Paper 2005/111 Original: eprint.iacr.org/2005/111 ↗
Weak Composite Diffie-Hellman is not Weaker than Factoring
Abstract
In1985, Shmuley proposed a theorem about intractability of Composite Diffie-Hellman [Sh85]. The Theorem of Shmuley may be paraphrased as saying that if there exist a probabilistic poly-time oracle machine which solves the Diffie-Hellman modulo an RSA-number with odd-order base then there exist a probabilistic algorithm which factors the modulo. In the other hand factorization of the module obtained only if we can solve the Diffie-Hellman with odd-order base. In this paper we show that even if there exist a probabilistic poly-time oracle machine which solves the problem only for even-order base and abstain answering the problem for odd-order bases still a probabilistic algorithm can be constructed which factors the modulo in poly-time for more than 98% of RSA-numbers.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2005-04-15: last updated
- 2005-04-15: published
- Short URL
- https://ia.cr/2005/111
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/111,
author = {Kooshiar Azimian and Javad Mohajeri and Mahmoud Salmasizadeh},
title = {Weak Composite Diffie-Hellman is not Weaker than Factoring},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/111},
year = {2005},
url = {https://eprint.iacr.org/2005/111}
}