'Irreducible polynomial' diaporamas de présentation

Cryptography and Network Security Chapter 4

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Cryptography and Network Security Chapter 4

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Cryptography and Network Security Chapter 4

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Cryptography and Network Security Chapter 4

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Polynomial Ideals

Polynomial Ideals. Euclidean algorithm Multiplicity of roots Ideals in F[x]. Euclidean algorithms. Lemma. f,d nonzero polynomials in F[x]. deg d ? deg f. Then there exists a polynomial g in F[x] s.t. either f-dg=0 or deg(f-dg)<deg f. Proof of lemma:.

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Modern Algebra Review

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Public key ciphers 2

Public key ciphers 2. Session 6. Contents. The discrete logarithm problem The Diffie-Hellman key exchange. The discrete logarithm problem. Over the real numbers, exponentiation (finding y = b x ) is not significantly easier than the inverse operation (finding x = log b ( y ))

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Chapter 11

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Definitions

Definitions. group , ring and field polynomial over a field F degree of a polynomial over F F[x] degree of a polynomial in F[x] gcd of two polynomials from F[x] irreducible polynomial over F function induced by a polynomial root of a polynomial

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