The biggest danger to Blockchain networks from quantum computing is its ability to break traditional encryption ^{3}.
Google sent shockwaves around the internet when it was claimed, had built a quantum computer able to solve formerly impossible mathematical calculations–with some fearing crypto industry could be at risk^{7}. Google states that its experiment is the first experimental challenge against the extended Church-Turing thesis — also known as computability thesis — which claims that traditional computers can effectively carry out any “reasonable” model of computation
What is Quantum Computing?
Quantum computing is the area of study focused on developing computer technology based on the principles of quantum theory. The quantum computer, following the laws of quantum physics, would gain enormous processing power through the ability to be in multiple states, and to perform tasks using all possible permutations simultaneously ^{5}.
A Comparison of Classical and Quantum Computing
Classical computing relies, at its ultimate level, on principles expressed by Boolean algebra. Data must be processed in an exclusive binary state at any point in time or bits. While the time that each transistor or capacitor need be either in 0 or 1 before switching states is now measurable in billionths of a second, there is still a limit as to how quickly these devices can be made to switch state. As we progress to smaller and faster circuits, we begin to reach the physical limits of materials and the threshold for classical laws of physics to apply. Beyond this, the quantum world takes over. In a quantum computer, a number of elemental particles such as electrons or photons can be used with either their charge or polarization acting as a representation of 0 and/or 1. Each of these particles is known as a quantum bit, or qubit, the nature and behavior of these particles form the basis of quantum computing ^{5}.
Quantum Superposition and Entanglement
The two most relevant aspects of quantum physics are the principles of superposition and entanglement.
Superposition: Think of a qubit as an electron in a magnetic field. The electron’s spin may be either in alignment with the field, which is known as a spin-up state, or opposite to the field, which is known as a spin-down state. According to quantum law, the particle enters a superposition of states, in which it behaves as if it were in both states simultaneously. Each qubit utilized could take a superposition of both 0 and 1.
Entanglement: Particles that have interacted at some point retain a type of connection and can be entangled with each other in pairs, in a process known as correlation. Knowing the spin state of one entangled particle – up or down – allows one to know that the spin of its mate is in the opposite direction. Quantum entanglement allows qubits that are separated by incredible distances to interact with each other instantaneously (not limited to the speed of light). No matter how great the distance between the correlated particles, they will remain entangled as long as they are isolated. Taken together, quantum superposition and entanglement create an enormously enhanced computing power. Where a 2-bit register in an ordinary computer can store only one of four binary configurations (00, 01, 10, or 11) at any given time, a 2-qubit register in a quantum computer can store all four numbers simultaneously, because each qubit represents two values. If more qubits are added, the increased capacity is expanded exponentially ^{5}.
Difficulties with Quantum Computers
- Interference – During the computation phase of a quantum calculation, the slightest disturbance in a quantum system (say a stray photon or wave of EM radiation) causes the quantum computation to collapse, a process known as de-coherence. A quantum computer must be totally isolated from all external interference during the computation phase.
- Error correction – Given the nature of quantum computing, error correction is ultra-critical – even a single error in a calculation can cause the validity of the entire computation to collapse.
- Output observance – Closely related to the above two, retrieving output data after a quantum calculation is complete risks corrupting the data.
What is Quantum Supremacy?
According to the Financial Times, Google claims to have successfully built the world’s most powerful quantum computer ^{7}. What that means, according to Google’s researchers, is that calculations that normally take more than 10,000 years to perform, its computer was able to do in about 200 seconds, and potentially mean Blockchain, and the encryption that underpins it, could be broken.
Asymmetric cryptography used in crypto relies on keypairs, namely a private and public key. Public keys can be calculated from their private counterpart, but not the other way around. This is due to the impossibility of certain mathematical problems. Quantum computers are more efficient in accomplishing this by magnitudes, and if the calculation is done the other way then the whole scheme breaks ^{3}.
It would appear Google is still some way away from building a quantum computer that could be a threat to Blockchain cryptography or other encryption.
“Google’s supercomputer currently has 53 qubits,” said Dragos Ilie, a quantum computing and encryption researcher at Imperial College London.
“In order to have any effect on bitcoin or most other financial systems it would take at least about 1500 qubits and the system must allow for the entanglement of all of them,” Ilie said.
