On different models of elliptic curves

Elliptic curves are an important topic of mathematics that has been studied in recent years by a very large group of scientists. Cryptology applications are quite striking. Due to the need in this field, various cryptosystems are involved, and in this seven-part study, different models of elliptic curves are examined. In the first part elliptic curve cryptography is introduced and in the second part Edwards curves and in the third part twisted Edwards curves are examined. In the fourth chapter, a four-level theta model for elliptic curves is introduced. In the fifth chapter, a new theta model for elliptic curves is discussed. In the sixth section, the cost analysis of these models is made and in the last section the cost comparison of some models and conclusion and discussion is made. The study is compilation.