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Binary Edwards Curves for Intrinsically Secure ECC Implementations for the IoT

: Even 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.