VLSI and Circuits, Embedded and Hardware Systems Commons^™

Efficient Hardware Architectures For Public-Key Cryptosystems, Mohammadamin Saburruhmonfared

Electronic Thesis and Dissertation Repository

Finite field arithmetic plays an essential role in public-key cryptography as all the underlying operations are performed in these fields. The finite fields are either prime fields or binary fields. Binary field elements can mainly be represented on a polynomial basis or a normal basis (NB). NB representation offers a simple squaring operation, especially in hardware. However, multiplication is typically complex, and a particular subset of NB called Gaussian Normal Basis (GNB) features an efficient multiplication operation used in this work. The first part of this thesis has focused on improving finite field arithmetic architectures over GNB. Among different arithmetic …