Fast and Secure Unified Field Multiplier for ECC Based on the 4-Segment Karatsuba Multiplication

In this paper we introduce an accelerator for the ECC kP operation in two different types of Galois fields i.e. GF(p) and GF(2n). In order to ensure fast execution of the multiplication in both cases we integrated the carry bit separation technique to speed-up the multiplication in GF(p). The two most important contributions of this paper are that the partial multiplier applied is used for both types of Galois field and the second one is that our design is resistant against Horizontal Collision Correlation Analysis. The latter was verified in 20 test runs per supported elliptic curve.