Primitive polynomials testing methodology

Vijayarangan, Natarajan; Vijayasarathy, R.

doi:10.1080/09720529.2005.10698050

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…A very important area in theory of finite fields is designing fast algorithms for finding irreducible and primitive polynomials over finite fields [8]. These polynomials have many applications in coding theory, In [5], Shparlinski shows that in any finite field Fp n a primitive root can be found in time (( ) ) O p 1/4 n f + .…”

Section: Introductionmentioning

confidence: 99%

Companion Matrix and Recognition of Primitive Polynomial

Huang¹,

Peng

2014

Journal of Discrete Mathematical Sciences and Cryptography

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This paper studies the properties of companion matrices of primitive polynomials over finite field and discusses the recognition of a primitive polynomial by companion matrix. It is showed-is a prime number then the recognition of a primitive polynomial over finite field Fp of degree n can reduce to the recognition of a primitive element. When 2, p 2 this can reduce the complexity of the recognition of a primitive polynomial.

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Section: Introductionmentioning

confidence: 99%

Companion Matrix and Recognition of Primitive Polynomial

Huang¹,

Peng

2014

Journal of Discrete Mathematical Sciences and Cryptography

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“…Despite the broad applications of primitive polynomials in computer science and PQC, existing classical algorithms for generating random degree n primitive polynomials over a finite field containing q elements, denoted

\mathbb {F}_{q}

, rely on the prime factorization of

q^n-1

to be efficiently implemented, [ 44–48 ] which greatly narrows their practical applications. Fortunately, integer factorization is efficiently solvable on quantum computers.…”

Section: Introductionmentioning

confidence: 99%

Quantum‐Accelerated Algorithms for Generating Random Primitive Polynomials Over Finite Fields

Huang,

Yin,

Chen

et al. 2023

Adv Quantum Tech

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Primitive polynomials over finite fields are crucial resources with broad applications across various domains in computer science, including classical pseudo‐random number generation, coding theory, and post‐quantum cryptography. Nevertheless, the pursuit of an efficient classical algorithm for generating random primitive polynomials over finite fields remains an ongoing challenge. In this work, it shows how this problem can be solved efficiently with the help of quantum computers. Moreover, the designs of specific quantum circuits to implement them are also presented. The research paves the way for the rapid and real‐time generation of random primitive polynomials in diverse quantum communication and computation applications.

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Primitive polynomials testing methodology

Cited by 2 publications

References 3 publications

Companion Matrix and Recognition of Primitive Polynomial

Companion Matrix and Recognition of Primitive Polynomial

Quantum‐Accelerated Algorithms for Generating Random Primitive Polynomials Over Finite Fields

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