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C'est la Z

Errors Are Hard To Find

Programming is amazing. You get the thrill of victory and the agony of defeat. It's a great feeling when you write something and it works - even it it's small and simple. It also feels good to hunt down, discover and eliminate subtle bugs in our code. On the other hand, I'll frequently feel like a bozo when I pour over my code for days only to find a super silly error. Unfortunately, that's the most kind of error. It helps if you can laugh at yourself. It's something I've written about before.

As a teacher it's something I try to convey to my students. When they don't see a bug, it's probably not them. It's like when they read an essay over and over and don't see their mistake because their brain autocorrects.

So, what had me kicking myself this time?

I'm going to be teaching a CS topics course as part of our teacher certification program this summer. I already have a lot of possible topics to choose form:

  • WebDev via Flask
  • 3D Graphics / transformations
  • Ray Tracing
  • Data mining
  • Machine Learning
  • NLP
  • and more

I had never quite grokked Blockchain - specifically its use as a platform so I thought I'd see about that as a topic. I started playing, exploring and building but when I got to signing transactions that led me to add Public Key Encryption as another topic.

Traditional encryption requires a key to be used by both parties. This means that both parties can both encrypt and decrypt so they must trust each other. This leads to some issues:

  1. Both parties have to share the key securely.
  2. All parties with the key can encrypt and decrypt.

On the other hand, public key encryption uses two keys. A public one that everyone has access to is used to encrypt data and a private one known only to the owner. This can be used to decrypt the data. This means I can share my public key with the world and receive secure transmissions that only I can decrypt. It also means that two parties can share secure data with each other without both parties knowing the others private key.

I decided that it would be a good idea to get my head around all of this.

There are a bunch of good resources on the web but the basic idea is that you take two primes - large primes, multiply them together, chant some mystic incantations and come up with a private and a public key. You can then use one key to encrypt a message and the other to decrypt that encrypted message.

For this to work, you want to use large primes but to work through the math and make sure I got it, I started with small numbers - 7 and 13. I went through all the math, everything worked and it made sense.

Now time to write some code.

I wrote up a small program and things seemed to work and then decided to set up a mock student application - something that would encrypt a sentence. If I were writing this "for real" I would figure out some reasonable way to chunk my data for encryption but for this test I figured it would be easy to just take each character from the input string and encrypt it.

First few tests worked. I encrypted and decrypted "ABC." Then I tried the classic "Hello World!" and things went kablooey.

I was getting weird results and couldn't for the life of me figure out why. Every time I did an individual test it seemed to work.

Finally, it clicked - Duh, of course it wasn't working.

When you encrypt or decrypt a number, which in our case is a character, it involves modulo arithmetic. Given a number X you calculate \(X^e\ mod\ n\ \) where e is your key and n is the product of the primes you selected. I chose 7 and 13 as my primes which made my n 91.

OF COURSE IT DIDN"T WORK!!!!! It worked for A, B, and C because they had ascii values of 65, 66, and 67 - all less than 91. Once I added lower case letters all was lost. The characeter 'e' has an ascii code of 101. There's no way I can get some encoded value back to 101 if I'm modding by 91.


From there it was an easy fix - I just had to account for this. I selected larger primes, derived new keys and everything worked.

I felt pretty stupid but on the other hand I got that surge of joy at it finally working.

Now I can confidently add both Public Key Encryption and Blockchain to possible topics for my classes. It was also another reminder that finding bugs is hard. That's something not only important for us to remember but also important that we convince our students of this.

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