• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.1
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• pp.90-96
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• 2011

In this paper, we propose a new discrete logarithm problem(DLP) based on the class semigroups of imaginary quadratic non-maximal orders using the special character of non-invertible ideal and analysis its security. To do this, we first explain the mathematical background explicitly and prove some properties of Cls (O) which relate to constructing the DLP and guaranteeing the security. To test the security of the proposed DLP, we compare the class number of the maximal order with that of the non-maximal order and investigate the unique factorization problems of ideals between class groups of the maximal orders and class semigroups of non-maximal orders to ensure the security of the cryptosystem.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.4
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• pp.737-744
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• 2018

The RSA cryptosystem is a one of the first public-key cryptosystems and is widely used for secure data transmission and electric signature. The security of the RSA cryptosystem is based on the difficulty of factoring large numbers.. Though many studies on finding methods for factoring large numbers are going on, the results of that are all experimental or probabilistic. We, in this paper, construct an algorithm for finding large prime factors of integers without factoring integers using properties of the structure of semigroup of imaginary quadratic order and non-invertible ideal, then propose our methods foe deterministic attack against RSA cryptosystem.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.4
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• pp.605-610
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• 2013

A cryptography for enforcing hierarchic groups 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 the key management systems for using one-way hash function, RSA algorithm, poset dimension and Clifford semigroup in the context of modern cryptography, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders. We, in this paper, show that Kim et al. cryptosystem is insecure in some reasons and propose a revised cryptosystem.