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Weak composite Diffie-Hellman

Azimian, K ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. Publisher: 2008
  3. Abstract:
  4. In1985, Shmuley proposed a theorem about intractability of Composite Diffie-Hellman. The theorem of Shmuley may be paraphrased as saying that if there exist a probabilistic polynomial time oracle machine which solves the Diffie-Hellman modulo an RSA-number with odd-order bases then there exist a probabilistic algorithm which factors the modulo. In the other hand Shmuely proved the theorem only for odd-order bases and left the even-order case as an open problem. In this paper we show that the theorem is also true for even-order bases. Precisely speaking we prove that even if there exist a probabilistic polynomial time oracle machine which can solve the problem only for even-order bases still a probabilistic algorithm can be constructed which factors the modulo in polynomial time for more than 98% of RSA-numbers
  5. Keywords:
  6. Computational number theory ; Diffie Hellman ; Diffie-Hellman problem ; Even orders ; Factoring ; Polynomial-time ; Probabilistic algorithm ; Probabilistic polynomial time ; Algorithms ; Number theory ; Polynomial approximation ; Problem solving ; Public key cryptography ; Theorem proving
  7. Source: International Journal of Network Security ; Volume 7, Issue 3 , 2008 , Pages 383-387 ; 1816353X (ISSN)
  8. URL: http://ijns.jalaxy.com.tw
  9. URL: http://ijns.jalaxy.com.tw/download_paper.jsp?PaperID=IJNS-2005-12-24-1&PaperName=ijns-v7-n3/ijns-2008-v7-n3-p383-387.pdf