Shifting Primes: Optimizing Elliptic Curve Cryptography for Smart Things

Abstract

The new generation of devices connected to Internet are moving towards billion of small and smart objects, so-called Smart Things. These Smart Things are destined to manage the security of our houses, watch our health, and optimize the energy consumption of our cities. They bring a new set of opportunities, but they also present high challenges regarding scalability, management, bootstrapping, identity verification and authentication. For that reason, this work is focused on addressing the security requirements for Smart Things providing an optimized family of primes for Elliptic Curve Cryptography(ECC), denominated Shifting Primes. ECC on Smart Things needs special optimizations for the cryptographic primitives that requires a precise study of the instruction set and the number of cycles for those instructions. The modular multiplication is the basic operation, critical for highly constrained microprocessors, in terms of which ECC is built. It is optimized and also analyzed the interaction between partial results in the chain of modular multiplications needed for ECC. This optimizations have been carried out over the MSP430, which is a widely extended microprocessor for Smart Things. MSP430 is featured by not offering hardware multiplier. For that reason, we have defined a special kind of prime numbers, the Shifting Primes. They are featured by offering a very fast multiplication algorithm for ECC through addition and shifting operations for the multiplications. It is presented the full faster multiplication algorithm for Shifting Primes. These results are presenting a lowest time and number of operations for the multiplication in ECC than the existing solutions. Finally, note that the presented primes can be applied also to other similar architectures with fast shifting operation on registers.