Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Computational Complexity, Diffie-Hellman, Factoring

Date: received 14 Apr 2005

Contact author: kushyaar at yahoo com

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Version: 20050415:035346 (All versions of this report)

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