Development of a search method of birationally equivalent binary edwards curves for binary weierstrass curves from DSTU 4145-2002

The paper is devoted to the analysis of well-known methods of Edwards elliptic curves search. The suggested method is irrationally equivalent to the elliptic curves in Weierstrass form. The practical aspects of efficient software implementation of search irrationally equivalent curves algorithm are also considered in the paper. Authors describe a proposed modified search algorithm. Software implementation of modified algorithm has allowed finding birationally equivalent Edwards curves to curves from DSTU 4145-2002.