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security considerations when using (end-user-defined) JavaScript code inside Java

I am working on a Java project. In it, we want to enable an end-user to define variables which are calculated based on a set of given variables of primitive types or strings. At some point, all given variables are set to specific values, and then the calculations should be carried out. All resulting calculated variables must then be sent to Java.
I am in the process of evaluating ways for the end-user to define his calculations. The (current) idea is to let him write JavaScript and let that code be interpreted/executed inside the Java program. I know of two ways for this to be done: Either use the javax.scripting API or GraalVM/Truffle. In both, we would do it like this:
The given variables are given into the script. In javax.scripting via ScriptEngine.put, in Graal/Truffle via Value.putMember.
The end-user can define variables in the global context (whose names must not collide with the ones coming from Java). How he sets their values is up to him - he can set them directly (to a constant, to one of the given variables, to the sum of some of them ...) or define objects and functions and set the values by calling those.
When the time comes where the given variables have a fixed value, the script is executed.
All variables that were defined in the global context by the script will be sent to Java. In javax.scripting via ScriptEngine.get, in Graal/Truffle via Value.getMember.
NOTE: We would not grant the script access to any Java classes or methods. In javax.scripting via check if the script contains the string Java.type (and disallow such a script), in Graal/Truffle via using the default Context (which has allowAllAccess=false).
The internet is full of hints and tips regarding JavaScript security issues and how to avoid them. On the one hand, I have the feeling that none of them apply here (explanation below). On the other hand, I don't know JavaScript well - I have never used it for anything else than pure, side-effect-free calculations.
So I am looking for some guidance here: What kind of security issues could be present in this scenario?
Why I cannot see any security issues in this scenario:
This is pure JavaScript. It does not even allow creating Blobs (which are part of WebAPI, not JavaScript) which could be used to e.g. create a file on disk. I understand that JavaScript does not contain any functionality to escape its sandbox (like file access, threads, streams...), it is merely able to manipulate the data that is given into its sandbox. See this part of https://262.ecma-international.org/11.0/#sec-overview:
ECMAScript is an object-oriented programming language for performing
computations and manipulating computational objects within a host
environment. ECMAScript as defined here is not intended to be
computationally self-sufficient; indeed, there are no provisions in
this specification for input of external data or output of computed
results. Instead, it is expected that the computational environment of
an ECMAScript program will provide not only the objects and other
facilities described in this specification but also certain
environment-specific objects, whose description and behaviour are
beyond the scope of this specification except to indicate that they
may provide certain properties that can be accessed and certain
functions that can be called from an ECMAScript program.
The sandbox in our scenario only gets some harmless toys (i.e. given variables of primitive types or strings) put into it, and after the child has played with them (the script has run), the resulting buildings (user-defined variables) are taken out of it to preserve them (used inside Java program).

(1) Code running in a virtual machine might be able to escape. Even for well known JS implementations such as V8 this commonly happens. By running untrusted code on your server, whenever such a vulnerability becomes known, you are vulnerable. You should definitely prepare for that, do a risk assessment, e.g. which other data is accessible on the (virtual) machine the engine runs on (other customers data?, secrets?), and additionally harden your infrastructure against that.
(2) Does it halt? What happens if a customer runs while(true); ? Does that crash your server? One can defend against that by killing the execution after a certain timeout (don't try to validate the code, this will never work reliably).
(3) Are the resources used limited (memory)? With a = ""; while(true) a += "memory"; one can easily allocate a lot of memory, with negative impact on other programs. One should make sure that also the memory usage is limited in such a way that the program is killed before resources are exhausted.

