Elliptic curve point multiplication in GF(2ⁿ) using polynomial residue arithmetic

Elliptic Curve Point Multiplication i. The main operation employed in all elliptic curve cryptosystems, as it form. The basis oy the Elliptic Curve Discrete Logarithm Problem. Therefore. The efficient realization of an Elliptic Curve Point Multiplier is of fundamental importance, as its performance is decisive for the performance oy the overall cryptosystem. This work present. The first practical implementation of an Elliptic Curve Point Multiplier in GF(2ⁿ) using Polynomial Residue Arithmetic. Unlik. The typical representation of GF(2ⁿ) elements as polynomials in GF(2)[x] of degree at most n -1, data are represented as their remainder modulo a set of L pairwlse prime polynomials m1, m2,...., m_L of degree w and such that Lw > 2n. The methodology for incorporating Polynomial Residue Arithmetic i. The elliptic curve point addition and doubling algorithms, as well at the VLSI architecture oy the proposed point multiplier are analyzed, thus forming an interesting alternative to Elliptic Curve Cryptography realization.