author        = {Michael Hutter and Marc Joye and Yannick Sierra},
  title         = {Memory-Constrained Implementations of Elliptic Curve Cryptography in Co-Z Coordinate Representation},
  booktitle     = {Progress in Cryptology -- AFRICACRYPT 2011, 4th International Conference on Cryptology in Africa, Dakar, Senegal, July 5-7},
  year          = {2011},
  editor        = {Abderrahmane Nitaj and David Pointcheval},
  volume        = {6737},
  series        = {Lecture Notes in Computer Science},
  pages         = {170--187},
  publisher     = {Springer},
  keywords      = {Public-key cryptography, elliptic curves, co-Z coordinates, out-of-place formulae, Montgomery ladder, embedded systems.},
  url           = {http://www.springerlink.com/content/v48358k011x82311/},
  abstract      = {It has been recently shown that sharing a common coordinate in elliptic curve cryptography implementations improves the performance of scalar multiplication. This paper presents new formulae 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 memory requirements of low-resource implementations. In addition, all given formulae make only use of out-of-place operations therefore insuring that it requires no additional memory for any implementation of the underlying finite field operations whatsoever. Our results outperform existing solutions in terms of memory and speed and allow a fast and secure implementation suitable for low-resource devices and embedded systems.}