Random number generationRandom number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of a physical environment's attribute that is constantly changing in a manner that is practically impossible to model.
Hardware random number generatorIn computing, a hardware random number generator (HRNG), true random number generator (TRNG) or non-deterministic random bit generator (NRBG) is a device that generates random numbers from a physical process capable of producing entropy (in other words, the device always has access to a physical entropy source), rather than by means of an algorithm. Such devices are often based on microscopic phenomena that generate low-level, statistically random "noise" signals, such as thermal noise, the photoelectric effect, involving a beam splitter, and other quantum phenomena.
RandomnessIn common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4.
Cryptographically secure pseudorandom number generatorA cryptographically secure pseudorandom number generator (CSPRNG) or cryptographic pseudorandom number generator (CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography. It is also loosely known as a cryptographic random number generator (CRNG). Most cryptographic applications require random numbers, for example: key generation nonces salts in certain signature schemes, including ECDSA, RSASSA-PSS The "quality" of the randomness required for these applications varies.
Randomized algorithmA randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables.
Analog-to-digital converterIn electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.
Random number generator attackThe security of cryptographic systems depends on some secret data that is known to authorized persons but unknown and unpredictable to others. To achieve this unpredictability, some randomization is typically employed. Modern cryptographic protocols often require frequent generation of random quantities. Cryptographic attacks that subvert or exploit weaknesses in this process are known as random number generator attacks.
Statistical randomnessA numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll or the digits of π exhibit statistical randomness. Statistical randomness does not necessarily imply "true" randomness, i.e., objective unpredictability. Pseudorandomness is sufficient for many uses, such as statistics, hence the name statistical randomness. Global randomness and local randomness are different.
Field-programmable gate arrayA field-programmable gate array (FPGA) is an integrated circuit designed to be configured after manufacturing. The FPGA configuration is generally specified using a hardware description language (HDL), similar to that used for an application-specific integrated circuit (ASIC). Circuit diagrams were previously used to specify the configuration, but this is increasingly rare due to the advent of electronic design automation tools. FPGAs contain an array of programmable logic blocks, and a hierarchy of reconfigurable interconnects allowing blocks to be wired together.
Randomness extractorA randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weak entropy source, together with a short, uniformly random seed, generates a highly random output that appears independent from the source and uniformly distributed. Examples of weakly random sources include radioactive decay or thermal noise; the only restriction on possible sources is that there is no way they can be fully controlled, calculated or predicted, and that a lower bound on their entropy rate can be established.
Linear congruential generatorA linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation.
PseudorandomnessA pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Simply put, the problem is that many of the sources of randomness available to humans (such as rolling dice) rely on physical processes not readily available to computer programs. The generation of random numbers has many uses, such as for random sampling, Monte Carlo methods, board games, or gambling.
Programmable logic arrayA programmable logic array (PLA) is a kind of programmable logic device used to implement combinational logic circuits. The PLA has a set of programmable AND gate planes, which link to a set of programmable OR gate planes, which can then be conditionally complemented to produce an output. It has 2N AND gates for N input variables, and for M outputs from PLA, there should be M OR gates, each with programmable inputs from all of the AND gates. This layout allows for many logic functions to be synthesized in the sum of products canonical forms.
Digital-to-analog converterIn electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application.
Randomness testA randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless). In stochastic modeling, as in some computer simulations, the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to show that the data are valid for use in simulation runs. In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1.
Programmable Array LogicProgrammable Array Logic (PAL) is a family of programmable logic device semiconductors used to implement logic functions in digital circuits introduced by Monolithic Memories, Inc. (MMI) in March 1978. MMI obtained a registered trademark on the term PAL for use in "Programmable Semiconductor Logic Circuits". The trademark is currently held by Lattice Semiconductor. PAL devices consisted of a small PROM (programmable read-only memory) core and additional output logic used to implement particular desired logic functions with few components.
Programmable logic deviceA programmable logic device (PLD) is an electronic component used to build reconfigurable digital circuits. Unlike digital logic constructed using discrete logic gates with fixed functions, a PLD has an undefined function at the time of manufacture. Before the PLD can be used in a circuit it must be programmed to implement the desired function. Compared to fixed logic devices, programmable logic devices simplify the design of complex logic and may offer superior performance.
Gate arrayA gate array is an approach to the design and manufacture of application-specific integrated circuits (ASICs) using a prefabricated chip with components that are later interconnected into logic devices (e.g. NAND gates, flip-flops, etc.) according to custom order by adding metal interconnect layers in the factory. It was popular during the upheaval in the semiconductor industry in the 1980s, and its usage declined by the end of the 1990s.
Pseudorandom binary sequenceA pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict and exhibits statistical behavior similar to a truly random sequence. PRBS generators are used in telecommunication, such as in analog-to-information conversion, but also in encryption, simulation, correlation technique and time-of-flight spectroscopy. The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR).
Ideal (ring theory)In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal.
