ECCC-Report TR05-047https://eccc.weizmann.ac.il/report/2005/047Comments and Revisions published for TR05-047en-usTue, 19 Apr 2005 01:52:15 +0300
Paper TR05-047
| Weak Composite Diffie-Hellman is not Weaker than Factoring |
Kooshiar Azimian,
Mahmoud Salmasizadeh,
Javad Mohajeri
https://eccc.weizmann.ac.il/report/2005/047In1985, 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.
Tue, 19 Apr 2005 01:52:15 +0300https://eccc.weizmann.ac.il/report/2005/047