Demystifying elliptic curve cryptography: Curve selection, implementation and countermeasures to attacks

Abstract

Elliptic curve cryptography (ECC) has been the main choice for the security experts from some time now. As the IoT has enveloped the world around us; ECC has became more popular as security solution for the resource-constrained devices which covers the physical layer of IoT. Different libraries are available for ECC. In this paper we have discussed various important aspects in the implementation of ECC, such as finite fields, selection of curve model and curves along with the attacks on ECC. Implementation of ECC has been carried out on NIST curve P-256 with ElGamal encryption.

Subject Classification:

• 68U99

Keywords:

• ECC
• Finite fields
• ECDH
• ECDSA
• Curve selection
• security