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GFSR

Generalized Feedback Shift Register is a shift-register-based PRNG using multiple feedback taps for long-period pseudo-random sequences. This gfsr4 variant uses a 521-word state with four-tap XOR recurrence, providing period 2^16672 and excellent statistical properties for simulations.

Properties

Property	Value
Category	Random Number Generators
Sub-category	Deterministic PRNG
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Robert C. Tausworthe
Year	1965
Origin	🇺🇸 United States
Source	algorithms/random/gfsr.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

• Tausworthe: Random Numbers Generated by Linear Recurrence Modulo Two (1965)
• Lewis and Payne: Generalized Feedback Shift Register Algorithm (1973)
• GNU Scientific Library - Random Number Generators
• Kirkpatrick and Stoll: Very Fast Shift-Register Sequence RNG (1981)
• Wikipedia: Generalized Feedback Shift Register

References

• GSL Source Code - gfsr.c
• Numerical Recipes: Random Number Generators

Test vectors

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

Vector 1 — Seed 0: First 8 outputs (32 bytes) - GFSR4 with LCG initialization

Field	Value
seed	0000000000000000
outputSize	32
input	null
expected	537f23f9ea1b5be4c41deb635a2b06a67dd535fd9eb47108c8a5d597d93ad76a

Vector 2 — Seed 1: First 8 outputs (32 bytes) - GFSR4 with LCG initialization

Field	Value
seed	0000000000000001
outputSize	32
input	null
expected	047a197ef9ed3f55ff9cab80a578514f7ebddba23a4db9d97f512644fbb216c3

Vector 3 — Seed 42: First 8 outputs (32 bytes) - GFSR4 with LCG initialization

Field	Value
seed	000000000000002a
outputSize	32
input	null
expected	67824c1b3f3a8efe10793ad5ee72a500d31ca0cf359e7122772601598c47a1c4

Vector 4 — Seed 12345: First 5 outputs (20 bytes) - GFSR4 with LCG initialization

Field	Value
seed	0000000000003039
outputSize	20
input	null
expected	7599787668d0218d03a2c8987599cda77c45717a

Vector 5 — Seed 999999: First 5 outputs (20 bytes) - GFSR4 with LCG initialization

Field	Value
seed	00000000000f423f
outputSize	20
input	null
expected	76f44b44e17b17c390529606e34c6e5d2bc5a368

Vector 6 — Seed 0xFFFFFFFFFFFFFFFF: First 5 outputs (20 bytes) - all bits set

Field	Value
seed	ffffffffffffffff
outputSize	20
input	null
expected	8af1b704bf8e1183312e2cc6d2cb011d11b89a28

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