Abstract
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.
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