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

• East Asian mathematical journal
• /
• v.33 no.2
• /
• pp.199-216
• /
• 2017

A rational number as operator is eventually that it is considered a mapping. Depending on how selecting domain (the target of operation by rational number) and codomain (including the results of operations by rational number), it is possible to see the rational in two aspects. First, rational numbers can be deal with functions if we choose the target of operation by rational number as a number field containing rationals. On the other hand, if we choose the target of operation by rational number as integral domain $\mathbb{Z}$, then rational numbers can be regarded as partial functions on $\mathbb{Z}$. In this paper, we regard the rational numbers with a view of partial functions, we investigate the theoretical background of the relationship between the multiplication of rational numbers and the composition of rational numbers as operators.

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