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MLCG (Multiplicative Linear Congruential Generator)

The Multiplicative Linear Congruential Generator is a simplified variant of LCG using only multiplication (no additive constant). It uses the formula X(n+1) = (a * X(n)) mod m. MLCG was one of the earliest PRNGs, introduced by D. H. Lehmer in 1951. While simple and fast, it has poor statistical properties and must never be used for cryptographic purposes.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Pseudorandom Number Generator
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	D. H. Lehmer
Year	1951
Origin	🇺🇸 United States
Source	algorithms/random/mlcg.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 16 bytes (128 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Lehmer, D. H.: Mathematical methods in large-scale computing units (1951)
• Wikipedia: Lehmer Random Number Generator
• Knuth, D. E.: The Art of Computer Programming, Vol. 2 (Seminumerical Algorithms), Section 3.2.1

References

• Park, Miller: Random Number Generators: Good Ones Are Hard To Find
• L’Ecuyer, P.: Tables of Linear Congruential Generators

Test vectors

4 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — MINSTD (Park-Miller MLCG) a=16807, m=2^31-1, seed=1 - First 10 values

Field	Value
seed	00000001
multiplier	000041a7
modulo	7fffffff
outputSize	40
input	null
expected	000041a710d63af160b7acd93ab50c2a 4431b7821c06dac806058ed856e509fe 56f32f4377a4044d

Vector 2 — MINSTD (Park-Miller MLCG) - 10,000th value should be 1043618065

Field	Value
seed	00000001
multiplier	000041a7
modulo	7fffffff
count	10000
outputSize	4
input	null
expected	3e345911

Vector 3 — MLCG with a=48271, m=2^31-1, seed=1 - First 5 values

Field	Value
seed	00000001
multiplier	0000bc8f
modulo	7fffffff
outputSize	20
input	null
expected	0000bc8f0ae257e24cf91f467220517d7be5f8f1

Vector 4 — Implicit modulo (2^64) with C# default multiplier, seed=12345

Field	Value
seed	0000000000003039
multiplier	5851f42d4c957f2d
modulo	(empty)
outputSize	40
input	null
expected	0807dc721521c10529e75c5d499968e1 47c1c8e2e1f40e8d6f3cc8211f2f81c9 f12741ce42b98755

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