3 ms·

Here's a similar use of Z3 as a keygen: http://www.slideshare.net/extremecoders/keygenning-using-the-z3-smt-solver http://www.slideshare.net/extremecoders/keyg

• xtacy 11y ago
  Interesting! Would love to hear more. What are the classes of firewall properties you can express in Z3?
  • ahelwer 11y ago
    Firewalls are sets of rules which culminate in a decision to accept or block a packet. The rules are easily expressed in predicate logic accepted by Z3. You can do all sorts of neat stuff then; check out https://github.com/Z3Prover/z3/wiki/Publications https://github.com/Z3Prover/z3/wiki/Publications Some general examples: * Does firewall 1 accept a subset of the packets accepted by firewall 2? * Does firewall 1 accept the same set of packets as firewall 2? * Does this firewall accept some arbitrary set of packets? (useful for proving implementation of security rules) * Do any of the firewall rules overlap? * Do any of the firewall rules conflict? Z3 will also provide examples or counter-examples to the above true/false questions. I like to think of Z3 as an Oracle. You give it a bunch of statements describing what you're looking for, and it magically spits out an answer.
    • xtacy 11y ago
      Thanks for the detailed explanation. It's interesting to note that firewall rules are well captured in the predicate logic. Just curious: Have you encountered rules that cannot be cast into predicate logic framework in Z3?
      • ahelwer 11y ago
        I've not. Firewall rules are of the form {predicate} -> {decision}, where {decision} is block/allow and {predicate} defines a set of packets: something like a source address range, source port range, destination address range, destination port range, and protocol. When a packet comes in, the firewall finds all matching predicates (there can be multiple) and makes a block/allow decision. Since checking for packet-predicate matches is done with simple and/or/not formulas, I can't think of a rule which could not be expressed in Z3. Also, this is hardly taxing Z3: it supports reasoning with real numbers and nonlinear constraints.
        • xtacy 11y ago
          Thanks again. I didn't know Z3 could handle formulae with real numbers. I will take a closer look at it. :) On the network firewall rules (at multi-tenant Azure, I presume), what were Z3's runtimes look like?
          • ahelwer 11y ago
            Z3 was able to check equivalence of firewalls with a few hundred rules in a fraction of a second on a standard workstation. I was extremely impressed, especially since the brute-force IPv4 packet search space is 2^112! There's some wizardry going on beneath the hood.