But the question these experts should be asking themselves is whether such a device could be possible within the 25 years they want to secure the information. A 20-million-qubit quantum computer certainly seems a distant dream today. That’s interesting work that should have important implications for anyone storing information for the future. But Gidney and Ekerå have found various ways to optimize it, significantly reducing the resources needed to run the algorithm. This process is the most computationally expensive operation in Shor’s algorithm. This is the process of finding the remainder when a number is raised to a certain power and then divided by another number. Their method focuses on a more efficient way to perform a mathematical process called modular exponentiation. “, the worst case estimate of how many qubits will be needed to factor 2048 bit RSA integers has dropped nearly two orders of magnitude,” they say. Indeed, they show that such a device would take just eight hours to complete the calculation. Now Gidney and Ekerå have shown how a quantum computer could do the calculation with just 20 million qubits. On that basis, security experts might well have been able to justify the idea that it would be decades before messages with 2048-bit RSA encryption could be broken by a quantum computer. That’s significantly more than the 70 qubits in today’s state-of-the-art quantum computers. In 2015, researchers estimated that a quantum computer would need a billion qubits to do the job reliably. Taking this into account dramatically increases the resources required to factor 2048-bit numbers. And the best way currently to tackle noise is to use error-correcting codes that require significant extra qubits themselves. The reason is that noise becomes a significant problem for large quantum computers. It turns out that quantum factoring is much harder in practice than might otherwise be expected. It’s easy to imagine that at this rate of progress, quantum computers should soon be able to outperform the best classical ones. Then in 2014 they used a similar device to factor 56,153. In 2012, physicists used a four-qubit quantum computer to factor 143.
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Shor showed that a sufficiently powerful quantum computer could do this with ease, a result that sent shock waves through the security industry.Īnd since then, quantum computers have been increasing in power. Indeed, computer scientists consider it practically impossible for a classical computer to factor numbers that are longer than 2048 bits, which is the basis of the most commonly used form of RSA encryption. But it is hard to start with the number 491,597 and work out which two prime numbers must be multiplied to produce it.Īnd it becomes increasingly difficult as the numbers get larger. For example, it is trivial to multiply two numbers together: 593 times 829 is 491,597. Trapdoor functions are based on the process of multiplication, which is easy to perform in one direction but much harder to do in reverse. Shor’s algorithm factors large numbers and is the crucial element in the process for cracking trapdoor-based codes. Back in 1994, the American mathematician Peter Shor discovered a quantum algorithm that outperformed its classical equivalent. The result will make uncomfortable reading for governments, military and security organizations, banks, and anyone else who needs to secure data for 25 years or longer.įirst some background. Consequently, these machines are significantly closer to reality than anyone suspected.