Cryptography relies on certain problems that we assume to be hard for computers to solve. These are the problems that we base encryption schemes on. For example, the factoring problem (restated generically): given two large primes $p$ and $q$, it is hard to find $p$ or $q$ given $N = pq$. Currently, we do not have efficient algorithms for classical computers to solve this problem, which makes it a great candidate for encryption and keeping our information safe from prying eyes. 


That being said quantum computers are changing the game. They enable new algorithms to be developed that can solve the hidden subgroup problem (see Lomont, Chris. (2004). The Hidden Subgroup Problem - Review and Open Problems.). Although they are currently in their infancy, quantum computers can break classical cryptography as we know it. 

There are certain assumptions that are believed to be post-quantum secure. A class of these problems are called lattice problems, which are believed to be hard for even quantum computers (there currently doesn't exist any efficient algorithms to solve these problems). The most well known of these problems is the Learning with Errors Problem [1]:

Given $m$ independent samples $(a_i,b_i) \in \mathbb{Z_q^n} \times \mathbb{Z}_q$ drawn from $A_{s,\chi}$ for a uniformly random $s \in \mathbb{Z}^n_q$ (fixed for all samples), find $s$.


This problem is related to other lattice problems (notably equivalent to SIS) and can be used to create cryptosystems like CRYSTALS Kyber and many others. 


The big question is why are lattice problems post-quantum secure? Meaning why are they difficult for even quantum computers to solve. 

Citations

[1] Chris Peikert, A Decade of Lattice Cryptography, 2016, doi: 10.1561/0400000074.

Lattice Problems

Building a web application requires two (sometimes one) components: a frontend and a backend, and a lot of infra-engineering. But ultimately, creating a full stack application can be outlined in a few steps:


<li/> Get a domain (usually from Namecheap or GoDaddy)
<li/> Choose your hosting platform (Heroku is simple, but AWS is quite often the go to)
<li/> Build your frontend and backend
<li/> Configure it all together


The first step is to get a domain, a lot people use a GitHub domain because it's free, but honestly domains are really cheap. You can find some for very cheap on Namecheap, and in my opinion make your website an order of magnitude better than not having one. 

Once you have a domain, I recommend going to Cloudflare and configuring your DNS records. Depending on where you got your domain, this process could be different. I'm not too familiar with how CDNs work, but I know that this process enables HTTPS on your website, which makes life infinitely better.

Once your domain is setup it's time to choose your hosting platform. Ideally, choosing one that has a lot of documentation, support, and most importantly YouTube content will make your life 10-20x better. Most people oft for Amazon Web Services, and that is the cloud provider I usually suggest. For a personal website the free EC2 instance is more than enough most of the time. AWS security groups also really come in handy down the line if you want to keep certain APIs behind a firewall. Heroku is also a viable option if your content is static (if you don't think a backend is necessary) and is a cheaper alternative.

Once all of the infrastructure is setup it's time to actually do some web development. My currently tech stack is Next.js (React.js) for the frontend and Flask for the backend. What you choose for your frameworks doesn't really matter, hopefully since you can just deploy it in a Docker container; just make sure to choose something that is modern, well supported, and has a lot of documentation. For absolute beginners, I suggest using vanilla HTML. Once you have the hang of Javascript and HTML syntax, a lightweight framework like React.js is pretty handy. To make your life a million times easier I suggest learning Docker and Git. This will make deploying applications to the cloud a lot simpler. 

Side note: For CSS styling I find Tailwind CSS to be really neat tool. Here is a list of really helpful tools for web development that I think is really helpful:

<li/> Postman
<li/> React Dev Tools (Chrome Extension)
<li/> Docker (docker-compose)
<li/> Tailwind CSS
<li/> Cypress
<li/> eslint
<li/> Jest

The backend can sometimes be tricky. The suggestion is to start really really small. Think about the bare minimum features you can add to your website for it to be pleasant enough for someone to look at it. Don't try to add too many things at once, build it up slowly over time. Most of the time you will find that adding a single feature (and making it work) takes up an enormous amount of time and you will be glad not to add too many. I like to use Flask (Python) with a basic PostgreSQL database. I store all my blog posts in the database, this serves as my simple CRM. I find this a lot cleaner than creating a new React.js file everytime I want to write a new blog post. But to each to their own. Some helpful tools for backend engineering with Flask:

