High-speed Curve25519 on 8-bit, 16-bit, and 32-bit microcontrollers

This paper presents new speed records for 128-bit secure elliptic-curve Diffie-Hellman key-exchange software on three different popular microcontroller architectures. We consider a 255-bit curve proposed by Bernstein known as Curve25519, which has also been adopted by the IETF. We optimize the X25519 key-exchange protocol proposed by Bernstein in 2006 for AVR ATmega 8-bit microcontrollers, MSP430X 16-bit microcontrollers, and for ARM Cortex-M0 32-bit microcontrollers. Our software for the AVR takes only 13 900 397 cycles for the computation of a Diffie-Hellman shared secret, and is the first to perform this computation in less than a second if clocked at 16MHz for a security level of 128 bits. Our MSP430X software computes a shared secret in 5 301 792 cycles on MSP430X microcontrollers that have a 32-bit hardware multiplier and in 7 933 296 cycles on MSP430X microcontrollers that have a 16-bit multiplier. It thus outperforms previous constant-time ECDH software at the 128-bit security level on the MSP430X by more than a factor of 1.2 and 1.15, respectively. Our implementation on the Cortex-M0 runs in only 3 589 850 cycles and outperforms previous 128-bit secure ECDH software by a factor of 3.