Hawkynt

LFSR113

LFSR113 is a combined linear feedback shift register using four Tausworthe components with primitive trinomials. With a period of approximately 2^113, it provides excellent statistical quality for simulations and Monte Carlo methods. Widely used in GNU Scientific Library (GSL).

Properties

Property	Value
Category	Random Number Generators
Sub-category	Tausworthe LFSR
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Pierre L’Ecuyer
Year	1999
Origin	🇨🇦 Canada
Source	algorithms/random/lfsr113.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

• L’Ecuyer: Tables of Maximally Equidistributed Combined LFSR Generators (1999)
• GNU Scientific Library: Random Number Generators
• GSL Source: gsl_rng_taus113
• Wikipedia: Combined Linear Congruential Generator

References

• TestU01: Statistical Testing Suite
• L’Ecuyer: Uniform Random Number Generation (2017)
• Panneton and L’Ecuyer: On the xorshift random number generators (2005)

Test vectors

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

Vector 1 — Seed (12345, 23456, 34567, 45678): First 5 outputs - verified against LFSR113 specification

Field	Value
seed	0000303900005ba0000087070000b26e
outputSize	20
input	null
expected	d6e2ee3420487a82b4b42f7b1ecb28ddf0404482

Vector 2 — Seed (987654321, 123456789, 362436069, 521288629): First 10 outputs - large seed values

Field	Value
seed	3ade68b1075bcd15159a55e51f123bb5
outputSize	40
input	null
expected	35ffd4a6874afbbae88a2f023f7c813f 06e12e04a2527763564d45d7861c1ffb 6c1a069f197ee877

Vector 3 — Seed (2, 8, 16, 128): Minimal valid seed values - edge case test

Field	Value
seed	00000002000000080000001000000080
outputSize	20
input	null
expected	00180820000419c8422006240082821431412e59

Vector 4 — Seed (1000000, 2000000, 3000000, 4000000): First 8 outputs - round seed values

Field	Value
seed	000f4240001e8480002dc6c0003d0900
outputSize	32
input	null
expected	beb9746d080a61e0ae650dc53685fc3f1b0bc9a487caff3b45b7800e7e08d479

Vector 5 — Seed (12345, 23456, 34567, 45678): Outputs 11-15 - verifies long-term state progression

Field	Value
seed	0000303900005ba0000087070000b26e
outputSize	20
skip	10
input	null
expected	f55194733f2f40acc83ad68ad2a5d8f01032c2db

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