Binary Edwards Curves for Intrinsically Secure ECC Implementations for the IoT

International audienceEven if recent advances in public key cryptography tend to focus on algorithms able to survive the post quantum era. At present, there is a urgent need to propose fast, low power and securely implemented cryptography to address the immediate security challenges of the IoT. In this document, we present a new set of Binary Edwards Curves which have been defined to achieve the highest security levels (up to 284-bit security level) and whose parameters have been defined to fit IoT devices embedding 32-bit general purpose processors. We optimized the choice of the point generator with the w-coordinate to save a multiplication in the addition and doubling formulae. We manage to compute one step of the Montgomery Ladder in 4 multiplications and 4 squares. On top of the performance benefits, cryptography over such curves have some intrinsic security properties against physical attacks