International Association
for Cryptologic Research

In this work we present the $\\lambda$-coordinates, a new system for

representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and timing results of our software implementation over the field $F_{2^{254}}$. As a result, we improved the known speed records for protected/unprotected single/multi-core software implementations of the random-point elliptic curve scalar multiplication at the 128-bit security level. When implemented on a Sandy Bridge 3.4GHz Intel Xeon processor, our software is able to compute a single/multi-core unprotected scalar multiplication in 72,300 and 47,900 clock cycles, respectively; and a protected single-core scalar multiplication in 114,800 cycles. These numbers improve by 2% on the newer Ivy Bridge platform.