Pseudorandom

Pseudorandom refers to sequences of numbers that appear random but are generated by deterministic algorithms. Unlike true randomness, which arises from inherently unpredictable physical processes, pseudorandom sequences rely on an initial value called a seed and follow a predefined rule to produce long strings of numbers that pass many statistical tests for randomness.

In practice, pseudorandom number generators produce outputs that are statistically close to uniform and independent for practical purposes. However, because the process is deterministic, the entire sequence is fully determined by the seed, and the generator eventually enters a repeating cycle. The period—the length before repetition occurs—depends on the algorithm and its parameters. Reproducing a result simply requires reusing the same seed and algorithm.

Common non-cryptographic pseudorandom generators include linear congruential generators, the Mersenne Twister, and various xorshift families. These are favored for speed and good statistical properties in simulations, numerical methods, and gaming. Cryptographically secure pseudorandom number generators are designed to resist prediction: given less than the full internal state, an attacker should gain negligible information about future outputs. Examples include designs based on cryptographic primitives such as block ciphers or hash functions, and practice often recommends using a cryptographic RNG when randomness is used for keys, nonces, or other security-sensitive material.

Applications of pseudorandom generators include Monte Carlo simulations, statistical sampling, randomized algorithms, and software testing. Their effectiveness hinges on both the quality of the algorithm and the quality of the seed or entropy source. While useful and efficient, pseudorandom sequences are not truly random and can be predictable if the state or seed is compromised.