Just some thoughts. You're essentially asking if you can trust your sandbox/vitual machine, for that you should either assume that you're using a good one or the only way to be really sure is to read through all its source code yourself. If you choose a trusted and well known sandbox, I'd guess you can just trust it (javascript shouldn't be able to affect file system stuff outside of it).
On the other hand why aren't you just doing all this calculations client side and then sending the result to your backend, it seems like a lot of setup just to be able to run javascript server side. If the argument for this is "not cheating" or something similar, then you can't avoid that even if your code is sent to the server (you have no idea who's sending you that javascript). In my opinion doing this setup just to run it server side doesn't make sense, just run it client side.
If you do need to use it server side then you need to consider if your java is running with root permissions (in which case it will likely also invoke the sandbox with root permissions). On my setup my nodejs is executing under ~/home so even if a worst case happens and someone manages to delete everything the worst they can do is wipe out the home directory. If you're running javascript server side then I'd strongly suggest at the very least never do so under root. It shouldn't be able to do anything outside that sandbox but at least then even in the worst case it can't wipe out your server.
Something else I'd consider (since I have no idea what your sandbox allows or limits) is whether you can request and make API calls with javascript in that sandbox (or anything similar), because if it's running under root and allows that it would give someone root access to your infrastructure (your infrastructure thinking it's your server making requests when it's actually malicious JS code).
You could also make a mistake or start up your VM with an incorrect argument or missing config option and it suddenly allows a vulnerability without you being aware of it, so you'll have to make sure you're setting it up correctly.
Something else is that if you ever store that JS in some database, instead of just executing it, then you have to make sure that it's not made directly available to any other users without checking it otherwise you'd have XSS happening. For example you build an app for "coding tests" and store the result of their test in a database, then you want to show that result to a potential employer, if you just directly display that result to them you'll execute malicious code in their browser.
But I don't really see a reason why you should care about any of this, just run it client side.

How do I create a global variable in Qualtrics Question Text?

How do I create a variable to use in my text using a Qualtrics survey in multiple questions? I am not using any embedded data or making variations. The variable would be for the sole purpose of editing future drafts of my survey more efficiently. For example I want something like:
myvar = 100
Q1. If you have %myvar% and I take away 50 how much is left?
Q2. If you have %myvar% and I give you 70 how much do you get?
...
The more thorough the explanation the better!

You don't need any JavaScript for this. What you want to do is very easy in Qualtrics.
First, at the beginning of your survey flow assign a value to an embedded data field:
myvar = 100
Then pipe the value into your question text like:
Q1. If you have ${e://Field/myvar} and I take away 50 how much is left?

This Qualtrics Community answer might help you:
Add a function to the Look & Feel header that sets and returns the variable. Call the function from the JS in your questions.
This support article implies you can add JavaScript to any question that can set global variables, however it isn't recommended:
As with any implementation of JavaScript, we recommend abstaining from global variable creation as it can collide with existing functionality on the page.
Here's the workflow they describe (the below images are from the article):
Click "Add JavaScript" in the settings dropdown on a question, and enter your (global variable assignment) code in one of these functions:
addOnload() – Executed when the page is loaded.
addOnReady() – Executed when the page is fully displayed.
addOnUnload() – Executed when a page is unloaded (when the page is left).
As an aside, here's a good answer from Brian Rasmussen explaining the problems with global variables:
The problem with global variables is that since every function has access to these, it becomes increasingly hard to figure out which functions actually read and write these variables.
To understand how the application works, you pretty much have to take into account every function which modifies the global state. That can be done, but as the application grows it will get harder to the point of being virtually impossible (or at least a complete waste of time).
If you don't rely on global variables, you can pass state around between different functions as needed. That way you stand a much better chance of understanding what each function does, as you don't need to take the global state into account.

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According to this article
http://www.mediaevent.de/javascript/globale-lokale-variablen.html
Global variables are in JS pretty dangerous.
I'm sorry that it's in German, but I'm gonna point out out the 2 main statements of the article.
The first is already in the 2nd paragraph of the head statement.
It says something like "In JS global var's are dangerous as they can get accessed by other scripts over the name" That's fine so far, as that's mostly the way why I want to use global var's don't I?
But in the article it sounds as this could happen randomly. and that's for sure not the expected behaving, is it?
But what is much more frightening me is the second last sentence. It forecasts that memory leaks will generated if a function that declares a
global variable is called multiple times.
But how could this happen if the name is still the same? how there can be multiple vars declared global with the same name?
Or is this article probably written by some one just "half-knowledge"? Or maybe just addressed to some one who isn't used to the difference between global and local at all?
Or is JS really behaving in this way?
Now a concrete example:
I want some one who logs in to my page to create a Random generated token and submit it by clicking login.
on each other button I want that this token is accessed by a different function and just submit it, so that just for a new login the key will be regenerated.
For that key I was thinking about using a global variable, which gets declared by one function and gets returned by another.
But as I will generate/regenerate the key possibly more then once, would this generate memory leaks? Or is this article I'm referring to probably just dramatizing?
If this is really the way JS is behaving, what would be a good way to make a variable accessable from different functions in my case?

