Y.: Memory-Constrained Implementations of Elliptic Curve Cryptography in Co-Z Coordinate Representation

Abstract. It has been recently shown that sharing a common coordi-nate in elliptic curve cryptography implementations improves the per-formance of scalar multiplication. This paper presents new formulæ for elliptic curves over prime fields that provide efficient point addition and doubling using the Montgomery ladder. All computations are performed in a common projective Z-coordinate representation to reduce the mem-ory requirements of low-resource implementations. In addition, all given formulæ make only use of out-of-place operations therefore insuring that it requires no additional memory for any implementation of the under-lying finite-field operations whatsoever. Our results outperform existing solutions in terms of memory and speed and allow a fast and secure im-plementation suitable for low-resource devices and embedded systems