Mastering Post-Quantum Cryptography: A Step-by-Step Tutorial
Written by  Daisie Team
Published on 10 min read


  1. Post-Quantum Cryptography Basics
  2. Building a Quantum-Resistant Algorithm
  3. Using Lattice-Based Cryptography
  4. Implementing Multivariate Polynomial Cryptography
  5. Applying Code-Based Cryptography
  6. Exploring Hash-Based Cryptography
  7. Isogeny-Based Cryptography in Practice
  8. Testing and Analyzing Quantum-Resistant Algorithms
  9. Future of Post-Quantum Cryptography
  10. Conclusion and Next Steps

Imagine a world where your digital secrets—passwords, credit card numbers, even your personal messages—are not safe anymore. That's the world we're heading to, and it's all thanks to the quantum computers. But don't worry, there's a solution: post-quantum cryptography. This post-quantum cryptography tutorial will help you understand and master the basics, and lead you step-by-step towards building your own quantum-resistant algorithms. Let's get started!

Post-Quantum Cryptography Basics

First things first, what is post-quantum cryptography? It's a type of cryptography that aims to keep our digital information safe in a world where quantum computers exist. To put it simply, it's like building a lock that not even a quantum computer can pick.

Now, how does it work? Well, it revolves around a concept called quantum resistance. This is the ability of an algorithm to withstand attacks from quantum computers. The idea is to create algorithms that are too complex for quantum computers to crack, thus ensuring data security.

Here are few things you need to know about post-quantum cryptography:

  1. It's not a replacement for classical cryptography. Instead, it's an addition, a new layer of security for the post-quantum world.
  2. It's still a work in progress. Researchers around the world are exploring different techniques to make it more reliable and efficient.
  3. It's not just about theory; it has practical applications too. For example, Google is already testing post-quantum cryptography in its Chrome browser.

Now that you have a basic understanding of what post-quantum cryptography is and why it's important, let's delve deeper into how to build a quantum-resistant algorithm—a key step in mastering the world of post-quantum cryptography.

Building a Quantum-Resistant Algorithm

The foundation of post-quantum cryptography is creating algorithms that even quantum computers find hard to crack. But how do you build such an algorithm? Well, it's all about making the problem too complex or time-consuming for a quantum computer to solve. Here's how:

  1. Pick a hard problem: Start by choosing a problem that's difficult to solve, even for a quantum computer. For instance, the problem of factoring large numbers or finding discrete logarithms in a finite field.
  2. Design the algorithm: Next, design an algorithm based on this hard problem. This algorithm is the heart of your cryptography system, the part that turns plain text into encrypted text and vice versa.
  3. Refine the algorithm: Now, refine your algorithm to make it more efficient and secure. This might involve tweaking the algorithm's parameters, improving its performance, or adding extra layers of security.

But remember, building a quantum-resistant algorithm is not a one-and-done deal. It's an ongoing process. With every new breakthrough in quantum computing, our algorithms need to evolve and adapt. Keep learning, keep refining, and keep testing—that's the key to mastering post-quantum cryptography.

Ready to dive even deeper? Let's move on to our next section, where we'll explore the world of lattice-based cryptography, one of the most promising techniques in the field of post-quantum cryptography.

Using Lattice-Based Cryptography

Lattice-based cryptography is a hot topic in the world of post-quantum cryptography. Why? Because it's based on mathematical problems that even quantum computers find tough to crack! So, how do you use it?

  1. Understand the basics: First, you need to understand what a lattice is. In simple terms, it's a grid of points in space. The problem of finding the closest point in this grid is called the "Closest Vector Problem" or CVP. It's a problem that quantum computers struggle with.
  2. Use a lattice-based cryptographic scheme: Next, you'd use a cryptographic scheme based on this hard problem. There are many schemes out there, but one of the most popular is the "Learning With Errors" or LWE scheme. In a nutshell, it involves adding a small amount of random noise to a linear equation and making the result look random.
  3. Keep your keys safe: Lastly, remember, the safety of your cryptographic system depends on the secrecy of your keys. Always keep them secure and confidential.

And there you have it—a simple, step-by-step guide to using lattice-based cryptography. But remember, this is just the tip of the iceberg. To truly master post-quantum cryptography, you'll need to familiarize yourself with several other techniques as well. So, let's move on to the next one, shall we?