The problem with globals is not memory, and it's not performance.
The problems with globals is entirely different. The problems are that they introduce global state and that scripts are not bound to a namespace.
Let's go through these problems one by one.
Having global state
This is the biggest issue here. Coding necessitates that the dependencies of a module be explicit and that communication between pieces of code is very clear.
When you have global variables which part of the code uses the variable is not nearly as clear and you can't be sure what part of the code needs it and what does not.
Let's say I have a Zoo project and I have a Bathe service that cleans an animal. Instead of passing Bathe around to each animal that needs it I have it on a global namespace and I just call Bathe(myAnimal).
Now I want to restructure my zoo and I want to know which animals need bathing because I want to optimize that. I have no way of knowing that other than going through my whole code. In order to see if my Giraffe needs bathing I have to read the entire code of the Giraffe class. If instead I passed Bathe to the constructor of Giraffe instead of using it or creating it inside giraffe (a concept called dependency injection) I can see that a Giraffe needs bathing just by reading the signature.
Now this can get way worse, what if I have state? If I'm actually changing a global variable in multiple places it becomes extremely hard to track. In a more than a few lines code base this means that you have state changing all around and no clear indication of who is changing it.
This is the main reason you should avoid globals altogether .
Scripts are not bound to a namespace
If I have two scripts on a page and my first script declares a A variable on the global namespace, the second script can access that variable. This is useful because scripts can interact this way but it's very harmful because it means that scripts can override each other's code, and communicate in an unclear way.
This of course is completely mitigated if you use a module loader like browserify or RequireJS which means your whole script only exposes two globals - require and define and then script loading is done through the loader.
This way the way independent pieces of code interact is well defined. That doesn't prevent you from creating variables on the global object, but it helps mitigating the need to do so in a uniform manner.
A note on security
Of course, anything on the client side is compromised, you can't do security or anything like that in client side JavaScript on an insecure browser (that is, you didn't prevent anything external on) because the client can just run arbitrary code on your code and read it.

There are three big problems with global variables:
name collisions
code complexity
garbage collection
Name collision
The problem with having variables in global scope is that you have less control over what else is in that scope. Your code uses a ga_ variable globally and works fine, but when you add a Google Analytics snippet that uses the same variable things unexpectedly fail and it can be quite hard to see why your shopping cart fails 2 out of 3 page loads.
If you can wrap your code in an IIFE to prevent having any variables in global scope, you should do that. Obviously there are cases where you actually want to have your code accessible globally (ex: jQuery library). In those cases, it is best practice to keep all your stuff in a single namespace (jQuery) with a relevant name.
Code complexity
It is usually a good idea to partition your code so that individual pieces have minimal interactions with each other. The more pieces interact the harder it is to make changes and to track down where bugs come from. Obviously a global variable can be accessed anywhere so when you have a problem with some code that accesses a global variable, you have to inspect every usage of that variable which can be quite a big pain. The thing to do to avoid these pains is to keep variables as local as they can be and encapsulate pieces of code so they can't interact with each other except through specific interfaces.
Memory leaks
In JavaScript you have little control over the garbage collection process. All that is guaranteed is that if you can access a variable it will not be garbage collected. This means that if you want something to be garbage collected, then you must make sure you can't access it anymore. While a global i variable which keeps a number won't be a big deal, as #Boluc Papuaccoglu mentioned when your global variable keeps more and more properties over time (an array of XHR requests for example, or array of created DOM objects), the memory consumption turn into a big deal.
All of these situations are worst case scenarios and you probably won't have issues with a small application. These recomendations have most value when you're starting to learn programming because they develop good habits and when you're working on complex applications when they save you time and money wasted on debug or difficult to do improvements.

