Accelerating elliptic curve scalar multiplication over GF(2m)GF(2m) on graphic hardwares

• We implement ECC library on GPU covering all parameter types of ECC-based protocols.
• We optimize ECC library by applying the best algorithms and GPU’s characteristics.
• Montgomery ladder is good for computing scalar multiplications using random scalars.
• TNAF-based method is good for computing scalar multiplications using fixed scalar.
• Field multiplication algorithms effect on the library’s throughput and latency.

In this paper, we present PEG (Parallel ECC library on GPU), which is efficient implementation of Elliptic Curve Scalar Multiplication over GF(2m)GF(2m) on Graphic Processing Units. While existing ECC implementations over GPU focused on limited parameterizations such as (fixed scalar and different curves) or (different scalars and same base point), PEG covers all parameter options ((a) fixed scalar and variable points, (b) random scalars and fixed input point, and (c) random scalars and variable points) which are used for ECC-based protocols such as ECDH, ECDSA and ECIES. With GPU optimization concerns and through analyzing parameter types used for ECC-based protocols, we investigate promising algorithms at both finite field arithmetic and scalar multiplication level for performance optimization according to each parameterization. PEG covers ECC implementations over GF(2163)GF(2163), GF(2233)GF(2233) and GF(2283)GF(2283) for 80-bit, 112-bit and 128-bit security on GTX285 and GTX480. PEG can achieve remarkable performance compared with MIRACL, one of the most famous ECC library, running on Intel i7 CPU (2.67 GHz).