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

Abstract: 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 presentation, 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 our novel modular multiplication and squaring architectures reaching ∼ 25% and ∼ 35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and ∼ 13% and ∼ 25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.

cryptography and securityMathematics

Audience: researchers in the discipline

Florida Atlantic University Crypto Café

Series comments: A seminar series of the FAU crypto group in the mathematics department. We welcome speakers, both online or in person, to join us and discuss their research or job-related opportunities. Beach lovers - come and believe!