Implementing Multivariate Polynomial Cryptography

Next up is Multivariate Polynomial Cryptography. This might sound like a mouthful, but don't worry—we're going to break it down into bite-sized pieces for you.

  1. Grasp the concept: Multivariate polynomial cryptography is all about equations. More specifically, it's about systems of multivariate polynomial equations. These are equations that have many variables and can be squared, cubed, or raised to any other power. Sounds complex? Well, that's the point! The more complex the equation, the harder it is for a quantum computer to solve.
  2. Choose a scheme: The next step is to select a cryptographic scheme that uses these equations. One such scheme is the "Hidden Polynomial Equations" or HFE scheme. This scheme hides the complex equations in a way that makes them look simple, but they're not—it's a clever trick!
  3. Secure your keys: Just like with lattice-based cryptography, the safety of your keys is paramount in multivariate polynomial cryptography. Protect them with the same rigor you would your most prized possession.

Well done! You've just navigated through the dense forest of multivariate polynomial cryptography. But remember, the journey doesn't end here. There's more to explore in the fascinating world of post-quantum cryptography. So, shall we proceed?

Applying Code-Based Cryptography

Let's take a leap into the world of Code-Based Cryptography. Now, you might be thinking, "What on earth is that?" Well, let me tell you—it's pretty cool stuff.

  1. Understand the basics: Code-Based Cryptography relies on the difficulty of decoding a general linear code. In layman's terms, it's like trying to solve a super tricky puzzle that's designed to keep intruders out. The more pieces the puzzle has, the harder it is to solve. And that's exactly what we want in post-quantum cryptography.
  2. Meet McEliece: One of the most famous Code-Based Cryptography systems is the McEliece cryptosystem. It's been around since the '70s and it's proven to be really tough to crack—even against quantum computers. In this system, the public key is a generator matrix of a linear code. Sounds a bit like secret agent stuff, right?
  3. Secure your keys: As with any cryptographic system, keeping your keys safe is of utmost importance. In Code-Based Cryptography, your keys are the puzzles that keep intruders out.

And there you have it! You've just stepped into the world of Code-Based Cryptography. But don't stop now, there's so much more to learn in this post-quantum cryptography tutorial. Ready to push further?

Exploring Hash-Based Cryptography

Alright, we've tackled code-based cryptography. Now, let's move on and explore the terrain of Hash-Based Cryptography. If you're picturing something to do with breakfast, we're not quite on the same page, but don't worry, I'll explain.

  1. What is it: Hash-Based Cryptography is another type of post-quantum cryptography. It's not about scrambling eggs, but scrambling data. Essentially, you take a chunk of data, put it through a hash function (the scrambler), and out comes a hash (the scrambled eggs). The thing is, you can't unscramble the eggs. That's what makes it secure.
  2. Famous example—Merkle’s tree: The Merkle signature scheme is a classic example of hash-based cryptography. It’s like a tree, but instead of leaves and branches, it has hashes and more hashes. The really cool part? Even quantum computers find it hard to chop this tree down.
  3. Limitations: Hash-based systems do have some limitations. One of them is that the number of signatures is limited. So, while they're great for some things, they might not be the best fit for everything in our post-quantum cryptography tutorial.

And just like that, you've explored Hash-Based Cryptography. I bet you didn't think you'd be scrambling data and climbing cryptographic trees today, did you? But don't pack away your climbing gear just yet—we've still got more ground to cover in this post-quantum cryptography tutorial.

Isogeny-Based Cryptography in Practice

Next up on the post-quantum cryptography tutorial, let's take a look at Isogeny-Based Cryptography. Now, I'm going to be honest with you — this isn't your everyday, run-of-the-mill type of cryptography. You might need to give your brain a bit of a stretch, but trust me, it's worth it.

  1. What is it: Isogeny-Based Cryptography relies on the complex mathematics of elliptic curves. Picture a smooth curve, like a rubber band stretched into an oval shape. Now, imagine you can transform this curve into another one, but in a way that's really hard to reverse. That's basically what's happening here.
  2. Well-known example—SIDH: Supersingular Isogeny Diffie-Hellman (SIDH) is a popular isogeny-based cryptographic system. It’s like a safe-deposit box that only you and a trusted friend can open, but with a twist—instead of a key, you're using these transformed curves.
  3. Limitations: One of the limitations of isogeny-based cryptography is that it involves some pretty heavy-duty math. So, while it's a powerful tool in our post-quantum cryptography toolkit, it might not be the first one you reach for.

