@article{LIU2005, 
author = {Duo LIU and Tao SONG and Yiqi DAI},
title = {Isomorphism and Generation of Montgomery-Form Elliptic Curves Suitable for Cryptosystems},
year = {2005},
journal = {Tsinghua Science and Technology},
volume = {10},
number = {2},
pages = {145-151},
keywords = {cryptography, elliptic curve, isomorphism, Montgomery-form},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(05)70046-8},
doi = {10.1016/S1007-0214(05)70046-8},
abstract = {Many efficient algorithms of Montgomery-form elliptic curve cryptology have been investigated recently. At present, there are no reported studies of the isomorphic class of the Montgomery-form elliptic curve over a finite field. This paper investigates the isomorphism of Montgomery-form elliptic curves via the isomorphism of Weierstrass-form elliptic curves and gives a table of (nearly) all the forms of Montgomery-form elliptic curves suitable for cryptographic usage. Then, an algorithm for generating a secure elliptic curve with Montgomery-form is presented. The most important advantages of the new algorithm are that it avoids the transformation from an elliptic curve’s Weierstrass-form to its Montgomery-form, and that it decreases the probability of collision. So, the proposed algorithem is quicker, simpler, and more efficient than the old ones.}
}