Recently, considerable research has been performed in cryptography and security to
optimize the area, power, timing, and energy needed for the point multiplication operations …

In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly
advanced. ECC, with much smaller key sizes, offers equivalent security when compared to …

In this work, we present new arithmetic formulas for a projective version of the affine point
representation (x, x+ y/x),(x, x+ y/x), for x ≠ 0, x≠ 0, which leads to an efficient computation …

In this paper, we introduce an FPGA-based processor for elliptic curve cryptography on
Koblitz curves. The processor targets specifically to applications requiring very high speed …

The availability of a new carry-less multiplication instruction in the latest Intel desktop
processors significantly accelerates multiplication in binary fields and hence presents the …

Fast and high-performance computation of finite-field arithmetic is crucial for elliptic curve
cryptography (ECC) over binary extension fields. In this brief, we propose a highly parallel …

The irreducible polynomials recommended for use by multiple standards documents are in
fact far from optimal on many platforms. Specifically they are suboptimal in terms of …

We design a state-of-the-art software implementation of field and elliptic curve arithmetic in
standard Koblitz curves at the 128-bit security level. Field arithmetic is carefully crafted by …

In this work we present the λ-coordinates, a new system for representing points in binary
elliptic curves. We also provide efficient elliptic curve operations based on the new …

The availability of a new carry-less multiplication instruction in the latest Intel desktop
processors significantly accelerates multiplication in binary fields and hence presents the …