Blog

Zeno's Paradox for a Bouncing Ball

2014 Jul 12 07:42 PM MDT | Math⁷ [2014]³ | Estimated 1-min read

If a ball is thrown up to a height $h$, falls to the ground, and retains a certain fraction $a$ of its energy when it bounces, it will stop bouncing after a certain amount of time. This is paradoxical as it will have bounced an infinite number of times when it stops.

Uniformly Distributed Tweets

2014 Mar 21 07:49 PM MDT | Math⁷ Programming¹⁸ [2014]³ | Estimated 1-min read

For my Grammar bot, I added a new feature: GPS coordinates are added to the tweets. This is just for fun and serves no practical purpose.

However, I wanted the tweets to be uniformly distributed over a sphere. Earth’s shape is not a sphere, but the error is under 1%.

$a$ and $b$ are random values uniformly distributed in $[-1,1]$ \(latitude=\theta=\sin^{-1}(u)\)
\(longitude=\phi=\pi v=(180^{\circ}) v\)

Buffalo buffalo ...

2014 Mar 6 04:06 PM MST | English⁵ Grammar⁴ Math⁷ [2014]³ | Estimated 2-min read

Although I have already proven that a repetition of the word 'buffalo' $n$ times is grammatically correct, if $n \geq 2$, a year ago, I am now publishing this finding.

• ‘buffalo’ is a plural noun, allowing the use of zero articles
• ‘buffalo’ is also a verb that means to bully, confuse, deceive, or intimidate

Theorem:

Repeating $n$ times, where $n \geq 2$, any word that can be a noun or verb forms a grammatically valid sentence.

Proof:

Partially Protecting Password Data in Transit

2013 Sep 27 08:39 PM MDT | Security² Web¹³ [2013]¹⁰ | Estimated 2-min read

**HTTP does not encrypt** any traffic. Any of the **internet routers** can see and log your traffic, and your passwords might be compromised if the server does nothing to alleviate this.

On my arcade, my login form requires JavaScript to be more secure, but it is not perfectly secure.

A diagram of the first transmission, unprotected from interception

The **first transmission of the password might be intercepted, which is a vulnerability** of this method.

Python Goto Decorator Improved

2013 Aug 13 05:15 PM MDT | Programming¹⁸ Python⁴ [2013]¹⁰ | Estimated 5-min read

When I found a nice hack to get GOTO statements in Python, I decided to make my own version of it. It has been tested on Python 2.7 but probably also works in Python 3.

To use it, import goto from goto and use the `@goto` decorator:

from goto import goto
@goto
def test():
  goto .end
  return False
  label .end
  return True
print test() # should be True

But first, you’ll need this code:

goto.py

Rewriting the Grammar Bot

2013 Aug 8 12:53 PM MDT | English⁵ Grammar⁴ Programming¹⁸ Python⁴ Web¹³ [2013]¹⁰ | Estimated 3-min read

I have rewritten my Grammar bot. Previously, it had used regular expressions to find errors, which means that it must check every character against the rules. In addition, Python 2.7 doesn't support variable-length lookbehinds, which adds extra regular expression checks for some rules. Also, it cannot provide good quotes if there is an overlap between two matches.

Hacking a Flash Payload Crypter with 1 line of code

2013 Jul 23 11:08 AM MDT | ActionScript² ActionScript-3¹ Assembly² Flash² Hacks⁹ Security² Web¹³ [2013]¹⁰ | Estimated 1-min read

If the flash file puts everything into a binary section and encrypts it, is there any way to decrypt it? If they cut off the header, you won't be able to memory-dump it, but would you give up there? Of course not!

Somewhere, they have the decrypted data so that they can load it. Just compile some code to intercept it, and inject it:

(new FileReference()).save(_loc_2, "dumped.swf");

In RABCDAsm (AS3), it looks like this:

findpropstrict      QName(PackageNamespace("flash.net"), "FileReference")
constructprop       QName(PackageNamespace("flash.net"), "FileReference"), 0
getlocal2
pushstring          "dumped.swf"
callpropvoid        QName(PackageNamespace(""), "save"), 2

So just put that in the code before it is loaded (call to `loadBytes`) and replace `getlocal2` with whatever will put the decrypted data onto the stack. Once the decrypted data is about to be loaded, you can save it to a file.

In AS2, you'd have to create a server script to echo the file back with FileReference, since it only accepts URL downloads. It’s still feasible though, but writing to a SharedObject and extracting from that might be easier.

In retrospection, I realized that I can also write a fake header if I manage to locate the flash data.

Flasm (ActionScript 2) Bytecode Equivalents

2013 Jul 19 06:55 PM MDT | ActionScript² ActionScript-2¹ Assembly² Flash² Programming¹⁸ Web¹³ [2013]¹⁰ | Estimated 2-min read

[Flasm](https://nowrap.de/flasm) allows people to disassemble flash files (.swf) into human-readable bytecode. I have discovered some of the Flash compiler techniques and other interesting things.

ActionScript // Flasm

Number.POSITIVE_INFINITY // POSITIVE_INFINITY or POSITIVE_INFINITYF
Number.NAN // _NAN or _NANF
return; // push UNDEF / return
trace(x) // push x / trace
// operators: push a / push b / [op]
| // bitwiseOr
^ // bitwiseXor
& // bitwiseAnd
<< // shiftLeft
>> // shiftRight
+ // add
- // subtract
* // multiply
/ // divide
% // modulo

What I find the most interesting is how it compiles logical expressions: