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Euclidean Weights Of Codes From Elliptic Curves Over Rings
 TRANS. AMER. MATH. SOC
"... We construct certain errorcorrecting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest. ..."
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Cited by 13 (5 self)
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We construct certain errorcorrecting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.
An Alternative to Factorization: a Speedup for SUDAN’s Decoding Algorithm and its Generalization to AlgebraicGeometric Codes
 INRIA, France, Rapport de recherche
, 1998
"... ..."
Monodromy Groups of Coverings of Curves
, 2003
"... We consider finite separable coverings of curves f: X → Y over a field of characteristic p ≥ 0. We are interested in describing the possible monodromy groups of this cover if the genus of X is fixed. There has been much progress on this problem over the past decade in characteristic zero. Recently F ..."
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Cited by 2 (0 self)
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We consider finite separable coverings of curves f: X → Y over a field of characteristic p ≥ 0. We are interested in describing the possible monodromy groups of this cover if the genus of X is fixed. There has been much progress on this problem over the past decade in characteristic zero. Recently Frohardt and Magaard completed the final step in resolving the Guralnick Thompson conjecture showing that only finitely many nonabelian simple groups other than alternating groups occur as composition factors for a fixed genus. There is an ongoing project to get a complete list of the monodromy groups of indecomposable rational functions with only tame ramification. In this article, we focus on positive characteristic. There are more possible groups but we show that many simple groups do not occur as composition factors for a fixed genus. We also give a reduction theorem reducing the problem to the case of almost simple groups. We also obtain some results on bounding the size of automorphism groups of curves in positive characteristic and discuss the relationship with the first problem. We note that
Constructive and Destructive Facets of Weil Descent on Elliptic Curves
 HP Labs Technical Reports, January
, 2003
"... function fields, divisor class group, cryptography, elliptic curves ∗ Internal Accession Date Only © Copyright HewlettPackard Company 2000 In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve ..."
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Cited by 1 (0 self)
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function fields, divisor class group, cryptography, elliptic curves ∗ Internal Accession Date Only © Copyright HewlettPackard Company 2000 In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a finite field of characteristic two of composite degree. We explain how this method can be used to construct hyperelliptic cryptosystems which could be as secure as cryptosystems based on the original elliptic curve. On the other hand, we show that this may provide a way of attacking the original elliptic curve cryptosystem using recent advances in the study of the discrete logarithm problem on hyperelliptic curves. We examine the resulting higher genus curves in some detail and propose an additional check on elliptic curve systems defined over fields of characteristic two so as to make them immune from the methods in this paper.
Cyclic Function Field Extensions With Ideal Class Number One
"... We list all imaginary cyclic extensions F q (x; y)=F q (x) with ideal class number equal to one. There are 55 such extensions, among which 8 are non isomorphic over F q . 1 ..."
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We list all imaginary cyclic extensions F q (x; y)=F q (x) with ideal class number equal to one. There are 55 such extensions, among which 8 are non isomorphic over F q . 1
Cyclotomic Function Fields With Ideal Class Number One
"... We list all imaginary cyclotomic extensions F q (x; M(x) )=F q (x) with ideal class number equal to one. Apart from the zero genus ones, there are 17 solutions up to F q (x) isomorphism: 13 of them are dened over F 3 and the 4 remainings are dened over F 4 . ..."
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We list all imaginary cyclotomic extensions F q (x; M(x) )=F q (x) with ideal class number equal to one. Apart from the zero genus ones, there are 17 solutions up to F q (x) isomorphism: 13 of them are dened over F 3 and the 4 remainings are dened over F 4 .
CSTR00016 CONSTRUCTIVE AND DESTRUCTIVE FACETS OF WEIL DESCENT ON ELLIPTIC CURVES
, 2000
"... Abstract. In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a nite eld of characteristic two of composite degree. We explain how this method can be used to construct hyperelliptic cryp ..."
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Abstract. In this paper we look in detail at the curves which arise in the method of Galbraith and Smart for producing curves in the Weil restriction of an elliptic curve over a nite eld of characteristic two of composite degree. We explain how this method can be used to construct hyperelliptic cryptosystems which could be as secure as cryptosystems based on the original elliptic curve. On the other hand, we show that the same technique may provide a way of attacking the original elliptic curve cryptosystem using recent advances in the study of the discrete logarithm problem on hyperelliptic curves. We examine the resulting higher genus curves in some detail and propose an additional check on elliptic curve systems de ned over elds of characteristic two soastomakethem immune from the methods in this paper. 1.