Internet Security and Quantum Computing
In 1994 a young mathematician named Peter Shor developed an algorithm that would forever connect him with the concept of quantum computing. At the time, Shor’s algorithm described a method by which a theoretical device could factor large numbers quickly, the basis of modern encryption.
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The algorithm described a way in which the factorization of the product of two primes could be calculated in polynomial time.
RSA encryption forms the basis of internet security. When multiplying two prime numbers together one creates an extremely computationally intensive problem that is easily solved by giving one of the factors of the number.
Classical computers would crack this code by using their massive computational power to try every single possible combination until the correct factors are found. Although theoretically possible, the amount of time that this would take makes breaking encryption with a classical machine is unfeasible.
It is clear that a quantum computer with enough logical qubits could crack RSA encryption with ease. The question remains, when will quantum computers be sufficiently advanced that this threat to security becomes serious? Based on the historical rate of development, the answer to this question has been decades.
However, recent developments at Google suggest that that amount of time may have been overestimated by several orders of magnitude. Consequently, machines of this power are significantly closer than had been anticipated, sending a chill down the spine of any organization that has long term plans to secure data.
In 2012 scientists used a four qubit computer to factor the number 143. Two years later in 2014 they used a similar device to factor 56,153. With this rate of advancement one could expect all data to be in danger but it’s not quite so easy.
As the numbers get larger, quantum factoring becomes significantly more difficult. The current solution to this is to use error correction codes which require a significant amount of additional qubits. It has been estimated that to break 2048 bit number a quantum computer would require a billion qubits. This is significantly greater than the current computers can offer.
However, recent work by researcher Craig Gidney and Martin Ekera has demonstrated that a twenty million qubit computer would be sufficient to factor such a large number representing an improvement of almost two orders of magnitude.
Their method focuses on using a more efficient mathematical technique that is a the basis of Shor’s algorithm called modular exponentiation.
At this moment in history there is little to be feared by the average person. But governments present and future will have more at stake. The great superpowers have taken an interest in quantum computation because they realize that we have moved into a “winner take all” world.
It is possible that those who win the race for “quantum supremacy” will win the future.