Towards High-performance X25519/448 Key Agreement in General Purpose GPUs

Abstract

Widely used in a large range of Internet security protocols such as TLS/SSL, the key exchange provides a method to establish a shared secret between two parties in unprotected channel. Among the key exchange algorithms, Elliptic Curve Diffie-Hellman is currently preferred and popularized by the industry. The prevailing ECDH employs NIST P Curves as the underlying elliptic curve, however, with the requirement of high performance and questioning of its security, in January, 2016, IRTF officially applied Curve25519/448 to key exchange in RFC 7748, called X25519/448 key exchange protocol. Now many mainstream open-source projects recommend X25519/448 as the default key exchange protocol. The bottleneck of X25519/448 lies in the scalar multiplication, whose performance in traditional CPU cannot serve the rapidly expanding demand in scenes with massive concurrent requests, such as cloud-computing, e-commerce, etc. In this contribution, we accelerate X25519/448 with Graphics Processing Units via various optimizations. The results of X25519/448 in GeForce GTX 1080 respectively reach 2.86 and 0.358 million operations per second, outperforming the previous fastest work by a large margin.