How to loop over array in Z3Py

Question

As part of a reverse engineering exercise, I'm trying to write a Z3 solver to find a username and password that satisfy the program below. This is especially tough because the z3py tutorial that everyone refers to (rise4fun) is down.

#include <iostream>
#include <string>

using namespace std;

int main() {
    string name, pass;
    cout << "Name: ";
    cin >> name;

    cout << "Pass: ";
    cin >> pass;

    int sum = 0;
    for (size_t i = 0; i < name.size(); i++) {
        char c = name[i];
        if (c < 'A') {
            cout << "Lose: char is less than A" << endl;
            return 1;
        }
        if (c > 'Z') {
            sum += c - 32;
        } else {
            sum += c;
        }
    }
    int r1 = 0x5678 ^ sum;

    int r2 = 0;
    for (size_t i = 0; i < pass.size(); i++) {
        char c = pass[i];
        c -= 48;
        r2 *= 10;
        r2 += c;
    }
    r2 ^= 0x1234;

    cout << "r1: " << r1 << endl;
    cout << "r2: " << r2 << endl;
    if (r1 == r2) {
        cout << "Win" << endl;
    } else {
        cout << "Lose: r1 and r2 don't match" << endl;
    }
}

I got that code from the assembly of a binary, and while it may be wrong I want to focus on writing the solver. I'm starting with the first part, just calculating r1, and this is what I have:

from z3 import *

s = Solver()
sum = Int('sum')
name = Array('name', IntSort(), IntSort())
for c in name:
    s.add(c < 65)
    if c > 90:
        sum += c - 32
    else:
        sum += c
r1 = Xor(sum, 0x5678)
print s.check()
print s.model()

All I'm asserting is that there are no letters less than 'A' in the array, so I expect to get back an array of any size that has numbers greater than 65.

Obviously this is completely wrong, mainly because it infinite loops. Also, I'm not sure I'm calculating sum correctly, because I don't know if it's initialized to 0. Could someone help figure out how to get this first loop working?

EDIT: I was able to get a z3 script that is close to the C++ code shown above:

from z3 import *

s = Solver()
sum = 0
name = Array('name', BitVecSort(32), BitVecSort(32))
i = Int('i')

for i in xrange(0, 1):
    s.add(name[i] >= 65)
    s.add(name[i] < 127)
    if name[i] > 90:
        sum += name[i] - 32
    else:
        sum += name[i]
r1 = sum ^ 0x5678

passwd = Array('passwd', BitVecSort(32), BitVecSort(32))
r2 = 0
for i in xrange(0, 5):
    s.add(passwd[i] < 127)
    s.add(passwd[i] >= 48)
    c = passwd[i] - 48
    r2 *= 10
    r2 += c
r2 ^= 0x1234

s.add(r1 == r2)

print s.check()
print s.model()

This code was able to give me a correct username and password. However, I hardcoded the lengths of one for the username and five for the password. How would I change the script so I wouldn't have to hard code the lengths? And how would I generate a different solution each time I run the program?

Answer 1

Arrays in Z3 do not necessarily have any bounds. In this case the index-sort is Int, which means unbounded integers (not machine integers). Consequently, for c in name will run forever because it enumerates name[0], name[1], name[2], ...

It seems that you actually have a bound in the original program (name.size()), so it would suffice to enumerate up to that limit. Otherwise you might need a quantifier, e.g., \forall x of Int sort . name[x] < 65. This comes with all the warnings about quantifiers, of course (see e.g., the Z3 Guide)

Answer 2

Suppose the length is to be determined. Here is what I think you could do:

length = Int('length')
x = Int('x')
s.add(ForAll(x,Implies(And(x>=0,x<length),And(passwd[x] < 127,passwd[x] >=48))))