Shifting primes: Optimizing elliptic curve cryptography for 16-bit devices without hardware multiplier

Abstract

Security for the Internet of Things (IoT) presents the challenge of offering suitable security primitives to enable IP-based security protocols such as IPSec and DTLS. This challenge is here because host-based implementations and solutions are not providing a proper performance over the devices used in the IoT. This is mainly because of the use of highly constraint devices in terms of computational capabilities. Therefore, it is necessary to implement new optimized and scalable cryptographic primitives which can use existing protocols to provide security, authentication, privacy and integrity to the communications. Our research focus on the mathematical optimization of cryptographic primitives for Public Key Cryptography (PKC) based on Elliptic Curve Cryptography (ECC). PKC has been considered, since the IoT requires high scalability, multi-domain interoperability, self-commissioning, and self-identification.

Specifically, this contribution presents a set of optimizations for ECC over constrained devices, and a brief tutorial of its implementation in the microprocessor Texas Instrument MSP430 (Briel, 2000)  [1] (commonly used in IoT devices such as 6LoWPAN, active RFID and DASH7). Our main contribution is the proof that these special pseudo-Mersenne primes, which we have denominated ‘shifting primes’ can be used for ECC primitives with 160-bit keys in a highly optimal way. This paper presents an ECC scalar multiplication with 160-bit keys within 5.4 million clock cycles over MSP430 devices without hardware multiplier. Shifting primes provide a set of features, which make them more compliant with the set of instructions available with tiny CPUs such as the MSP430 and other 8 and 16-bit CPUs.