ON THE ARITHMETIC OF ENDOMORPHISM RING End(Zp² x Zp) AND ITS RSA VARIANTS.

Bergman (1974) found that for any prime number p, the endomorphism ring End(Z_p x Z_p²) is a semilocal ring which has p5 elements and can not be embedded in matrices over any commutative ring. Later on, Climent et al. (2011) found that each element of endomorphism ring End(Z_p x Z_p²) can be identified as a two by two matrix of Ep where the first and the second row entries belong to Z_p and Z_p² respectively. By this characterization, Long D. T., Thu D. T., and Thuc D. N. constructed a new RSA variant based on End(Z_p x Z_p²) (2013). In this paper, we state the characteristic of the endomorphism ring End (Z_p² x Z_p) and the RSA analogue cryptosystem based on it. [ABSTRACT FROM AUTHOR]