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LCG (Linear Congruential Generator)

The Linear Congruential Generator is one of the oldest and most well-known pseudorandom number generator algorithms. It uses the formula X(n+1) = (a * X(n) + c) mod m to generate a sequence of numbers. Despite its simplicity and speed, it has poor statistical properties and should not 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	1949
Origin	🇺🇸 United States
Source	algorithms/random/lcg.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

• Wikipedia: Linear Congruential Generator
• Knuth, D. E.: The Art of Computer Programming, Vol. 2 (Seminumerical Algorithms)
• Park, Miller: Random Number Generators: Good Ones Are Hard To Find

References

• Park-Miller-Carta Pseudo-Random Number Generators
• Numerical Recipes in C: The Art of Scientific Computing
• GLIBC rand() implementation

Test vectors

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

Vector 1 — MINSTD (Park-Miller) a=16807, c=0, m=2^31-1, seed=1 - First 10 values

Field	Value
seed	00000001
multiplier	000041a7
increment	00000000
modulo	7fffffff
outputSize	40
input	null
expected	000041a710d63af160b7acd93ab50c2a 4431b7821c06dac806058ed856e509fe 56f32f4377a4044d

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

Field	Value
seed	00000001
multiplier	000041a7
increment	00000000
modulo	7fffffff
count	10000
outputSize	4
input	null
expected	3e345911

Vector 3 — Numerical Recipes a=1664525, c=1013904223, m=2^32, seed=1 - First 10 values

Field	Value
seed	00000001
multiplier	0019660d
increment	3c6ef35f
modulo	0100000000
outputSize	40
input	null
expected	3c88596c5e8885db8116017eb4733ac5 0cf06d605e98c13fc656dd928e625fc9 0438e694a3a5a0e3

Vector 4 — ANSI C (glibc) a=1103515245, c=12345, m=2^31, seed=1 - First 8 values

Field	Value
seed	00000001
multiplier	41c64e6d
increment	00003039
modulo	80000000
outputSize	32
input	null
expected	41c67ea6167eb0e72781e494446b9b3d794bdf3215fb748359e2b6001cfbae39

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