by Eloisa Marchesoni
Today, I will talk about the recent creation of really intelligent machines, able to solve difficult problems, to recreate the creativity and versatility of the human mind, machines not only able to excel in a single activity but to abstract general information and find solutions that are unthinkable for us. I will not talk about blockchain, but about another revolution (less economic and more mathematical), which is all about computing: quantum computers.
Quantum computing is not really new, as we have been talking about it for a couple of decades already, but we are just now witnessing the transition from theory to realization of such technology. Quantum computers were first theorized at the beginning of the 1980s, but only in the last few years, thanks to the commitment of companies like Google and IBM, a strong impulse has been pushing the development of these machines. The quantum computer is able to use quantum particles (imagine them to be like electrons or photons) to process information. The particles act as positive or negative (i., the 0 and the 1 that we are used to see in traditional computer science) alternatively or at the same time, thus generating quantum information bits called “qubits”, which can have value either 0 or 1 or a quantum superposition of 0 and 1. This is because, while in traditional computers the 0 and the 1 of the binary code are encoded either by a closed circuit or by an open one (that is, through the passage or not of electricity), in quantum computers the 0 and the 1 are encoded by the physical states in which the subatomic particles used are found. The properties of the subatomic world are rather bizarre. In fact, a particle can exist in a superposition of states, in such case encoding an overlap of states of 0 and 1. This means that all probabilities are taken into consideration in a short time, allowing projections and analysis to be carried out much more quickly and efficiently than was previously ever possible for current binary computers.
We generate a lot of data every day, hour, minute, second, but until now we have not been able to use enough computing power to get a real advantage from all this information. Quantum computers could help to understand the data that we are generating, and this is possible with the help of Artificial Intelligence. Machine learning, the artificial intelligence applied to machines, is based on a learning technique called deep learning, which can be implemented in the context of a technology based on artificial neural networks, a beautiful biologically-inspired programming paradigm which enables a computer to learn from observational data. Neural networks are inspired by the functioning of our brain, based on interconnections between neurons, but, unlike a biological brain in which any neuron can connect to any other within a certain physical distance, these networks are characterized by layers, connections and directions of propagation of discrete data, in which every node of the network assigns a percentage of probability to the fact that the data supplied as input is correct or not, thus determining the final output as the total of these evaluations. The result given in output is also called probability vector: an educated hypothesis, based on statistic weighting of the data transferred from node to node. What neural networks needs is training, as a lot of inputs must be weighed.
The study of integration between quantum computing and artificial intelligence is in its embryonic stage, as any machine learning algorithms are still theoretical. However, combination between the two opens up really important perspectives, but there are risks as well. The National Security Agency (NSA) raised the question that a quantum computer could possibly learn to break public-key cryptography within just a few decades. In this context, therefore, it is already time to consider how to prevent cyber criminals from setting up any type of fraud, such as identity theft. The contraindications for our privacy must also to be taken into consideration.
Among the quantum algorithms under development and experimentation, there is a certain typology, that of Shor factoring, that could be exploited to destroy the blockchain cryptography, which is based on the ECDSA (Elliptic Curve Digital Signature Algorithm). Such algorithm provides that only the person in charge of a transaction can create a digital signature, keeping his private key, while everyone can verify its authenticity by using the public key. The operations through which the private key is secured could easily be reverse-computed by a quantum computer, thus revealing such secret in just a few minutes. We know that every Bitcoin owner has a public and a private key and that anyone who enters the private key of another user could use that person’s account, so, when the security of the coins can no longer be guaranteed, there is likely to be increased risks.
It is important to remark that quantum computers do not mark the end of cryptography, but only a paradigm shift. Solutions must be sought in the development of quantum-proof cryptography, such as lattice-based cryptography and Fully Homomorphic Encryption (FHE). Lattice-based cryptography uses two-dimensional algebraic constructs known as “lattices”, resistant to quantum computational schemes. A lattice is an infinite grid of points; the computational problem on which the lattice-based technology is based is the “Shortest Vector Problem”, which requires to identify the point in the grid that is closest to a fixed central point in space, called origin. This is an easy problem to solve in a two-dimensional grid, but as the number of dimensions increases, even a quantum computer will no longer able to solve the problem efficiently. Lattice-based cryptography is also the basis for the development of Fully Homomorphic Encryption, which could allow to perform file calculations without having to decrypt them, with an obvious advantage in terms of streamlining processes. Carrying out an operation using encrypted data gives an encrypted result which, once decrypted, is equal to the result obtained by carrying out the same operation on the unencrypted data.
In the meantime, quantum computer-proof algorithms will also be developed, as Quantum Resistant Ledger is trying to do. Almost certainly, therefore, in parallel to the quantum algorithms, new quantum-proof systems will likely be developed, which will then be implemented in the blockchain-based cryptocurrency protocols through so-called forks, in order to restore and guarantee the immutability of transactions again.