Elliptic net and its cryptographic application

摘要

Elliptic net is a generalization of elliptic divisibility sequence and in cryptography field, most cryptographic pairings that are based on elliptic curve such as Tate pairing can be improved by applying elliptic nets algorithm. The elliptic net is constructed by using n dimensional array of values in rational number satisfying nonlinear recurrence relations that arise from elliptic divisibility sequences. The two main properties hold in the recurrence relations are for all positive integers m>n, h_(m+n)h_(m-n)=h_(m+1)h_(m-1)h_n~2 - h_(n+1)h_(n-1)h_m~2 and h_n divides h_m whenever n divides m. In this research, we discuss elliptic divisibility sequence associated with elliptic nets based on cryptographic perspective and its possible research direction.