Meanwhile, scaling quantum computers is “a huge challenge,” according to Ilie ^{1}.
Blockchain networks including Bitcoin’s architecture relies on two algorithms: Elliptic Curve Digital Signature Algorithm (ECDSA) for digital signatures and SHA-256 as a hash function. A quantum computer could use Shor’s algorithm [8] to get your private from your public key, but the most optimistic scientific estimates say that even if this were possible, it won’t happen during this decade.
“A 160-bit elliptic curve cryptographic key could be broken on a quantum computer using around 1000 qubits while factoring the security-wise equivalent 1024-bit RSA modulus would require about 1500 to 2000 qubits”. By comparison, Google’s measly 53 qubits are still no match for this kind of cryptography. According to research paper on the matter published by Cornell University.
But that isn’t to say that there’s no cause for alarm. While the native encryption algorithms used by Blockchain’s applications are safe for now, the fact is that the rate of advancements in quantum technology is increasing, and that could, in time, pose a threat. “We expect their computational power will continue to grow at a double exponential rate” Google researchers.
Quantum cryptography?
Quantum cryptography uses physics to develop a cryptosystem completely secure against being compromised without knowledge of the sender or the receiver of the messages. The word quantum itself refers to the most fundamental behavior of the smallest particles of matter and energy.
Quantum cryptography is different from traditional cryptographic systems in that it relies more on physics, rather than mathematics, as a key aspect of its security model.
Essentially, quantum cryptography is based on the usage of individual particles/waves of light (photon) and their intrinsic quantum properties to develop an unbreakable cryptosystem (because it is impossible to measure the quantum state of any system without disturbing that system.)
Quantum cryptography uses photons to transmit a key. Once the key is transmitted, coding and encoding using the normal secret-key method can take place. But how does a photon become a key? How do you attach information to a photon’s spin?
This is where binary code comes into play. Each type of a photon’s spin represents one piece of information – usually a 1 or a 0, for binary code. This code uses strings of 1s and 0s to create a coherent message. For example, 11100100110 could correspond with h-e-l-l-o. So a binary code can be assigned to each photon – for example, a photon that has a vertical spin ( | ) can be assigned a 1.
“If you build it correctly, no hacker can hack the system. The question is what it means to build it correctly” said physicist Renato Renner from the Institute of Theoretical Physics in Zurich.
Regular, non-quantum encryption can work in a variety of ways but generally a message is scrambled and can only be unscrambled using a secret key. The trick is to make sure that whomever you’re trying to hide your communication from doesn’t get their hands on your secret key. Cracking the private key in a modern crypto system would generally require figuring out the factors of a number that is the product of two insanely huge prime numbers.
The numbers are chosen to be so large that, with the given processing power of computers, it would take longer than the lifetime of the universe for an algorithm to factor their product.
Encryption techniques have their vulnerabilities. Certain products – called weak keys – happen to be easier to factor than others. Also, Moore’s Law continually ups the processing power of our computers. Even more importantly, mathematicians are constantly developing new algorithms that allow for easier factorization.
Quantum cryptography avoids all these issues. Here, the key is encrypted into a series of photons that get passed between two parties trying to share secret information. The Heisenberg Uncertainty Principle dictates that an adversary can’t look at these photons without changing or destroying them.
“In this case, it doesn’t matter what technology the adversary has, they’ll never be able to break the laws of physics,” said physicist Richard Hughes of Los Alamos National Laboratory in New Mexico, who works on quantum cryptography ^{6}.
References:
[2] https://decrypt.co/9642/what-google-quantum-computer-means-for-bitcoin/
[3] https://www.coindesk.com/how-should-crypto-prepare-for-googles-quantum-supremacy?
[4] https://www.ccn.com/google-quantum-bitcoin/
[5] https://www.linkedin.com/pulse/20140503185010-246665791-quantum-computing/
[6] https://www.linkedin.com/pulse/20140608053056-246665791-understanding-quantum-cryptography/
[7] https://ai.googleblog.com/2019/10/quantum-supremacy-using-programmable.html
[8] https://qudev.phys.ethz.ch/static/content/QSIT15/Shors%20Algorithm.pdf
Ahmed Banafa
Faculty | Author | Speaker | IoT Expert
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