So, there you have it—the basics of Isogeny-Based Cryptography. Remember, even if it feels like you're twisting your brain into a pretzel, that's just part of the journey. You're not just learning new concepts, you're reshaping the way you think about cryptography in a post-quantum world. And that's pretty impressive, don't you think?

Testing and Analyzing Quantum-Resistant Algorithms

Now that you've had a taste of different types of post-quantum cryptography strategies, let's move on to the next step in our tutorial: testing and analyzing quantum-resistant algorithms. This is a crucial stage in the process, as it ensures the security of the algorithms. Let's break it down into three main points:

  1. Testing methodologies: Testing a quantum-resistant algorithm is like putting it through a rigorous boot camp. You need to verify if the algorithm can withstand quantum attacks. Some of these methods include timing attacks, where you attempt to crack the code by measuring how long computations take, or power analysis attacks, where you measure the power consumption during the computation.
  2. Performance Analysis: You also need to evaluate how well your algorithm performs. This involves measuring the algorithm's speed, the size of the keys it uses, and the size of the messages it can encrypt. Think of it as a physical exam for your algorithm, checking its vital signs to make sure it's in top shape.
  3. Choosing the right tools: Fortunately, there are tools available to help you with these tests, such as the Cryptographic Algorithm Validation Program (CAVP) and the Cryptographic Module Validation Program (CMVP). These tools can be a great help in your quest to master post-quantum cryptography.

This might seem like an overwhelming task, but remember, Rome wasn't built in a day. Testing and analyzing quantum-resistant algorithms is a complex process, but it's an essential part of mastering post-quantum cryptography. So take a deep breath, roll up your sleeves, and let's get testing!

Future of Post-Quantum Cryptography

With our eye on the future, let's talk about where post-quantum cryptography is heading. As we continue to make strides in quantum computing, our understanding and application of post-quantum cryptography will evolve. So, what might the future landscape look like?

  1. Standardization: The National Institute of Standards and Technology (NIST) is currently working on standardizing post-quantum cryptography. This means that, one day, there could be a universally accepted set of guidelines for how it should be implemented and used.
  2. Increased Security: As quantum computing continues to advance, so too will our ability to defend against potential threats. It's like a never-ending game of chess, with moves and counter-moves happening in real time. The future will likely see even more robust, secure algorithms that can resist quantum attacks.
  3. Wider Adoption: As more organizations realize the potential impact of quantum computing on their security, they'll start to implement post-quantum cryptography. This could lead to widespread adoption across various industries, from finance to healthcare.

One thing's for sure, the future of post-quantum cryptography is exciting. As we venture into a new era of quantum computing, post-quantum cryptography will play a vital role in keeping our information secure. So, get ready to be a part of that exciting journey!

Conclusion and Next Steps

Now you're up to speed with the basics of post-quantum cryptography, and you've got a glimpse into its future. But, we're just scratching the surface here. The world of post-quantum cryptography is vast and ever-evolving. So, what's your next move in mastering this fascinating field?

  1. Continue Learning: This post-quantum cryptography tutorial is a great starting point, but there's so much more to learn. Keep reading, asking questions, and diving deeper into the subject. Remember, knowledge is power!
  2. Practice, Practice, Practice: There's no better way to understand post-quantum cryptography than by getting your hands dirty. Try implementing some of the algorithms we've discussed in this tutorial. It's okay if you don't get it right the first time. Mistakes are just stepping stones to success.
  3. Stay Updated: The field of post-quantum cryptography is advancing rapidly. Staying updated with the latest research and developments is key to staying ahead of the curve. So, make it a habit to read about the latest breakthroughs and trends in this field.

In summary, post-quantum cryptography isn't just a passing trend. It's a critical piece of our digital future. With the potential to secure our data against quantum-powered threats, it's a topic that deserves our attention. So, here's to your journey in mastering post-quantum cryptography. It's a thrilling ride, and you're in the driver's seat!

If you're looking to expand your knowledge on cryptography and its applications in the digital world, check out the workshop 'Crypto For Creators, Part 1: The Backbone Of The Digital Economy' by Tom Glendinning. This workshop will provide you with a strong foundation in cryptography and help you understand its importance in the digital economy.