Photo: Andrew Harnik/AP
Security in a digital world requires that our communications be protected from digital eavesdroppers. The way we do this is by encrypting our messages using mathematical tools. The most powerful of them use hidden door functions; that is, functions that work easily in one direction (makes encryption easier) and not in the other (makes decryption more difficult).
Trapdoor functions use a property of multiplication, namely its asymmetry. It’s easy to multiply two numbers, say 971 and 1.249, to get 1,212,779, but it’s rather difficult to start with 1,212,779 and figure out which two prime numbers(s) need to be multiplied to produce it. And the task gets exponentially harder as the original numbers get bigger. That’s why until now computer scientists believe it’s impossible. in practice factoring any number longer than 2,048 bits, no matter how powerful, for a conventional computer. Why? Because it would take the machine 300 trillion years to solve the problem, about 22,000 times the age of the universe (to use just one of the popular analogies).
This explains why the 2,048 bit limit is the basis for the most widely used form of asymmetric encryption today; this is the RSA system based on the difficulty of factoring the product of two large prime numbers, numbers that are only divisible by themselves. and 1. This does not mean that RSA encryption is unbreakable (mathematicians never say never) – it just means that it will not be cracked in the near future so that the world can be sure, for example, that it will be good for the world. next 25 years
As a careful reader, you will have already noticed the critical fly in this soothing ointment – the assumption that the computers we will use 25 years from now will be similar to the computers we use today. Since the early 1980s, physicists and computer scientists such as Richard Feynman, Paul Benioff, Yuri Manin (who died last weekend at age 85) and David Deutsch from Britain have been considering a different idea – using some ideas from subatomic physics for design. a new and very different computing engine – a quantum computer. In 1985 Deutsch published a proposal. And recently, companies like Google and IBM have started building them.
Why is this relevant? Mainly because quantum computers are potentially much more powerful than traditional computers based on digital bits – entities with only two possible states, on and off (or 1 and zero). Quantum machines are built around qubits or quantum bits. simultaneous be in two different situations
Experience so far shows that these machines are extremely difficult to build and even harder to scale up.
At this point, you may be anxiously checking the nearest exit. Before you do this, remember that in order to understand subatomic physics, you must first of all purify yourself of everything you think you know about the physical world in which we ordinary mortals live. We may be rude sometimes to people who believe in fairies, but particle physicists fervently believe in the neutrino, a subatomic particle that can pass through Earth nonstop, and we take these scientists seriously.
In 1994, mathematician Peter Shor showed why we might be right to do so. He argued that any entity equipped with a sufficiently powerful quantum computer could potentially crack the most commonly used cryptographic codes, including RSA. The problem was that the dream machine needed a billion qubits to do the job reliably. Other researchers recently calculated that it would need “only” 20 million qubits, but could do the computation in about eight hours.
However, a recent paper by a group of Chinese researchers claiming they can crack 2,048-bit RSA has caused a brief flurry in cryptographic circles. It was quickly refuted by several experts, including US computer scientist Scott Aaronson, who described it as “one of the most actively misleading quantum computing papers I’ve seen in 25 years, and I’ve seen . . . many.”
Where that comes from, there will be more. So it’s time for a reality check. Quantum computers are interesting, but experience so far shows that they are extremely difficult to build and even harder to scale up. There are currently about 50 working machines and most of them are very small in qubits. The largest is one of IBM’s, which has 433 qubits, which means it may take some time to scale up to 20 million qubits. This would lead realists to conclude that RSA encryption is secure for now, and critics say it is like nuclear fusion and artificial general intelligence – always 50 years in the future. This will no doubt prevent Rishi Sunak from declaring his intention to make the UK a “world leader in the quantum space”, but my money is safe in the RSA for the rest of my life and possibly even Sunak’s.
what was i reading
Hari Kunzru’s Exit is a terrific essay. Harper’s A magazine on the ideological foundations of the tech industry.
Worth noting on the Literary Hub platform is Nothing Is Real: Craig Brown on the Slippery Art of Biography.
What ChatGPT Reveals About the Collapse of Political/Institutional Support for the Humanities/Higher Education is a depressing article by Eric Schliesser on the Crooked Timber blog.