Multiplicative Polynomial Inverse Over GF(73): Crisis of EEA and Its Solution

Zaman, Jesse; Ghosh, Ranjan

doi:10.1007/978-81-322-1988-0_6

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Algebraic Methods To Find Irreducible Polynomials Over Gf(p M )1

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2015

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“…At present, for all irreducible polynomials with p=2, one can find multiplicative inverses of all elemental polynomials for all values of m following Extended Euclidean Algorithm (EEA). It is observed that for irreducible polynomials with p>2 one cannot find multiplicative inverses of all elemental polynomials using EEA [17]. With little modification, the proposed algorithm can find multiplicative inverses of all irreducible polynomials for p > 2 with any value of m.…”

Section: Resultsmentioning

confidence: 99%

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An Algorithm to Find the Irreducible Polynomials Over Galois Field GF(pm)

KMSadiqueUzZaman¹,

Dey²,

Ghosh³

2015

IJCA

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Irreducible Polynomials over GF(p m) and the multiplicative inverses under it are important in cryptography. Presently the method of deriving irreducible polynomials of a particular prime modulus is very primitive and time consuming. In this paper, in order to find all irreducible polynomials, be it monic or non-monic, of all prime moduli p with all its order m, a fast deterministic computer algorithm based on an algebraic method producing a (m×m) matrix is proposed. The maximum number of terms in each column of the matrix is 2 j where j is the column index.

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Section: Resultsmentioning

confidence: 99%

“…2.2 for m=3. One can also refer [17] for understanding of k-matrix. It is interesting to note that column-wise elements of the k-matrix have a generalized similar pattern for mthe patterns are presented in Sec.2.3 for 2 ≤ m ≤ 5.…”

Section: Algebraic Methods To Find Irreducible Polynomials Over Gf(p M )mentioning

confidence: 99%