Completing the Complete ECC Formulae with Countermeasures

Abstract

This work implements and evaluates the recent complete addition formulae for the prime order elliptic curves of Renes, Costello and Batina on an FPGA platform. We implement three different versions:(1) an unprotected architecture; (2) an architecture protected through coordinate randomization; and (3) an architecture with both coordinate randomization and scalar splitting in place. The evaluation is done through timing analysis and test vector leakage assessment (TVLA). The results show that applying an increasing level of countermeasures leads to an increasing resistance against side-channel attacks. This is the first work looking into side-channel security issues of hardware implementations of the complete formulae.

Keywords

• elliptic curve cryptography
• FPGA
• Weierstrass curves
• complete formulas
• side-channel attacks and countermeasures