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Lehmer128

Lehmer128 is a 128-bit multiplicative congruential generator (MCG) considered the minimal standard for modern 64-bit PRNGs. Based on Lehmer’s original MCG (1951) with a carefully chosen multiplier from PCG research providing excellent spectral properties. It passes BigCrush and PractRand tests up to 32 TB, making it the simplest PRNG suitable for serious use.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Multiplicative Congruential Generator
Security status	🎓 Educational Only
Complexity	Beginner
Inventor	D. H. Lehmer (original), optimized variant
Year	1951
Origin	🇺🇸 United States
Source	algorithms/random/lehmer128.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

• D. H. Lehmer: Mathematical methods in large-scale computing units (1951)
• PCG Random: Does it beat the minimal standard?
• P. L’Ecuyer: Tables of linear congruential generators (1999)

References

• TestU01: BigCrush Statistical Testing Suite
• PractRand: Practical Random Number Generator Testing

Test vectors

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

Vector 1 — Seed 1 (SplitMix64 initialization): First 5 outputs

Field	Value
seed	0000000000000001
outputSize	40
input	null
expected	c63f51f8161177a4e6aecdfdf79bc7d4 8c9cbc663aeb810975a8d07cef123243 f567b888929801d9

Vector 2 — Seed 0 (SplitMix64 initialization): First 5 outputs

Field	Value
seed	0000000000000000
outputSize	40
input	null
expected	8b0f2b375c2d67c74c1d2980cd9389d4 4cd926f3f2f9ddab04e60c22ee2f62ef 143862ac141e19d3

Vector 3 — Seed 42 (SplitMix64 initialization): First 5 outputs

Field	Value
seed	000000000000002a
outputSize	40
input	null
expected	85b9aac0926bdc09599b8a2e6781aedf 539f0aa577fab11f1b382c2f9e57b996 e86006e444071702

Vector 4 — Direct state 0x123456789ABCDEF0123456789ABCDEF0: First 3 outputs

Field	Value
state	123456789abcdef0123456789abcdef0
outputSize	24
input	null
expected	b66df1da3bd6e94cd8b959473b03b16211208f133bafce12

Vector 5 — State initialized to 1 (minimal non-zero state): First 10 outputs

Field	Value
state	00000000000000000000000000000001
outputSize	80
input	null
expected	0fc94e3bf4e9ab329f4c53132cb5b55a 04f16bbaa6c209fe9c0827f89f0f242f 5b5349ddf2ca02869a09a2d3e4f52267 f4e9e997e821367bd23cf34fc72f4155 56a2d7e343d7f1b573b5f20e34a8238c

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