ReDoS

The most severe type of problem happens with backtracking regular expression matches, where some patterns have a runtime that is exponential in the length of the input string.[9] For strings of ${\displaystyle n}$ characters, the runtime is ${\displaystyle O(2^{n})}$. This happens when a regular expression has three properties:

• the regular expression applies repetition (+, *) to a subexpression;
• the subexpression can match the same input in multiple ways, or the subexpression can match an input string which is a prefix of a longer possible match;
• and after the repeated subexpression, there is an expression that matches something which the subexpression does not match.

The second condition is best explained with two examples:

• in (a|a)+$, repetition is applied to the subexpression a|a, which can match a in two ways on each side of the alternation.
• in (a+)*$, repetition is applied to the subexpression a+, which can match a or aa, etc.

In both of these examples we used $ to match the end of the string, satisfying the third condition, but it is also possible to use another character for this. For example (a|aa)*c has the same problematic structure.

All three of the above regular expressions will exhibit exponential runtime when applied to strings of the form ${\displaystyle a...a!}$. For example, if you try to match them against aaaaaaaaaaaaaaaaaaaaaaaa! on a backtracking expression engine, it will take a significantly long time to complete, and the runtime will approximately double for each extra a before the !.

It is also possible to have backtracking which is polynomial time ${\displaystyle O(n^{x})}$, instead of exponential. This can also cause problems for long enough inputs, though less attention has been paid to this problem as malicious input must be much longer to have a significant effect. An example of such a pattern is "a*b?a*x", when the input is an arbitrarily long sequence of "a"s.

So-called "evil" or vulnerable regexes have been found in online regular expression repositories. Note that it is enough to find a vulnerable subexpression in order to attack the full regex:

1. RegExLib, id=1757 (email validation) - see red part
   ^([a-zA-Z0-9])(([\-.]|[_]+)?([a-zA-Z0-9]+))*(@){1}[a-z0-9]+[.]{1}(([a-z]{2,3})|([a-z]{2,3}[.]{1}[a-z]{2,3}))$
2. OWASP Validation Regex Repository, Java Classname - see red part
   ^(([a-z])+.)+[A-Z]([a-z])+$

These two examples are also susceptible to the input aaaaaaaaaaaaaaaaaaaaaaaa!.

If the regex itself is affected by user input, such as a web service permitting clients to provide a search pattern, then an attacker can inject a malicious regex to consume the server's resources. Therefore, in most cases, regular expression denial of service can be avoided by removing the possibility for the user to execute arbitrary patterns on the server. In this case, web applications and databases are the main vulnerable applications. Alternatively, a malicious page could hang the user's web browser or cause it to use arbitrary amounts of memory.

However, if a vulnerable regex exists on the server-side already, then an attacker may instead be able to provide an input that triggers its worst-case behavior. In this case, e-mail scanners and intrusion detection systems could also be vulnerable. Fortunately, in most cases, the problematic regular expressions can be rewritten as "non-evil" patterns. For example, (.*a)+ can be rewritten to ([^a]*a)+.

In the case of a web application, the programmer may use the same regular expression to validate input on both the client and the server side of the system. An attacker could inspect the client code, looking for evil regular expressions, and send crafted input directly to the web server in order to hang it.[10]