Hawkynt

ACRNG (Additive Congruential RNG)

The Additive Congruential Random Number Generator uses cascading additions through a state array, where each element is updated by adding the previous (newly updated) element. This creates a dependency chain distinct from typical lagged Fibonacci generators. Fast and simple, but not cryptographically secure.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Deterministic PRNG
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Donald Knuth
Year	1997
Origin	🇺🇸 United States
Source	algorithms/random/acrng.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 8 bytes (64 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• Knuth: The Art of Computer Programming Vol. 2, Section 3.2.2
• Wikipedia: Linear Congruential Generator (Related Algorithm)
• C# Reference Implementation

References

• SplitMix64 (used for state initialization)
• TestU01 Statistical Testing Suite

Test vectors

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

Vector 1 — ACRNG order=12, implicit modulo (2^64), seed=0: First 8 outputs (64 bytes)

Field	Value
seed	0000000000000000
order	12
modulo	null
outputSize	64
input	null
expected	80de6c41ff947f8323ada7ab849c1f4d 1829d6c3d65999983834669e0759a381 20fa987227ad02f258c87338a1c8fe2c e59e98a337cfe90519aa71a2997f1e74

Vector 2 — ACRNG order=12, implicit modulo (2^64), seed=1: First 8 outputs (64 bytes)

Field	Value
seed	0000000000000001
order	12
modulo	null
outputSize	64
input	null
expected	84e6e8aa35bdd945987c4da32714a28c 77396d87d11bcb5953dbf93125371bbd 052bd52374f843b24a91588a9723b6ea 4cd40d5385a95d74469279f6ad4c280f

Vector 3 — ACRNG order=12, implicit modulo (2^64), seed=42: First 8 outputs (64 bytes)

Field	Value
seed	000000000000002a
order	12
modulo	null
outputSize	64
input	null
expected	7519c1f49dda4850d8aaa63cc2aae849 652d5163487f134bdf346bf650785de2 e376c4db79c67deb3bda3cffd4bcd9b9 e90e68a25e07f5271a03b3cc067a8c69

Vector 4 — ACRNG order=12, implicit modulo (2^64), seed=1234567: First 5 outputs (40 bytes)

Field	Value
seed	000000000012d687
order	12
modulo	null
outputSize	40
input	null
expected	5cbefabf9c666daedfcfc7a2c85f1cee 695bd837c36f809268479c6444f4d82b 1d75265f5d690a31

Vector 5 — ACRNG order=5, implicit modulo (2^64), seed=42: First 5 outputs (40 bytes)

Field	Value
seed	000000000000002a
order	5
modulo	null
outputSize	40
input	null
expected	a48f3117d94fa0e63102a4464575d185 21bd544c486ed973a3bfe0962dcf51d8 f120de0995d56ec9

Vector 6 — ACRNG order=12, modulo=2^31-1, seed=1: First 8 outputs (32 bytes)

Field	Value
seed	0000000000000001
order	12
modulo	7fffffff
outputSize	32
input	null
expected	3f8baaaf580d3e883f8eaa324cef1da87f5023482c4708441f532a983a755751

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