Cache sizing for low-energy Elliptic Curve Cryptography

Public-key (asymmetric) cryptography (PKC) is one the pillars of secure communication, since it includes user authentication, key exchange, and digital signatures. PKC dominates energy consumption for transactions shorter than 100KB. Elliptic Curve Cryptography (ECC) allows for shorter key and signature sizes while maintaining the same security level as other PKC algorithms. Since ECC algorithms become more computationally expensive with growing key sizes and since many communicating artifacts are battery-powered devices (e.g. smartphones, smart sensors, and implantable medical devices), secure communication requires energy-efficient ECC as the security level raises and/or as transaction length shrinks. That is why this paper breaks down the energy spent in the memory system for full-software ECC implementations running in a 32-bit RISC processor under growing cache sizes (from 1KB to 16KB) and for the different levels of security provided by distinct elliptic curves (P224, P256/P25519, P384, and P521). We report the ideal cache sizes for each elliptic curve when targeting a 32nm technology node. We show that energy-efficient ECDH requires an instruction cache of around 8KB (or larger) and a data cache or scratchpad at least 4 times as small. We also show that the adoption of P25519, instead of P256, leads to 15 times less energy consumption in the memory system and half the required cache capacity, while keeping the same level of security.