New Operation and Problems on Elliptic Curve and Their Application
Masaaki Shirase · 2018
In this paper, a new operation Me(P,Q) or P ⊕ Q and Me-scalar multiplication Pn,Zwith auxiliary Z are defined for P, Q, Z ∈ E(Fp) and n ∈ N, where E is an elliptic curve over Fp. Although (E(Fp),⊕) does not form a group, it is shown that Me-scalar multiplication has properties suitable for constructing cryptosystems such as (Pn,Z)m,Z= (Pm,Z)n,Z. Next, the MeDLP and the MeCDH, which are Me-scalar multiplication version of the ECDLP and the ECCDH, are defined. Last, under the assumption that MeCDH is hard, cryptosystems using Me-scalar multiplication are proposed.