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Security of cryptosystems based on class groups of imaginary quadratic orders
, 2000
"... In this work we investigate the difficulty of the discrete logarithm problem in class groups of imaginary quadratic orders. In particular, we discuss several strategies to compute discrete logarithms in those class groups. Based on heuristic reasoning, we give advice for selecting the cryptographic ..."
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Cited by 7 (1 self)
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In this work we investigate the difficulty of the discrete logarithm problem in class groups of imaginary quadratic orders. In particular, we discuss several strategies to compute discrete logarithms in those class groups. Based on heuristic reasoning, we give advice for selecting the cryptographic parameter, i.e. the discriminant, such that cryptosystems based on class groups of imaginary quadratic orders would offer a similar security as commonly used cryptosystems.
Solvability by Radicals from an Algorithmic Point of View
, 2001
"... Any textbook on Galois theory contains a proof that a polynomial equation with solvable Galois group can be solved by radicals. From a practical point of view, we need to nd suitable representations of the group and the roots of the polynomial. We first reduce the problem to that of cyclic extension ..."
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Cited by 4 (1 self)
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Any textbook on Galois theory contains a proof that a polynomial equation with solvable Galois group can be solved by radicals. From a practical point of view, we need to nd suitable representations of the group and the roots of the polynomial. We first reduce the problem to that of cyclic extensions of prime degree and then work out the radicals, using the work of Girstmair. We give numerical examples of Abelian and nonAbelian solvable equations and apply the general framework to the construction of Hilbert Class fields of imaginary quadratic fields.
A Signature Scheme Based on the Intractability of Computing Roots
 Designs, Codes and Cryptography
, 2000
"... We present RDSA, a variant of the DSA signature scheme, whose security is based on the intractability of extracting roots in a finite abelian group. We prove that RDSA is secure against an adaptively chosen message attack in the random oracle model if and only if computing roots in the underlying gr ..."
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Cited by 4 (1 self)
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We present RDSA, a variant of the DSA signature scheme, whose security is based on the intractability of extracting roots in a finite abelian group. We prove that RDSA is secure against an adaptively chosen message attack in the random oracle model if and only if computing roots in the underlying group is intractable. We report on a very efficient implementation of RDSA in the class group of imaginary quadratic orders. We also show how to construct class groups of algebraic number fields of degree > 2 in which RDSA can be implemented.
A Survey on IQ Cryptography
 In Proceedings of Public Key Cryptography and Computational Number Theory
, 2001
"... This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying p ..."
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Cited by 3 (1 self)
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This paper gives a survey on cryptographic primitives based on class groups of imaginary quadratic orders (IQ cryptography, IQC). We present IQC versions of several well known cryptographic primitives, and we explain, why these primitives are secure if one assumes the hardness of the underlying problems. We give advice on the selection of the cryptographic parameters and show the impact of this advice on the eciency of some IQ cryptosystems.
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, 2011
"... ter verkrijging van de graad van do�or aan de Technische Universiteit Eindhoven, op gezag van de re�or magni�cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 14 juli 2011 om 14.00 uur door ..."
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ter verkrijging van de graad van do�or aan de Technische Universiteit Eindhoven, op gezag van de re�or magni�cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 14 juli 2011 om 14.00 uur door