Avoiding Side-Channel Attacks by Computing Isogenous and Isomorphic Elliptic Curves

Smart cards are being attacked increasingly more, due to their numerous uses and the valuable information stored inside. For this reason, efficient and secure cryptosystems need to be designed. The main problem is that smart cards are resource constrained. Moreover, they are vulnerable to side-channel attacks. In this paper, we use an algorithm to compute side-channel-resistant alternatives to the curves given in the NIST standard and to the new elliptic curves recently presented by Microsoft Research. The algorithm does this by computing isogenous and isomorphic elliptic curves. © 2018, Springer International Publishing AG, part of Springer Nature.