<li/> loguru
<li/>SQLAlchemy
<li/> Poetry

Once the application is wrapped up nicely, it's time to deploy the application to the web. Login to the cloud platform you chose and set up the infrastructure. There are a lot of available cloud infra out there so I won't describe them all. A basic AWS setup might be creating a simple EC2 instance and deploying it there. The setup that I use can be found: https://github.com/lipet2k/ec2_setup. AWS automatically sets up the static public IP for you, take note of this address and use it to setup your DNS via Cloudflare.

Once you have configured your public IP with the DNS, your website should be all setup (sometimes the DNS takes a few hours to propagate, if after a few hours it still doesn't work, you know that things are wrong). Congratulations! You have a fully functioning website. To make your website more robust consider creating a VPN server, Jenkins CI/CD pipeline, admin portal etc., but for now this is enough to get you up and running.

How to Over Engineer a Website

It's definitely not easy to build a company. For the last 5 years I've been trying to launch companies full-time and on the side. Here are some lessons I've learned throughout that process.

It's Not All Fun And Games

Startups are glamorized in the media. The movies and TV shows that portray these films often highlight the highs of startup life. The Initial Public Offerings, fund raising parties, the success of creating multi-billion dollar corporations. The truth is very very few startups reach any form of success. Most die before a series A. What the viewers at home don't see are the brutal lonely nights coding in your bedroom, the hundreds of venture capital rejections, customer churn, employee politics, and the myriad of problems along the way. To build a successful business takes years, if not decades. 

In my sophomore year of college at Northeastern, a friend of mine and I decided to create a web development business. We would build WordPress websites for small businesses. We were so excited about starting a company that we created a business bank account, phone service provider, payment provider, etc., to get our company going. What we didn't realize was that the fees started to eat up our profits. Even worse, we began to realize that malicious customers would perform chargebacks on our service, creating problems with our payment provider (we didn't have a high enough credit score back then to get a reputable payment provider), and killing our business. In months, we realized that our business would collapse.

Looking back we made a lot of mistakes that could have been prevented, but we were so wrapped up in the excitement of creating a company that we didn't analyze the basic necessities of starting a business.


Optimize For Customers, Not For Funding

A lot of founders fall into this trap. They optimize for fund raising instead of creating an actual product that people want to use. In a contradictory way they allude themselves into believing that raising money from venture capitalists equals actual profit. I'm not saying that VC doesn't have its merit. Venture capitalists have seen hundreds of different startups and their opinion can be a good indicator of how viable your idea is. That being said, you shouldn't raise VC money if you don't have to (i.e. you need to scale). Personally, I believe that the majority of businesses don't ever require funding to get started. If it requires major capital to get started, maybe it's time to rethink your business plan. The broad expansive missions like space exploration and electric cars aren't for the faint of heart and definitely not a viable business for first time founders. First time founders shouldn't focus on a big broad mission, they should capture a small market first.


Don't be captured by the narratives that are pushed around every few months in Silicon Valley. And most of all you shouldn't build a company to capture a narrative. Shape your company around your own vision, even if it doesn't align with the current narratives of the industry. What I'm not advocating is arrogantly following an idea that clearly doesn't work. Venture is a pretty good thermometer for vetting your ideas. If people are not likely to fund your idea, it doesn't mean that you should give up, but it does mean that you should re-evaluate. What you should care about is what your customers think. If your customers hate your product, that's the end of the story.

Don't Build Billion Dollar Businesses (at least in the beginning)

My opinions here might be really controversial, so I'll give a few examples. When people think modern entrepreneur, they think Elon Musk, Mark Zuckerberg, and Steve Jobs, the most iconic entrepreneurs of our time. But the companies that they're known for Tesla, SpaceX, Microsoft, Apple, aren't their first companies. Before space faring, Elon had already built two successful abiet less well known companies: Zip2 and X.com (now PayPal). Before Tesla and SpaceX, Elon had already built and exited two successful companies for millions of dollars. He would use this money to fund his later ventures.

