Java Puzzle: Square Root

http://corner.squareup.com/2013/03/puzzle-square-root.html

by crazybob • 13 years ago

50 56 13 years ago

corner.squareup.com

Someone should just modify the StackSort algorithm that was posted yesterday (made up by xkcd) to search for Square Root functions instead and run them.

http://gkoberger.github.com/stacksort/

sumzup• 13 years ago

That won't work. The point here is that you don't have the number available.

mingpan• 13 years ago

Are they asking for a timing attack, then?

uribs• 13 years ago

The only possibilities seem to be a timing attack, exploiting a bug or taking advantage of an implementation that puts the dividend value in the exception when dividing by zero.

I'm not sure anyone will bother writing the timing attack since he apparently gives out no prize.

ISL• 13 years ago

Unless there's something in Java that allows you to manipulate private copies of private variables without access to the stored values.

I'm familiar with Java, but not so familiar that I can state with authority that such a thing is impossible.

powera• 13 years ago

I'm not sure this is interesting. Unless I'm missing something, the question is "find what way of breaking the compartmentalization of the JVM we haven't forbidden in these English-language rules".

craigching4• 13 years ago

Yes, I believe you and cromwellian have hit upon the main point. Or, to be more succinct, "do you know about Java spi."

cromwellian3• 13 years ago

Consider that SecureRandom is really a facade around multiple providers that can plug in varying implementations. :)

GhotiFish2• 13 years ago

ah ha! That might of being too big of a hint, good sir.

somethingnew2• 13 years ago

How about this one? http://xkcd.com/221/

Jeremysr• 13 years ago

Heh, not knowing Java very well, I scoured the BigInteger docs for quirks and loopholes, then gave up and found your comment. I guess "java.security.SecureRandom" sounded too impregnably secure to be worth looking into.

mattvanhorn2• 13 years ago

...and that you can remove all the existing ones and insert your own.

spiralpolitik• 13 years ago

You can't change Providers while running under the SecurityManager he specifies you must use in the rules.

SecurityManager.checkSecurityAccess(java.lang.String) is called if you try and mess with the Providers.

raylu5• 13 years ago

SquareRoot.n is static, so it runs before any code in your main().

cromwellian3• 13 years ago

Java Service Providers (SPI) trigger before main() is run. You can create a SecureRandom() provider, add it to the classpath with SPI, removing other providers.

harryh• 13 years ago

If that's really the answer they are looking for then it's a stupid question.

Trying to write a timing attack sounds much more interesting.

jlebar2• 13 years ago

Use reflection to read n. Reflection lets you bypass |private|.

GhotiFish2• 13 years ago

that should throw an exception with the security manager on. I think. I might of read the docs wrong.

jlebar2• 13 years ago

Ahh, I see.

craigching4• 13 years ago

He specifically says you need to leave the security manager in place and you can't use setAccessbile() which you need to do with the default security manager.

TallboyOne2• 13 years ago

Can someone explain what this is asking? I don't know java

Semaphor2• 13 years ago

There is a really big number you don't know. You should get the square root for it.

TallboyOne2• 13 years ago

So why are people talking about vulnerabilities and 'timing attacks' then? and how are you supposed to get the square root of a number you dont know..

Eduard• 13 years ago

1: Pause debugging session. 2: Look into SquareRoot.n

martinced• 13 years ago

Is this just like String that are actually mutable on most JVM implementations out there where the underlying char[] can be accessed using reflection?

doctorpangloss• 13 years ago

Hint: Many pseudo-random number generators take the square of a seed value to advance to the next sequence.

IvyMike3• 13 years ago

I'm surprised nobody's given the obvious algorithm yet: while(i < BigInt(2).pow(10000)) ++i;

Before anyone complains, this algorithm is correct and does not break any of the rules as far as I can tell. :)

I think the timing attack is probably what he's really looking for.

