Random Numbers: does God play dice?

By Cameron Scott

You may be surprised to hear of the dependence that modern human society has built around random numbers. From the cryptographic keys that keep our emails safe to the weather forecasts that inform us if it would be wise to bring a waterproof jacket, random numbers lie behind the scenes of much that we do. To expound upon cryptography as an illustrative example, encryption relies on the generation of keys which, to greatly simplify things, are nothing more than random numbers with loads of digits. Complicated mathematical operations must be carried out on these random numbers to unlock data; without knowledge of what the operation is, this can take an extremely long time. As such, our confidential data remains safe from eavesdroppers with nefarious motives. But suppose that these random keys were not so random after all, what if someone knew how the numbers were generated? It is not unreasonable to then assume that the process could be reverse engineered and the security that we value so highly would now be compromised.

The methods just described for producing encryption keys are known as pseudo random number generators (RNGs) with the prefix ‘pseudo’ indicating that although the process seems to be successful at producing random outputs, a glance under the surface of the code reveals deterministic computer algorithms which can, in principle, be understood to predict which random numbers will be generated. To counteract this vulnerability, security researchers and computer scientists construct ever more complicated algorithms requiring ever more expensive computer systems to operate on. The security arms race has begun.

Instead of this pattern of ballooning complexity, scientists have taken note of certain physical processes which are said to be truly random. There is no algorithm behind the scenes generating outputs and so no vulnerability to be exploited. This true randomness comes about from physical phenomena that are dictated by quantum mechanics.

Consider a process that generates one of two outputs. The typical example would be that of a coin flip. The outcome would be either heads or tails and for a fair coin, each outcome should occur with equal probability. However, there are some subtleties to this scenario which make it less random than it at first appears. What if a computer knew the exact force at which the coin was flipped? Or the humidity of the air? Or the speed of air currents in the room? Presumably, with all this data, a computer could predict the exact outcome of a coin flip from the initial conditions. This process is deterministic.

Quantum mechanics exhibits true randomness

Not so for quantum mechanics. The analogous situation is that of an electron heading towards a wall. You measure the electron at some time and find it to be on the left of the wall. After enough time has passed in which the electron could have hit the wall, you measure it again and you find that sometimes, the electron has passed through and ended up on the right-hand side. This process is called quantum mechanical tunnelling and, as is so often said, is the microscopic equivalent of running into a wall and passing straight through. By tuning the width of the wall, you can make the electron appear on either side of the wall with equal probability. You have essentially made a subatomic coin toss. The key difference here is that the laws of quantum mechanics mean that there is no way, even in principle, to determine what side the electron will be before the measurement is made. The quantum mechanical situation is probabilistic.

Einstein was famously unhappy with inherent quantum randomness and pithily remarked “Does God play dice?”. He believed that there were microscopic equivalents to air pressure or initial force that would allow you to determine which side of the wall the electron would end up but, experiments in the 1990s revealed that these hidden variables do not exist. Quantum mechanics exhibits true randomness. God does play dice.

This property has recently been exploited in new technological developments. Instead of constructing complicated pseudo RNGs, a team at Sandia National Laboratories in the US have developed the Co-designed Improved Neural Foundations Leveraging Inherent Physics Stochasticity (a cheeky backronym for COINFLIPS) to employ the electron/wall scenario to generate random numbers. Inspired by the seemingly random network of inputs and outputs in human neuron networks, the team developed a truly random number generator using the quantum tunnelling experiment just described. By tuning the width of the wall, the distribution of electrons on the left or right can be controlled and other scenarios can be modelled (like an unfair coin).

This method of generation can be used to produce much cheaper, RNGs as the essential process can be performed using only two transistors. Not only will this reduce the cost of cybersecurity systems, but the outputs will be truly random. When random numbers are needed in the future to model stochastic processes like the dynamics of interstellar gas clouds, it is interesting to reflect on how the fundamental randomness comes from nothing more complicated than COINFLIPS.

Photo: Jonathan Greenaway via Unsplash

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