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 language | English |
|---|---|
| Title of host publication | Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings |
| Editors | Kaisa Nyberg |
| Publisher | Springer Verlag |
| Pages | 294-307 |
| Number of pages | 14 |
| ISBN (Print) | 3540645187, 9783540645184 |
| DOIs | |
| Publication status | Published - Jan 1 1998 |
| Event | International Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1998 - Espoo, Finland Duration: May 31 1998 → Jun 4 1998 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 1403 |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | International Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1998 |
|---|---|
| Country | Finland |
| City | Espoo |
| Period | 5/31/98 → 6/4/98 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
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 proceeding › Conference contribution
}
TY - GEN
T1 - A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption
AU - Hühnlein, Detlef
AU - Jacobson, Michael J.
AU - Paulus, Sachar
AU - Takagi, Tsuyoshi
PY - 1998/1/1
Y1 - 1998/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84957614726&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84957614726&partnerID=8YFLogxK
U2 - 10.1007/BFb0054134
DO - 10.1007/BFb0054134
M3 - Conference contribution
AN - SCOPUS:84957614726
SN - 3540645187
SN - 9783540645184
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 294
EP - 307
BT - Advances in Cryptology — EUROCRYPT 1998, International Conference on the Theory and Application of Cryptographic Techniques, Proceedings
A2 - Nyberg, Kaisa
PB - Springer Verlag
ER -