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Reducing Logarithms in Totally Non-maximal Imaginary Quadratic Orders to Logarithms in Finite Fields

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ASIACRYPT '99: Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology

Pages 219 - 231

Published: 14 November 1999 Publication History

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Lipmaa H(2012)Secure accumulators from euclidean rings without trusted setupProceedings of the 10th international conference on Applied Cryptography and Network Security10.1007/978-3-642-31284-7_14(224-240)Online publication date: 26-Jun-2012
https://dl.acm.org/doi/10.1007/978-3-642-31284-7_14
Kim HMoon S(2003)Public-key cryptosystems based on class semigroups of imaginary quadratic non-maximal ordersProceedings of the 8th Australasian conference on Information security and privacy10.5555/1760479.1760534(488-497)Online publication date: 9-Jul-2003
https://dl.acm.org/doi/10.5555/1760479.1760534
Hühnlein DJacobson MWeber D(2003)Towards Practical Non-Interactive Public-Key Cryptosystems Using Non-Maximal Imaginary Quadratic OrdersDesigns, Codes and Cryptography10.1023/A:102574612777130:3(281-299)Online publication date: 1-Nov-2003
https://dl.acm.org/doi/10.1023/A%3A1025746127771
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The problem of computing logarithms over finite fields has proved to be of interest in different fields [4]. Subexponential time algorithms for computing logarithms over the special cases GF(p), GF(p ²) and GF(p ^m) for a fixed p and m have been ...
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Let @__ __>0 be a square-free integer congruent to 3 mod 4 and O"K the ring of integers of the imaginary quadratic field K=Q(-@__ __). Codes C over rings O"K/pO"K determine lattices @L"@__ __(C) over K. If p@__ __@__ __ then the ring R:=O"K/pO"K is ...

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ASIACRYPT '99: Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology

November 1999

411 pages

ISBN:3540666664

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Springer-Verlag

Berlin, Heidelberg

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Published: 14 November 1999

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Lipmaa H(2012)Secure accumulators from euclidean rings without trusted setupProceedings of the 10th international conference on Applied Cryptography and Network Security10.1007/978-3-642-31284-7_14(224-240)Online publication date: 26-Jun-2012
https://dl.acm.org/doi/10.1007/978-3-642-31284-7_14
Kim HMoon S(2003)Public-key cryptosystems based on class semigroups of imaginary quadratic non-maximal ordersProceedings of the 8th Australasian conference on Information security and privacy10.5555/1760479.1760534(488-497)Online publication date: 9-Jul-2003
https://dl.acm.org/doi/10.5555/1760479.1760534
Hühnlein DJacobson MWeber D(2003)Towards Practical Non-Interactive Public-Key Cryptosystems Using Non-Maximal Imaginary Quadratic OrdersDesigns, Codes and Cryptography10.1023/A:102574612777130:3(281-299)Online publication date: 1-Nov-2003
https://dl.acm.org/doi/10.1023/A%3A1025746127771
Jaulmes ÉJoux A(2000)A NICE cryptanalysisProceedings of the 19th international conference on Theory and application of cryptographic techniques10.5555/1756169.1756205(382-391)Online publication date: 14-May-2000
https://dl.acm.org/doi/10.5555/1756169.1756205

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On Computing Logarithms Over Finite Fields

Discrete Logarithms and Factoring

Codes over rings of size p2 and lattices over imaginary quadratic fields

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