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The Lehmer random number generator [1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
Unfortunately, most programming languages make the latter much easier to write (X % r), so it is very commonly used. The generator is not sensitive to the choice of c, as long as it is relatively prime to the modulus (e.g. if m is a power of 2, then c must be odd), so the value c=1 is commonly chosen.
The problem here is that the low-order bits of a linear congruential PRNG with modulo 2 e are less random than the high-order ones: [6] the low n bits of the generator themselves have a period of at most 2 n. When the divisor is a power of two, taking the remainder essentially means throwing away the high-order bits, such that one ends up with ...
Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers). This list includes many common types, regardless of quality or applicability to a given use case.
RS: A random (input-dependent) shift, for cases where rotates are more expensive. Again, the output is half the size of the input. Beginning with a 2 b -bit input word, the top b −3 bits are used for a shift amount, which is applied to the next-most-significant 2 b −1 +2 b −3 −1 bits, and the least significant 2 b −1 bits of the ...
These are summed, modulo 1, to produce the result. [2] Summing three generators produces a pseudorandom sequence with cycle exceeding 6.95 × 10 12. [3] Specifically, the moduli are 30269, 30307 and 30323, producing periods of 30268, 30306 and 30322. The overall period is the least common multiple of these: 30268×30306×30322/4 = 6 953 607 871 ...
Blum Blum Shub takes the form + =, where M = pq is the product of two large primes p and q.At each step of the algorithm, some output is derived from x n+1; the output is commonly either the bit parity of x n+1 or one or more of the least significant bits of x n+1.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]