Even before Mark Zuckerberg created Facebook, he had years of experience building products: music sharing applications, Facemash, etc. . And the iconoclastic story of Jobs and Wozniak's venture into blue boxes is just one of the examples of the pair's salesmanship even before Apple.


The aim of a startup (if it's your first one) shouldn't be to build a unicorn. Very few ever become billion dollar companies, and you may be severely disappointed. Find a niche and determine what the customers really really need and will come back to use.


Take The Jump

After I graduated, I had two options: take a high paying stable job in the middle of nowhere or join an startup. A lot of times people are afraid to take the plunge because they're afraid that it might be the wrong choice and mess up their future. Very few times is that, actually the case. There is a really good video by Y Combinator called What to focus on in your twenties that really resonates with me. Think about what the worst case outcome for each option would be. If the startup doesn't work out, what happens? You have to get a job? Oh no (sarcasm)! At worst you'll have gained valuable experience at a startup, most of the time taking on responsibility you wouldn't have been able to at a larger company. On the other hand what will happen if you take the corporate job? Stable income, you might further your career a bit more. Ultimately, the benefits are marginal compared to joining a startup.


That being said, definitely don't join a startup if you have liabilities (student loans, family, etc.). I'm not saying a startup is the solution to all your problems, but if you can tolerate the risk the upside is unimaginable.

Startups are hard

Competitive programming is a great way to sharpen your skill in data structures and algorithms. Overall, it's a fun and gamified way of improving at coding. At the same time, it's not a skill that can be learned in a day. Here are some things I've learned so far in my competitive programming journey.


Going To The Gym

In more ways than one, competitive programming is like going to the gym. Practicing coding problems requires persistent and repeated effort over a long period of time. At the end of the day, being good at competitive programming boils down to pattern recognition (hot take, maybe this is why LLMs are so good at Codeforces). Doing difficult problems will help you improve at competitive programming. When you take a day off, some of that muscle memory will deteriorate, so it's important to practice consistently and often.

It's More Fun In Teams

Competitive programming is 10x more fun with other people. Perhaps it's just human nature, but finding people to compete with motivates you a lot more to improve and get better. The same is true with youth sports. Think about it, when you join a sport, even if it's individual (cross country, skiing, tennis, etc.), there are always opportunities to meet different people and compete. In competitive programming it's a little different. Your opponents are hidden behind a UI, maybe in a completely different geographic location. This lack of personal interaction greatly restricts motivation to compete. When you can't even see your opponent, are they even real (or just AI)? That's why it's important to find a community. Discord communities, highschool/college teams, or even a few friends will greatly help you in the long run.


Start Immediately

Continuing with the gym metaphor, coding is not really a glamorous activity and it's really to excuse yourself from practicing. This is a bad strategy, if you want to get better. There's no replacement for practicing. The best way to get started is just start looking at easy problems. A good place to look is Codeforces, they have thousands of problems to choose from, with multiple difficulty levels. Doing problems each day will help you gain momentum which is a great motivator to do more problems.

Competitive Programming

Recently, I listened to an episode of the "Security. Cryptography. Whatever." podcast (which you should definitely check out). In that episode, they talked about the inadequate and hilarious security of the Telegram messaging app. That got me digging into different private messaging applications that claim to have end-to-end encryption (e.g. Telegram). Surprisingly, or perhaps unsurprisingly, these applications remain incredibly insecure in most scenarios. For example, while Apple's iMessage claims to be end-to-end encrypted (this means that Apple won't be able to read your messages) if you have iCloud enabled, this immediately becomes moot. Apple's compliance with the EU's Digital Markets Act (and a rumored push for a security backdoor) should be a huge red flag to the world of private messaging. 


Perhaps these security concerns are besides the point. What is interesting is that there are currently no ways to test our cryptographic features on a consumer messaging product. This would be really useful for applied cryptography. I'm thinking about creating an End-to-End Encrypted messaging application so that I can test out different encryption standards and compare their efficiency and feasibility in the wild.

Peter's 2AM Thoughts

Lattice Problems

How to Over Engineer a Website

Startups are hard

Competitive Programming

End to End Encryption