Time-Efficient Finite Field Microarchitecture Design for Curve448 and Ed448 on Cortex-M4

The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and pique the interest of academics and engineers aiming at studying and optimizing the schemes. When addressing low-end IoT devices, however, the literature indicates little work on these curves. In this paper, we present an efficient design for both protocols based on Montgomery curve Curve448 and its birationally equivalent Edwards curve Ed448 used for key agreement and digital signature algorithm, specifically the X448 function and the Ed448 DSA, relying on efficient low-level arithmetic operations targeting the ARM-based Cortex-M4 platform. Our design performs point multiplication, the base of the Elliptic Curve Diffie-Hellman (ECDH), in 3,2KCCs, resulting in more than 48% improvement compared to the best previous work based on Curve448, and performs sign and verify, the main operations of the Edwards-curves Digital Signature Algorithm (EdDSA), in 6,038KCCs and 7,404KCCs, showing a speedup of around 11% compared to the counterparts. We present novel modular multiplication and squaring architectures reaching similar to 25% and similar to 35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and similar to 13% and similar to 25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.