Random flip-flop

Random flip-flop (RFF) is a theoretical concept of a non-sequential logic circuit capable of generating true randomness. By definition, it operates as an "ordinary" edge-triggered clocked flip-flop, except that its clock input acts randomly and with probability p = 1/2. Unlike Boolean circuits, which behave deterministically, random flip-flop behaves non-deterministically. By definition, random flip-flop is electrically compatible with Boolean logic circuits. Together with them, RFF makes up a full set of logic circuits capable of performing arbitrary algorithms, namely to realize Probabilistic Turing machine.

Symbol
Random flip-flop comes in all varieties in which ordinary, edge triggered clocked flip-flop does, for example: D-type random flip-flop (DRFF). T-type random flip-flop (TRFF), JK-type random flip-flop (JKRFF), etc. Symbol for DRFF, TRFF and JKRFF are shown in the Fig. 1.

While varieties are possible, not all of them are needed: a single RFF type can be used to emulate all other types. Emulation of one type of RFF by the other type of RFF can be done using the same additional gates circuitry as for ordinary flip-flops. Examples are shown in the Fig. 2.

Practical realization of random flip-flip
By definition, action of a theoretical RFF is truly random. This is difficult to achieve in practice and is probably best realized through use of physical randomness. A RFF, based on quantum-random effect of photon emission in semiconductor and subsequent detection, has been demonstrated to work well up to a clock frequency of 25 MHz. At a higher clock frequency, subsequent actions of the RFF become correlated. This RFF has been built using bulk components and the effort resulted only in a handful of units. Recently, a monolithic chip containing 2800 integrated RFFs based on quantum randomness has been demonstrated in Bipolar-CMOS-DMOS (BCD) process.

Applications and prospects
One straightforward application of a RFF is generation of random bits, as shown in the Fig. 3.

Since each RFF operates independent of all others, N RFFs can generate N bits per clock, thus the overall generation throughput of a random number generator is only limited by the number of available RFFs and their maximum operating clock frequency.

The biggest difference between a RFF and a true random number generator is that a plethora of RFFs can work concurrently, independently of each other, with or without any synchronicity among them. This is useful in stochastic computing,    also known as Random Pulse Computing (RPC)[1 ], where many information-processing circuits work in parallel. RFF could also find its use in: prosthetic implants such as artificial cochlear or prosthetic limbs using, near-sensor image processing as well as in artificial intelligence processors. Furthermore, having in mind its high speed, a single RFF can be used to generate on the order of hundred thousand 256-bit cryptographic keys per second, or nonce data, without requiring any special or proprietary protocol to communicate with, making it potentially indispensable piece of security hardware such as IoT devices, smart cards, car keys, as well as of any computer or digital communication device.

While the technology of realizing a RFF on a chip is young, it is conceivable that in the future RFF as an electronic element will appear in universal logic chips (such as 7400-series integrated circuits), in Application Specific Integrated Circuits (ASIC), and in Field-Programmable Gate Array (FPGA) chips, thus facilitating designs that could benefit from it.