Quantum Random Numbers

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. - J. Von Neumann

Intro to Random Numbers

Random number generation is a process by which a sequence of numbers or symbols that cannot be reasonably predicted is generated.

Before the advent of quantum security, and even today in most scenarios, random numbers are pseudorandom. A pseudorandom number generator (PRNG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed. PRNGs are central in applications such as simulations, electronic games, and cryptography.

Quantum Random Number Generators

Quantum random number generators use principles of quantum mechanics as a source of entropy. By doing so they are able to provide true random numbers. There are many different methods of using quantum physics principles as an entropy source.

QRNG represents the system that satisﬁes the single random quantum effect of resetting to the initial settings after system value measurements. Due to the laws of quantum physics, each measurement with identical initial conditions and the same measurement mode provides different values. Therefore, such a system has a broad application of random number generators where the randomness of measured values is highly desirable.

Such systems include the smallest units such as electrons (smallest quantity of charge) or qubits (smallest quantity of information). A single quantum of light (photon) can be used as qubit carrier which is favorable due to laws of quantum mechanics that prevents making a faithfully qubit's copy. In the early development of QRNGs, schemes based on measuring qubit states were widely adopted due to theoretical simplicity. A qubit cannot be split, copied or amplified without introducing detectable disturbances and it can be represented as a linear combination of two basic states (horizontal and vertical):

Parameters α and β are probability amplitudes: the probability that the outcome of the measurement will be a vertical or a horizontal base, respectively. Unlike the classical bit, which can only have two possible values, 0 or 1.

RNGs that rely on quantum processes (QRNGs), offer guaranteed in-determinism and entropy, since quantum processes are intrinsically random.

True-randomness are based on non-numeric techniques. One intriguing aspect of quantum mechanics is that properties of a particle are not determined with arbitrary precision until one measure them, consequently the individual result of a measurement contains an inevitable intrinsic random component. This characteristic of the quantum theory provides fundamental randomness that can be used for generating true random numbers.

Quantum mechanical random numbers are random numbers that are derived from the fundamental principles of random processes from quantum mechanics. Due to the laws of quantum physics, each measurement with identical initial conditions and the same measurement mode provides different values.

Unpredictability of QRNG's

In terms of unpredictability, a stream of Quantum random numbers exhibits two forms:

• Forward unpredictability If the seed is unknown, the next output bit in the sequence should be infeasible to predict, regardless of any knowledge of previous bits in the sequence.

• Backward unpredictability It should also not be feasible to determine the seed from knowledge of any generated values. No correlation between a seed and any value generated from that seed should be evident; each element of the sequence should appear to be the outcome of an independent random event whose probability is 50%.

PRNG vs QRNG - A comparison

Entropy Source

Randomness based on complexity of process and partial ignorance.

Fundamental randomness.

Ease of certification

Limited ability to certify the underlying physical process, which is inherently a complex one. Certification of the quality of the output based on standard tests.

Can validate the underlying physical processes. Certification of the quality of the output based on standard tests.

Resistance to tampering

Some ability to run health check on entropy source.

Built-in check based on simplicity of process and more sensitive to tampering. Device-independent versions offer highest resistance against tampering of entropy source itself, even by the providers themselves.

Quality of entropy

Various degrees. The underlying process used as entropy source may work in a physical regime where there are large bias and relatively high correlations (that is, small entropy)

High entropy from the start based on the simple design of the source; a QRNG entropy source can be argued to be very close to i.i.d. from the start.

Speed

Can be very high, and several sources may be combined to obtain higher rates.

High, also because of the quality of the initial entropy, but device-independent implementations may be slow, for example.

Size

Can be very small and embedded on chip, e.g.: exploiting a randomness source like thermal noise.

Varies substantially, going from embeddable in smartphones to room-size dimensions for implementing device-independent randomness generation based on non-locality.

Use of Quantum RNG in Ozonechain

In contrast to deterministic random number generators that generate random values with entropy that is limited by the entropy of the initial seed, Ozonechain uses non-deterministic random number generators that rely on the quantum state of matter for generation of truly random numbers. By fact, quantum physics is fundamentally random in nature and is confirmed by theory and experimental research.

The process: Single Photon Splitting

Ozonechain uses laser-based quantum source to generate the randomness for its cryptography, hashing and digital signatures. It is a highly-sophisticated engineering innovation which involves the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics and quantum physics working together to create the highest level of randomness possible.

Photon Generation

A laser produces a stream of the elementary particle, photon. The photons generated from the laser are used to generate the random numbers.

Photons unlike classical objects are unpredictable under certain situations. When incident on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse to. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. This process is illustrated in the diagram,

Photons to high entropy random numbers

The following diagram depicts the process from photon generation to random number output.

The process starts with the generation of light from a laser source, which is converted into single-photon level using attenuators. The photons are then sent onto a semi-transparent mirror for the superposition phenomenon and are detected using SPD (Single Photon Detector). They are then converted into bits of 1’s and 0’s, depending on the clicks generated on the SPD. Then there is post-processing in FPGAs to do the conditioning, statistical checks and then deliver the random numbers to the outside world.

The test suits check the randomness of the bits. Only if the conditions are met, they are forwarded to the Ozonechain nodes, Ozonechain wallet and D-Apps deployed in Ozonechain.

How QRNG adds to Ozone chain's security?

Ozone chain's unparalleled Quantum Random Number Generators (QRNGs) leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

• The source of randomness is unpredictable and controlled by quantum process.

• The entropy source tends to produce true random output.

• Live/real-time monitoring of entropy source is possible and highly effective as well.

• All attacks on the entropy source are detectable.

• The above factors indicate that our QRNG is provably secure.

• Ozone Chain's QRNGs embed elementary components that can be easily monitored to detect any failure or attacks.

• Environmental perturbations can be ruled out by simple health checks, guaranteeing QRNG always produce high quality entropy.

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