Cryptanalysis of the Dickson-Scheme

Müller, Winfried; Nöbauer, Rupert

doi:10.1007/3-540-39805-8_7

Cited by 40 publications

(15 citation statements)

References 6 publications

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“…These calculations use so-called Lucas recurrent sequences. For full details the reader should consult [2], [22] (where the name 'LUCDIF' was proposed), [17], [16], [19] and [14].…”

Section: Representing Elements By Their Minimal Polynomialsmentioning

confidence: 99%

Looking beyond XTR

Bosma

Hutton

Verheul

2002

Lecture Notes in Computer Science

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Abstract. XTR is a general method that can be applied to discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the Brouwer-Pellikaan-Verheul conjecture, originally posed in [4], concerning the size of XTR-like representations of elements in extension fields of arbitrary degree. If true this conjecture would provide even more compact representations of elements than XTR in extension fields of degree thirty. We test the conjecture by experiment, showing that in fact it is unlikely that such a compact representation of elements can be achieved in extension fields of degree thirty.

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“…These calculations use so-called Lucas recurrent sequences. For full details the reader should consult [2], [22] (where the name 'LUCDIF' was proposed), [17], [16], [19] and [14].…”

Section: Representing Elements By Their Minimal Polynomialsmentioning

confidence: 99%

Looking beyond XTR

Bosma

Hutton

Verheul

2002

Lecture Notes in Computer Science

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“…In a similar way, Bob can construct S from A. It is indicated in [2], that the above scheme coincides with the variant of the DiffieHellman key-exchange scheme that was proposed and analyzed by a series of authors; [15] (where the name 'LUCDIF' was proposed), [11], [10], [12] and [8].…”

Section: A Different View Of the Lucdif Cryptosystemmentioning

confidence: 93%

Doing More with Fewer Bits

Brouwer

Pellikaan

Verheul

1999

Advances in Cryptology - ASIACRYPT’99

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“…A variation called Kravitz-Reed, using irreducible binary polynomials [898], is insecure [451,589]. Winfried MŸller and Wilfried Nöbauer use Dickson polynomials [1127,1128,965]. Rudolph Lidl and MŸller generalized this approach in [966,1126] (a variant is called the Réidi scheme), and Nöbauer looked at its security in [1172,1173].…”

Section: Lucmentioning

confidence: 99%