A Signature Scheme Based on the Intractability of Computing Roots

Authors:
Ingrid Biehl;Johannes Buchmann;Safuat Hamdy;Andreas Meyer
Affiliations:
TU Darmstadt, Fachbereich Informatik, Alexanderstr. 10 Darmstadt, Germany D-64283 ingi@cdc.informatik.tu-darmstadt.de;TU Darmstadt, Fachbereich Informatik, Alexanderstr. 10 Darmstadt, Germany D-64283 buchmann@cdc.informatik.tu-darmstadt.de;TU Darmstadt, Fachbereich Informatik, Alexanderstr. 10 Darmstadt, Germany D-64283 hamdy@cdc.informatik.tu-darmstadt.de;TU Darmstadt, Fachbereich Informatik, Alexanderstr. 10 Darmstadt, Germany D-64283 amy@cdc.informatik.tu-darmstadt.de
Venue:
Designs, Codes and Cryptography
Year:
2002

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Abstract

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.