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Arithmetic Units For The Elliptic Curve Cryptography With Concurrent Error Detection Capability, Arash Hariri

Electronic Thesis and Dissertation Repository

The elliptic curve cryptography is an important branch in public-key cryptography. In this thesis, we consider the elliptic curve cryptography over binary extension fields from two different points of view. First, we investigate the underlying arithmetic operations in the elliptic curve cryptography. The main arithmetic operation is the scalar multiplication. This operation is based on two elliptic curve operations, known as the point addition and point doubling. Implementing these two elliptic curve operations requires finite field arithmetic, specifically, finite field addition, multiplication, squaring, and inversion. We focus on two finite field operations, namely finite field multiplication and squaring. For the …