On the security of multilevel cryptosystems over class semigroups of imaginary quadratic non-maximal orders

  • Authors:

  • Yongtae Kim;Chang Han Kim;Taek-Young Youn

  • Affiliations:

  • Dept. of Mathematics Education, Gwangju National Univ. of Education, Gwangju, Korea;Dept. of Information and Security, Semyung Univ., Jecheon, Korea;Center for Information Security Technologies(CIST), Korea Univ., Seoul, Korea

  • Venue:
  • EuroPKI 2006 Proceedings of the Third European conference on Public Key Infrastructure: theory and Practice
  • Year:
  • 2006

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Abstract

A cryptography for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set was introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. To overcome this shortage, in 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment. In 2005, Kim et al. proposed key management systems for multilevel security using one-way hash function, RSA algorithm, Poset dimension and Clifford semigroup in the context of modern cryptography. In particular, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders is based on the fact that the computation of a key ideal K0 from an ideal EK0 seems to be difficult unless E is equivalent to O. We, in this paper, show that computing preimages under the bonding homomorphism is not difficult, and that the multilevel cryptosystem based on the Clifford semigroup is insecure and improper to the key management system.