What is a quantum computer? In what ways does it differ from a standard computer? Why does any of this matter for Bitcoin?
Fresh participants in the Bitcoin ecosystem inevitably encounter these inquiries and must confront the associated challenges regarding Bitcoin’s vulnerability to what would represent an existential danger if a functional quantum machine were ever built.
The ability to hold bitcoin relies on the core premise that, absent directly leaking a duplicate, nobody apart from the private key holder can sign transactions utilizing coins protected by that key. Quantum computing places that foundational premise in doubt.
Quantum machines are not simply faster regular computers. They operate via an entirely distinct mechanism, making them vastly superior to classical processors when tackling specific computational tasks. Obviously, I will not detail the exact mechanics of quantum hardware within four pages, but I will deliver the essential intuition behind their core divergence from traditional machines.
Let us examine how both hardware varieties process large cryptographic keys.
Classical Computers
Everything saved inside a traditional computer (referred to simply as a computer moving forward) is recorded as strings of ones and zeros. Each bit (a one or zero) is definitively a one or a zero with no uncertainty. When information gets retained, it consists of ones and zeros. When data undergoes manipulation or alteration, it happens bit by bit, sequentially, across each individual one or zero.
That is the operational model of a computer. It processes distinct, unambiguous units of stored data linearly, one sequence following another. It cannot skip ahead or take shortcuts regarding its procedural steps—not counting mathematically more efficient methodologies—and must execute every single stage of a computation consecutively.
When generating a private key on a machine, it captures a randomized value derived from dice rolls, general user actions, hardware entropy, and so on, keeping it in memory as ones and zeros. From there, it multiplies that value against the generator point of an elliptic curve to yield a public key. This procedure utilizes an algorithm that, at its foundational level, provides literal directions on which bits to select, how to alter them, which physical circuits to push them through to achieve that change, and finally returns the modified value back into memory bit by bit.
Additional procedures are required to generate a legitimate address, though they are unnecessary to cover in depth here; they function similarly by offering sequential directions for altering memory bits.
So, what if an individual attempted to utilize a computer to guess another person’s private key?
There exist 2256 potential private keys, totaling 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 distinct possibilities.
A traditional computer would be forced to test every single one of those candidate keys sequentially, or however many it can manage simultaneously, following the exact key generation instructions outlined previously. Attempting to verify more combinations in parallel demands higher processing capacity without offering any means to bypass that resource requirement.
Minimizing your processing power increases the duration required, whereas shortening the duration demands greater computing capability.
This objective is impossible to achieve with a standard computer. On one side, the computational expense exceeds the capacity of every machine on Earth, while on the other, the time required is so immense that every star in the cosmos would extinguish before the verification finished.
Achieving this objective demands alternative methods beyond linear or parallel single-item checks, which is precisely where quantum computing enters the picture.
Quantum Computers
Quantum computers do not operate using discrete states where everything is strictly a one or a zero. The foundational unit of data within a quantum system is the qubit, which is the quantum counterpart to a bit. Unlike ordinary bits, a qubit exists in a superposition state where it acts as both a one and a zero concurrently. It only resolves into a definite state upon being observed.
This serves as a primary building block enabling alternative quantum computation. The second key component is entanglement. Qubits are not held in isolation; the physical atoms representing them that collapse into discrete states upon observation remain entangled together. Consequently, when entangled atoms are observed and settle into a single state, those linked atoms collapse into identical states regardless of their physical distance.
This is where things turn unusual and require a slightly generalized explanation, yet you should still retain an intuitive grasp of why quantum machines differ fundamentally from classical ones. A classical algorithm comprises instructions taking specific bits and modifying them step by step until producing a finished array of new bits. Thus, the algorithm transitions discrete states step by step.
Qubits retain probabilities rather than discrete states prior to observation and collapse. When managing a set of entangled qubits of any magnitude, such as our hypothetical 2256 scenario, every potential outcome features a distinct probability of collapse.
Rather than providing sequential commands for operating on discrete states, quantum algorithms offer instructions on manipulating those entangled qubits to shift the probabilities of different results. Constructive interference enhances the likelihood of a correct result, whereas destructive interference diminishes the probability of incorrect outcomes, distinguishing this from the physical noise that complicates precise quantum operations.
Therefore, while a traditional machine must test private keys individually to match a public key, a quantum device can simply execute the appropriate algorithm a few times to reach the correct solution. It achieves this without checking all possibilities simultaneously by simply shifting the collapse probabilities of a superposition.
This capability explains why a quantum computer could compromise the premises supporting elliptic curve cryptography while a classical machine cannot, highlighting why quantum systems excel exclusively at specific computational problems involving massive search spaces.
Don’t Panic
This core distinction between classical and quantum processing means that if a functional, correctly operating quantum machine is actually built, the underlying assumption protecting every Bitcoin holder’s funds becomes compromised, leaving those assets vulnerable.
Indeed, this represents a severe hazard if such hardware is successfully manufactured and functions correctly, but we are far from helpless. We grasp the challenge, recognize our exposure, and are formulating numerous prospective remedies addressing various aspects of the dilemma.
Breathe and remain calm. The remainder of this issue will guide you through the complete problem.
Originally published at https://bitcoinmagazine.com/print/the-quantum-issue-wtf-is-quantum-computing.
