab数值错误，稍微修改一下：

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c=16396023285324039009558195962852040868243807971027796599580351414803675753933120024077886501736987010658812435904022750269541456641256887079780585729054681025921699044139927086676479128232499416835051090240458236280851063589059069181638802191717911599940897797235038838827322737207584188123709413077535201099325099110746196702421778588988049442604655243604852727791349351291721230577933794627015369213339150586418524473465234375420448340981330049205933291705601563283196409846408465061438001010141891397738066420524119638524908958331406698679544896351376594583883601612086738834989175070317781690217164773657939589691476539613343289431727103692899002758373929815089904574190511978680084831183328681104467553713888762965976896013404518316128288520016934828176674482545660323358594211794461624622116836
n=21173064304574950843737446409192091844410858354407853391518219828585809575546480463980354529412530785625473800210661276075473243912578032636845746866907991400822100939309254988798139819074875464612813385347487571449985243023886473371811269444618192595245380064162413031254981146354667983890607067651694310528489568882179752700069248266341927980053359911075295668342299406306747805925686573419756406095039162847475158920069325898899318222396609393685237607183668014820188522330005608037386873926432131081161531088656666402464062741934007562757339219055643198715643442608910351994872740343566582808831066736088527333762011263273533065540484105964087424030617602336598479611569611018708530024591023015267812545697478378348866840434551477126856261767535209092047810194387033643274333303926423370062572301
e = 65537
N=str(n)
ab=int(str(int(N[:200])-1)+N[600:])
a2b2=(n-ab*pow(10,400)-ab)//pow(10,200)

现在就对了，已经知道了$ab,a^2+b^2$，用一些中学数学知识就能得到$a+b,a-b$，进而得到$a,b$，最终得到$p,q$，得解：

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from Crypto.Util.number import *
import gmpy2

c=16396023285324039009558195962852040868243807971027796599580351414803675753933120024077886501736987010658812435904022750269541456641256887079780585729054681025921699044139927086676479128232499416835051090240458236280851063589059069181638802191717911599940897797235038838827322737207584188123709413077535201099325099110746196702421778588988049442604655243604852727791349351291721230577933794627015369213339150586418524473465234375420448340981330049205933291705601563283196409846408465061438001010141891397738066420524119638524908958331406698679544896351376594583883601612086738834989175070317781690217164773657939589691476539613343289431727103692899002758373929815089904574190511978680084831183328681104467553713888762965976896013404518316128288520016934828176674482545660323358594211794461624622116836
n=21173064304574950843737446409192091844410858354407853391518219828585809575546480463980354529412530785625473800210661276075473243912578032636845746866907991400822100939309254988798139819074875464612813385347487571449985243023886473371811269444618192595245380064162413031254981146354667983890607067651694310528489568882179752700069248266341927980053359911075295668342299406306747805925686573419756406095039162847475158920069325898899318222396609393685237607183668014820188522330005608037386873926432131081161531088656666402464062741934007562757339219055643198715643442608910351994872740343566582808831066736088527333762011263273533065540484105964087424030617602336598479611569611018708530024591023015267812545697478378348866840434551477126856261767535209092047810194387033643274333303926423370062572301
e = 65537
N=str(n)
ab=int(str(int(N[:200])-1)+N[600:])
a2b2=(n-ab*pow(10,400)-ab)//pow(10,200)
ajiab=gmpy2.iroot(a2b2+2*ab,2)[0]
ajianb=gmpy2.iroot(a2b2-2*ab,2)[0]
a=(ajiab+ajianb)//2
b=(ajiab-ajianb)//2
p=pow(10,200)*a+b
q=pow(10,200)*b+a
phi=(p-1)*(q-1)
d=gmpy2.invert(e,phi)
m=pow(c,d,n)
print(long_to_bytes(m))