Journal of Information and Optimization Sciences

1989

DOI: 10.1080/02522667.1989.10698971

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A Deterministic Algorithm for Factorizing Polynomials over Extensions GF(p^m) of GF(p), p a Small Prime

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Cited by 6 publications

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“…For special fields see: Moenck (1977); von zur Gathen (1987); Mignotte and Schnorr (1988) when p − 1 has only small prime factors, Bach et al (1999) when some Φ k (p) has this property. See Rónyai (1989a), Thiong Ly (1989), Shoup (1991a), Shoup (1991b), and Menezes et al (1992) for related results.…”

Section: Deterministic Algorithmsmentioning

confidence: 99%

Factoring Polynomials Over Finite Fields: A Survey

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2001

Journal of Symbolic Computation

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This survey reviews several algorithms for the factorization of univariate polynomials over finite fields. We emphasize the main ideas of the methods and provide an up-to-date bibliography of the problem.

“…For special fields see: Moenck (1977); von zur Gathen (1987); Mignotte and Schnorr (1988) when p − 1 has only small prime factors, Bach et al (1999) when some Φ k (p) has this property. See Rónyai (1989a), Thiong Ly (1989), Shoup (1991a), Shoup (1991b), and Menezes et al (1992) for related results.…”

Section: Deterministic Algorithmsmentioning

confidence: 99%

Factoring Polynomials Over Finite Fields: A Survey

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,

²

2001

Journal of Symbolic Computation

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This survey reviews several algorithms for the factorization of univariate polynomials over finite fields. We emphasize the main ideas of the methods and provide an up-to-date bibliography of the problem.

“…Some algorithms in computer algebra and coding theory also require at some stages the computation of multi-exponentiations [26] [27].…”

Section: Introductionmentioning

confidence: 99%

Algorithms for multi-exponentiation based on complex arithmetic

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Proceedings 13th IEEE Sympsoium on Computer Arithmetic

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In this paper we propose new algorithms for multiple modular exponentiation operations. The major aim of these algorithms is to speed up the pe~ormance of some cryptographic protocols based on multi-exponentiation. The algorithms proposed are based on binary-like complex arithmetic, introduced by Pekmestzi and generalized in this paper.

Factoring ofx n?1 and orthogonalization over finite fields of characteristic 2

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1995

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Abstract. We present a new deterministic algorithm which gives a complete factorization of x"-1 over finite fields of characteristic 2. To do so we adapt a well-known procedure of orthogonalization in order to compute primitive idempotents over extensions instead of over GF(2).

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