Edit: as mattvanhorn pointed out, answer() is void, but that's ok... changed to a "constant time" algorithm. :)

mattvanhorn2• 13 years ago

answer() has a void return, although I suppose you might be able to watch System.out to see if it worked.

raylu5• 13 years ago

Nobody said you had to stop after reaching that line ;)

nire• 13 years ago

Yup, just set a new PrintStream(new ByteArrayOutputStream()) in System.setOut() and you're good.

lancefisher• 13 years ago

The BigInteger is really big.

An i7 does about 109 gigaFLOPS, or 109 operations per nanosecond. [1]

Suppose we can do 1 guess per operation. There are 2^10,000 possible roots. [2]

2^10,000 / 109 nanoseconds is 5.804×10^2991 years. [3]

The stars will burn out before you brute force it.

[1] http://en.wikipedia.org/wiki/FLOPS

[2] http://bit.ly/ZIWkkt (parens in the original link)

[3] http://www.wolframalpha.com/input/?i=2%5E10%2C000+%2F+109+na...

IvyMike3• 13 years ago

I must dryly point out that this does not invalidate the correctness of the algorithm.

IvyMike3• 13 years ago

As an optimist, I must point out that if Moore's law holds for the next 10000 doublings we'll have the answer in 20000 years, plus 9 picoseconds.

uvdiv2• 13 years ago

Force a race condition on the variable `root'.

    if (n.divide(root).equals(root)) {

Try to set it to 2^20001 on the first funcall and 0 on the second.

mtpettyp2• 13 years ago

BigInteger is immutable so this won't work

uvdiv2• 13 years ago

You're right! Good catch.

huherto• 13 years ago

I think you can create a new instance of SecureRandom() that provides the same value that we are looking for.

wheaties• 13 years ago

I hate to break it to you but "n" is not final. Hence, you can reassign any BigInteger to it. Why not just set n = 9 and the root = 3...

Immutability is your friend. Use it or lose it.

craigching4• 13 years ago

But n is also private, so you can't reassign it without using setAccessible or changing the security manager, both forbidden by the rules.

tantalor2• 13 years ago

You can't assign anything to a private variable.

coolbrow• 13 years ago

But "n" is private and the rules state the solution must be in a different class. Thus you can't simply reassign it.

wisesascha• 13 years ago

is using the ASM library not a legitimate way or would that violate the rules in some way?

mtpettyp2• 13 years ago

I read "Solve the problem in a single separate .java file which compiles and runs with JDK 6 or 7." to mean that the entire solution has to be in one Java file.

tantalor2• 13 years ago

I'd start by trying to create an evil subclass of BigInteger, as it is not a final class.

raylu5• 13 years ago

I've tried this but failed to create something that was evil enough to pass on .equals but benign enough that it didn't choke on .divide

web0072• 13 years ago

Subclass BigInteger, and override equals() on your subclass to "return true;"?

raylu5• 13 years ago

equals() isn't being called on your class; it's being called on the result of n.divide()

web0072• 13 years ago

I don't know Java, clearly, as I don't even know what to name a file that's going to do the override. Also, as mentioned elsewhere, SecureRandom seems the easier target as it's a pluggable interface for entropy providers.

That said, can't you override the equals() for your subtype? I'm talking about the implementation of BigInteger::equals(MyBigInt x), not MyBigInt::equals(BigInteger x). Or does that need to be done on BigInteger-proper, versus its subclass?

itsdrewmiller• 13 years ago

Not really a Java guy, but could you subclass BigInteger in such a way that when .divide is called and accesses root's representation of the data, that property access reflectively examines the calling expression to find out n's representation of the data, then just square roots that and sets it as its own representation before allowing the expression to evaluate? Or something along those lines, anyway?

mcgin• 13 years ago

Presumably something from the java.lang.instrument package will allow you to solve this

asabil• 13 years ago

Maybe read /proc/self/maps and /proc/self/mem and try to locate the BigInteger value in the JVM heap?

Java Puzzle: Square Root

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