Paper 2010/511 Original: eprint.iacr.org/2010/511 ↗
On the complexity of Decomposition Attack
Abstract
In recent researches, it is discovered that index calculus is useful for solving the discrete logarithm problems (DLP) of the groups of the Jacobian of curves (including elliptic curve) over finite field, which are widely used to cryptosystems. In these cases, the probability that an element of the group is written by the summation of N elements of large primes and factor bases is O(1) where N is some pre-fixed constant. So the situation is little different to the normal index calculus and it is proposed that it should be called another name, ”decomposition attack”. In decomposition attack, first, some relations are collected and the graph, whose vertexes are the set of large primes and whose edges are the relations, is considered and the elimination of large prime is done by using this graph. However, in the proposed algorithm, the randomness of the graph, which is difficult to define, is needed. In this paper, we first formulate the decomposition attack and next propose a new algorithm, which does not require the randomness of the graph and its worst complexity can be estimated.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2010-12-11: last updated
- 2010-10-07: published
- Short URL
- https://ia.cr/2010/511
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2010/511,
author = {Koh-ichi Nagao},
title = {On the complexity of Decomposition Attack},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/511},
year = {2010},
url = {https://eprint.iacr.org/2010/511}
}