Remarks on Cheon's Algorithms for Pairing-Related Problems

— In EUROCRYPT 2006, Cheon proposed breakthrough algorithms for pairing-related problems such as the q-weak/strong Diffie-Hellman problem. Using that the exponents of an element in an abelian group G of prime order p form the ring Z/pZ structure even if G is a generic group, Cheon’s algorithms reduce their complexity by Polig-Hellman like method over (Z/pZ)∗ or its extension. The algorithms are more efficient than solving the relative discrete log. problems in certain cases. This paper shows that Cheon’s algorithms are faster than the result obtained by the complexity analysis in Cheon’s paper, and also an improvement of one of the algorithms. These two results lead that the q-weak Diffie-Hellman problem on an abelian group of prime order p can be solved within O( p/d)

• Type: Conference
• Year: 2007
• Where: PAIRING
• Authors: Shunji Kozaki, Taketeru Kutsuma, Kazuto Matsuo
• Keywords: Abelian Group, Algorithms, Cheon’s Algorithms, Cryptography, PAIRING 2007