Undoubtedly, the current developments in the world of technology are very closely related to the basic sciences, and these advances are due to the results that these sciences have achieved and provided to us over the years. Linear algebra and its laws have long solved many technical problems for us, one of which is to perform complex calculations to implement efficient models for encrypting digital data of any kind by performing some techniques in the field of algebra. Linearly, effective steps have been taken to optimize the results obtained. One of the cryptographic techniques is the use of lattice properties, which has recently received a lot of attention and effective measures have been taken in this field. In this article, we demonstrate the very important features of 𝑨 𝟓 lattices, and we introduce a new method for finding the generators of similar sub lattices of 𝑨 𝟓 lattice.