Paper 2005/111
Weak Composite Diffie-Hellman is not Weaker than Factoring
Kooshiar Azimian, Javad Mohajeri, and Mahmoud Salmasizadeh
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
- Published elsewhere. Unknown where it was published
- Keywords
- Computational ComplexityDiffie-HellmanFactoring
- Contact author(s)
- kushyaar @ yahoo com
- History
- 2005-04-15: received
- Short URL
- https://ia.cr/2005/111
- License
-
CC BY
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}
}