Regarding memory leaks: Let's say you have a function, and within it you define a var, and use it for some purpose then return from the function. In this case, the memory used by the variable will be freed. However, if you relied on a global variable to do the same thing, then the memory would continue to be allocated long after your function exited. Extending the same scenario, imagine that your function adds properties to this variable with names that depend on the data the function is processing (like Order ID, Customer Name, etc.) Now, each time your function gets called, more and more properties will be appended to this variable and it will grow and grow.

Is it possible to manipulate every Javascript variables, objects while or after running?

It seems there's no way to completely hide source/encrypt something to prevent users from inspecting the logic behind a script.
Aside from viewing the source, then, is it possible to manipulate every variables, objects while a script is running?
It seems it is possible to some degree: by using Chrome's developer tools or Firebug, you can easily edit variables or even invoke functions on the global scope.
Then what about variables, functions inside of an instantiated objects or self invoked anonymous functions? Here is an example:
var varInGlobal = 'On the global scope: easily editable';
function CustomConstructor()
{
this.exposedProperty = 'Once instantiated, can be easily manipulated too.';
this.func1 = function(){return func1InConstructor();}
var var1InConstructor = 'Can be retrived by invoking func1 from an instantiated object';
// Can it be assigned a new value after this is instantiated?
function func1InConstructor()
{
return var1InConstructor;
}
}
var customObject = new CustomConstructor();
After this is ran on a browser:
// CONSOLE WINDOW
varInGlobal = 'A piece of cake!';
customObject.exposedProperty = 'Has new value now!';
customObject.var1InConstructor; // undefined: the variable can't be access this way
customObject.func1(); // This is the correct way
At this stage, is it possible for a user to edit the variable "var1InConstructor" in customObject?
Here's another example:
There is a RPG game built on Javascript. The hero in the game has two stats: strength and agility. the character's final damage is calculated by combining these two stats. It is clear that players can find out this logic by inspecting the source.
Let's assume the entire script is self invoked and stats/calculate functions are inside of objects' constructors so they can't be reached by normally after instantiated. My question is, can the players edit the character's str and agi while the game is running(by using Firebug or whatever) so they can steamroll everything and ruin the game?

The variable var1InConstructor cannot be re-bound under normal ECMAScript rules as it is visible only within the lexical scope. However, as alex (and others) rightly say, the client should not be trusted.
Here are some ways the user can exploit the assumption that the variable is read-only:
Use a JavaScript debugger (e.g. FireBug) and re-assign the variable while stopped at a breakpoint within the applicable scope.
Copy and paste the original source code, but add a setter with access to the variable. The user could even copy the entire program invalidating almost every assumption about execution.
Modify or inject a value at a usage site: an exploitation might be possible without ever actually updating the original variable (e.g. player.power = function () { return "godlike" }).
In the end, with a client-side program, there is no way to absolutely prevent a user from cheating without a centralized authority (read: server) auditing every action - and even then it still might be possible to cheat by reading additional game state, such as enemy positions.
JavaScript, being easy to read, edit, and execute dynamically is even easier to hack/fiddle with than a compiled application. Obfuscation is possible but, if someone wants to cheat, they will.

I don't think this constitutes an answer, it could be seen as anecdotal, but it's a bit long for a comment.
Everything you do when it comes to the integrity of your coding on this issue has to revolve around needing to verify that the data hasn't changed outside of the logic of your game.
My experience with game development (via flash, primarily...but could be compared to javascript) is that you need to think about everything being a handshake where possible. When you are expecting data to come to the server from the client you want to make sure that you have some form of passage of communication that lessens the chance of someone simply sending false data. Store data on the server side as much as possible and use the client side code to call for it when it's needed, and refresh this data store often.
You'll find that HTML games tend to do a lot of abstraction of the logic to the server side, even for menial tasks. Attacking an enemy, picking up an item, these are calls to functions within server-side code, and is why the game animation could carry on in some of these games while the connection times out in the background, causing error messages to pop up and refresh the interface to the server's last known valid state.
Flash was easier in this regard as you didn't have any access to alter any data or corrupt it unless it left the flash environment

Yes, anything ran on the client should be untrusted if you're using the data from it to update a server side state.

