Quantum Computing and Blockchain

In this series of articles starting here, I want to share some thoughts and research regarding what may mean the construction and massification of a quantum computer for current cryptography and in particular, for the world of Blockchain and cryptocurrencies.

The implications are varied and theories abound about what can happen in a scenario where the use of a quantum computer is widespread.

It has been speculated that the current cryptographic protocols will be violated since the algorithmic and computing capacities of such computers are, in theory, far superior to any current computer, even the supercomputers there exist now.

Later, we will go deeper into detail and rigor over what algorithmic capacity means.

Another side of this problem is in cryptocurrencies.

We know that the security of cryptocurrencies is not only in their consensus method, where block data is unalterable thanks to the distribution of data. But when it comes to user accounts, the cryptographic keys that allow you to access your accounts and authorize transactions, come from very specific cryptographic protocols.

You should know that the generation of the cryptographic keys of the main cryptocurrencies, such as Bitcoin or Ethereum, among others are based on the cryptography of elliptic curves.

Returning to the point: elliptic curves. What are they?

An elliptical curve is something like this:

But how are these curves used in cryptography? Well, first of all, the curves we use in cryptography are not exactly like that.

These curves are actually the set of points that satisfies a certain equation.

The coefficients of this equation “live” in another mathematical structure that is not the Real numbers. They are part of a finite field we call 𝔽q, where q is a prime number.

Thus, an elliptical curve of this type looks like:

Public key cryptography is based on the computational complexity of a robust mathematical problem.

For example, if we have two prime numbers, whose product is a large number, then given the product it is computationally hard to find the two numbers that generated it.

In the cryptography of elliptic curves, a similar problem is used, called the Discrete Logarithm Problem (DLP).

Given two numbers, calculating the exponential can be relatively simple for a regular computer. But calculating the inverse operation, that is, the logarithm is much more complicated to solve for a computer.

But there is a quantum algorithm, called Shor’s algorithm, that has the ability to solve the DLP.

In practical terms, if an efficient quantum computer is built, some malicious entities could take your Bitcoin address, for example, and in a relatively short time solve the discrete logarithm problem to get your private keys and steal your funds!

Fortunately, this is still not the case. Nor is it as easy as the previous paragraph states, because the cryptocurrency addresses go through a coding and hashing process that also add certain layers of additional security.

But the latent danger is there.

In concussion. I think it is relevant to investigate, define, and test cryptographic methods that are resistant to a quantum computer.

We do not need the quantum computer to exist to try other alternatives, there are current investigations and published papers in this regard, with protocols that can be used in current computers and would be resistant to quantum computers.

In the next article, we will explore these alternatives called post-quantics.

Thanks for reading.

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