Hawkynt

LFSR88

LFSR88 is a combined linear feedback shift register using three Tausworthe components with primitive trinomials. With a period of approximately 2^88, it provides excellent statistical quality for simulations and Monte Carlo methods. Simpler and faster than LFSR113, 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	1996
Origin	🇨🇦 Canada
Source	algorithms/random/lfsr88.js

Parameters

Parameter	Supported values
Seed sizes	1 byte (8 bits) to 12 bytes (96 bits)

Capabilities

Flag	Value
IsDeterministic	Yes
IsCryptographicallySecure	No

Security

Status: 🎓 Educational Only

No vulnerabilities are recorded for this implementation.

Documentation

• L’Ecuyer: Maximally Equidistributed Combined Tausworthe Generators (1996)
• GNU Scientific Library: Random Number Generators
• GSL Source: gsl_rng_taus
• L’Ecuyer: Tables of Maximally Equidistributed Combined LFSR Generators

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): First 5 outputs - verified against LFSR88 specification

Field	Value
seed	0000303900005ba000008707
outputSize	20
input	null
expected	0d063a5739786e63455d3d002ca381e2805afcf6

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

Field	Value
seed	3ade68b1075bcd15159a55e5
outputSize	40
input	null
expected	38e0e6ebb81c2db71e43dc1d9567cf51 78b9be0ccd95f930e9903cb4b3d3529e c1423895391f9e51

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

Field	Value
seed	000000020000000800000010
outputSize	20
input	null
expected	0020208002002c8048088062804d2000428049a0

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

Field	Value
seed	000f4240001e8480002dc6c0
outputSize	32
input	null
expected	784c7d760fa83ede80fde985b34c4faeeaacedf0b65239864005b43bc328d759

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

Field	Value
seed	0000303900005ba000008707
outputSize	20
skip	10
input	null
expected	93f757cdb1d16696117eee33dd3fcfdd2b582a1e

---

← All algorithms

This site is open source. Improve this page.