Fast and compact elliptic-curve cryptography

Elliptic curve cryptosystems have improved greatly in speed over the past few years. Here we outline a new elliptic curve signature and key agreement implementation which achieves record speeds while remaining relatively compact. For example, on Intel Sandy Bridge, a curve with about 2250 points produces a signature in just under 52k clock cycles, verifies in under 170k clock cycles, and computes a DiffieHellman shared secret in under 153k clock cycles. Our implementation has a small footprint: the library is under 60kB. Our implementation is also fast on ARM processors, verifying a signature in under 625k Tegra-2 cycles. We introduce faster field arithmetic, a new point compression algorithm, an improved fixed-base scalar multiplication algorithm and a new way to verify signatures without inversions or coordinate recovery. Some of these improvements should be applicable to other systems.