As you suggested, you can't hide the logic/client-side code. You can make it "harder" for people to read the source by obfuscating it, but it's very trivial to undo.
Assuming you're making a game from your example, the first rule of networked games is "never trust the client". You need to either run all the game logic on a server, or you need to validate all the input on a server. Never update the game state based on input from a client without validating it first.

You can't hide any variable.
Also, if the user is so good in javascript, he can easily edit your script, without editing the variables value through the console.

JS code that is injected into an HTML using Ajax is pretty darn difficult to get your hands on, but it also has it's limitations. Most notably, you can't use JS includes in injected HTML . . . only inline JS.
I've been working with some of that recently actually and it's a real pain to debug. You can't see it, step into it, or add breakpoints to it in any way that I can figure out . . . in Firebug or Chrome's built-in tool.
But, as others have said . . . I still wouldn't consider it trusted.

How do I safely "eval" user code in a webpage?

I'm working on a webapp to teach programming concepts. Webpages have some text about a programming concept, then let the user type in javascript code into a text editor window to try to answer a programming problem. When the user clicks "submit", I analyse the text they've typed to see if they have solved the problem. For example, I ask them to "write a function named f that adds three to its argument".
Here's what I'm doing to analyse the user's text:
Run JSLint on the text with strict settings, in particular without assuming browser or console functions.
If there are any errors, show the errors and stop.
eval(usertext);
Loop through conditions for passing the assignment, eval(condition). An example condition is "f(1)===4". Conditions come from trusted source.
Show passing/failing conditions.
My questions: is this good enough to prevent security problems? What else can I do to be paranoid? Is there a better way to do what I want?
In case it is relevant my application is on Google App Engine with Python backend, uses JQuery, has individual user accounts.

So from what I can tell if you are eval'ing a user's input only for them, this isn't a security problem. Only if their input is eval'd for other users you have a problem.
Eval'ing a user's input is no worse than them viewing source, looking at HTTP headers, using Firebug to inspect JavaScript objects, etc. They already have access to everything.
That being said if you do need to secure their code, check out Google Caja http://code.google.com/p/google-caja/

This is a trick question. There is no secure way to eval() user's code on your website.

Not clear if the eval() occurs on client or server side. For client side:
I think it's possible to eval safely in an well configured iframe (https://www.html5rocks.com/en/tutorials/security/sandboxed-iframes/)
This should be 100% safe, but needs a couple of libraries and has some limitations (no es6 support): https://github.com/NeilFraser/JS-Interpreter
There are lighter alternatives but not 100% safe like https://github.com/commenthol/safer-eval.
Alternatively, I think something similar can be implemented manually wrapping code in a with statement, overriding this, globals and arguments. Although it will never be 100% safe maybe is viable in your case.

It can't be done. Browsers offer no API to web pages to restrict what sort of code can be executed within a given context.
However, that might not matter. If you don't use any cookies whatsoever on your website, then executing arbitrary Javascript may not be a problem. After all, if there is no concept of authentication, then there's no problem with forging requests. Additionally, if you can confirm that the user meant to execute the script he/she sent, then you should also be protected from attackers, e.g., if you will only run script typed onto the page and never script submitted via GET or POST data, or if you include some kind of unique token with those requests to confirm that the request originated with your website.
Still, the answer to the core question is that it pretty much is that it can't be done, and that user input can never be trusted. Sorry :/

Your biggest issue will always be preventing infinite loops for occurring in user-provided code. You may be able to hide "private" references by running eval in the right context, e.g.:
let userInput = getUserInput();
setTimeout(() => {
let window = null;
let global = null;
let this = null;
// ... set any additional references to `null`
eval(userInput);
}, 0);
And you could wrap the above code in a try/catch to prevent syntax and logic errors from crashing outside of the controlled eval scope, but you will (provably) never be able to detect whether incoming user input defines an infinite loop that will tie up javascript's single thread, rendering its runtime context completely stalled. The only solution to a problem like this is to define your own javascript interpreter, use it to process the user's input, and provide a mechanism to limit the number of steps your javascript interpreter is willing to take. That would be a lot of trouble!