Small generic hardcore subsets for the discrete logarithm : short secret DL-keys

  • Let G be a group of prime order q with generator g. We study hardcore subsets H is include in G of the discrete logarithm (DL) log g in the model of generic algorithms. In this model we count group operations such as multiplication, division while computations with non-group data are for free. It is known from Nechaev (1994) and Shoup (1997) that generic DL-algorithms for the entire group G must perform p2q generic steps. We show that DL-algorithms for small subsets H is include in G require m/ 2 + o(m) generic steps for almost all H of size #H = m with m <= sqrt(q). Conversely, m/2 + 1 generic steps are su±cient for all H is include in G of even size m. Our main result justifies to generate secret DL-keys from seeds that are only 1/2 * log2 q bits long.

Download full text files

Export metadata

Author:Claus Peter SchnorrGND
Document Type:Article
Year of Completion:2000
Date of first Publication:2000/09/27
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/07/04
Tag:computational complexity; cryptography; discrete logarithm (DL); generic algorithms; generic complexity; hardcore subsets
Page Number:7
First Page:1
Last Page:7
Erschienen in: Information processing letters, 79.2001, S. 93-98
Source:Publ. in Information Processing Letter 79 (2001), pp. 93-98 ,
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht