A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption

Detlef Hühnlein, Michael J. Jacobson, Sachar Paulus, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

We introduce a new cryptosystem with trapdoor decryption based on the difficulty of computing discrete logarithms in the class group of the nonmaximal imaginary quadratic order N Δq, where δq = δq2, δ square-free and q prime. The trapdoor information is the conductor q. Knowledge of this trapdoor information enables one to switch to and from the class group of the maximal order N Δ, where the representatives of the ideal classes have smaller coefficients. Thus, the decryption procedure may be performed in the class group of N Δ rather than in the class group of the public N Δq, which is much more efficient. We show that inverting our proposed cryptosystem is computationally equivalent to factoring the non-fundamental discriminant δq, which is intractable for a suitable choice of δ and q. We also describe how signature schemes in N Δq may be set up using this trapdoor information. Furthermore, we illustrate how one may embed key escrow capability into classical imaginary quadratic field cryptosystems.

Original languageEnglish
Title of host publicationAdvances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings
EditorsKaisa Nyberg
PublisherSpringer Verlag
Pages294-307
Number of pages14
ISBN (Print)3540645187, 9783540645184
DOIs
Publication statusPublished - Jan 1 1998
EventInternational Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1998 - Espoo, Finland
Duration: May 31 1998Jun 4 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1403
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherInternational Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1998
CountryFinland
CityEspoo
Period5/31/986/4/98

Fingerprint

Class Group
Cryptosystem
Cryptography
Maximal Order
Discrete Logarithm
Imaginary Quadratic Field
Square free
Factoring
Signature Scheme
Conductor
Discriminant
Switches
Switch
Computing
Coefficient

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Hühnlein, D., Jacobson, M. J., Paulus, S., & Takagi, T. (1998). A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. In K. Nyberg (Ed.), Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 294-307). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1403). Springer Verlag. https://doi.org/10.1007/BFb0054134

A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. / Hühnlein, Detlef; Jacobson, Michael J.; Paulus, Sachar; Takagi, Tsuyoshi.

Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Kaisa Nyberg. Springer Verlag, 1998. p. 294-307 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1403).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hühnlein, D, Jacobson, MJ, Paulus, S & Takagi, T 1998, A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. in K Nyberg (ed.), Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1403, Springer Verlag, pp. 294-307, International Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1998, Espoo, Finland, 5/31/98. https://doi.org/10.1007/BFb0054134
Hühnlein D, Jacobson MJ, Paulus S, Takagi T. A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. In Nyberg K, editor, Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings. Springer Verlag. 1998. p. 294-307. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0054134
Hühnlein, Detlef ; Jacobson, Michael J. ; Paulus, Sachar ; Takagi, Tsuyoshi. / A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Kaisa Nyberg. Springer Verlag, 1998. pp. 294-307 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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