On the hastad's attack to LUC4,6 cryptosystem and compared with other RSA-type cryptosystem

The LUC4,6 cryptosystem is a system analogy to RSA cryptosystem and extended from LUC and LUC3 cryptosystems. Therefore, the security problem of the LUC4,6 cryptosystem is based on integer factorization which is similar to RSA, LUC and LUC3 cryptosystems. The Hastad's attack is one of the polynomial attack which relied on the polynomial structure of RSA-type cryptosystem. In this paper, Hastad's Theorem will be used to solve a system of multivariate modular equations and Coppersmith Theorem will be used to find a root of a modular equation. Thus, the number of plaintexts which are required to succeed the attack can be found