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codeql/python/ql/lib/semmle/python/security/regexp/ExponentialBackTracking.qll

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/**
* This library implements the analysis described in the following two papers:
*
* James Kirrage, Asiri Rathnayake, Hayo Thielecke: Static Analysis for
* Regular Expression Denial-of-Service Attacks. NSS 2013.
* (http://www.cs.bham.ac.uk/~hxt/research/reg-exp-sec.pdf)
* Asiri Rathnayake, Hayo Thielecke: Static Analysis for Regular Expression
* Exponential Runtime via Substructural Logics. 2014.
* (https://www.cs.bham.ac.uk/~hxt/research/redos_full.pdf)
*
* The basic idea is to search for overlapping cycles in the NFA, that is,
* states `q` such that there are two distinct paths from `q` to itself
* that consume the same word `w`.
*
* For any such state `q`, an attack string can be constructed as follows:
* concatenate a prefix `v` that takes the NFA to `q` with `n` copies of
* the word `w` that leads back to `q` along two different paths, followed
* by a suffix `x` that is _not_ accepted in state `q`. A backtracking
* implementation will need to explore at least 2^n different ways of going
* from `q` back to itself while trying to match the `n` copies of `w`
* before finally giving up.
*
* Now in order to identify overlapping cycles, all we have to do is find
* pumpable forks, that is, states `q` that can transition to two different
* states `r1` and `r2` on the same input symbol `c`, such that there are
* paths from both `r1` and `r2` to `q` that consume the same word. The latter
* condition is equivalent to saying that `(q, q)` is reachable from `(r1, r2)`
* in the product NFA.
*
* This is what the library does. It makes a simple attempt to construct a
* prefix `v` leading into `q`, but only to improve the alert message.
* And the library tries to prove the existence of a suffix that ensures
* rejection. This check might fail, which can cause false positives.
*
* Finally, sometimes it depends on the translation whether the NFA generated
* for a regular expression has a pumpable fork or not. We implement one
* particular translation, which may result in false positives or negatives
* relative to some particular JavaScript engine.
*
* More precisely, the library constructs an NFA from a regular expression `r`
* as follows:
*
* * Every sub-term `t` gives rise to an NFA state `Match(t,i)`, representing
* the state of the automaton before attempting to match the `i`th character in `t`.
* * There is one accepting state `Accept(r)`.
* * There is a special `AcceptAnySuffix(r)` state, which accepts any suffix string
* by using an epsilon transition to `Accept(r)` and an any transition to itself.
* * Transitions between states may be labelled with epsilon, or an abstract
* input symbol.
* * Each abstract input symbol represents a set of concrete input characters:
* either a single character, a set of characters represented by a
* character class, or the set of all characters.
* * The product automaton is constructed lazily, starting with pair states
* `(q, q)` where `q` is a fork, and proceeding along an over-approximate
* step relation.
* * The over-approximate step relation allows transitions along pairs of
* abstract input symbols where the symbols have overlap in the characters they accept.
* * Once a trace of pairs of abstract input symbols that leads from a fork
* back to itself has been identified, we attempt to construct a concrete
* string corresponding to it, which may fail.
* * Lastly we ensure that any state reached by repeating `n` copies of `w` has
* a suffix `x` (possible empty) that is most likely __not__ accepted.
*/
private import semmle.python.RegexTreeView::RegexTreeView as TreeView
// ExponentialBackTracking should be used directly from the shared pack, and not from this file.
deprecated private import codeql.regex.nfa.ExponentialBackTracking::Make<TreeView> as Dep
import Dep