Computing the Modular Inverse of a Polynomial Function over GF(2(superscript P)) Using Bit Wise Operation

Rajaram Ramasamy ； Amutha Prabakar Muniyandi

《International Journal of Network Security》 10卷2期 (2010/03) Pp. 107-113

https://doi.org/10.6633/IJNS.201003.10(2).04

並列摘要

Most public key crypto systems use finite field modulo arithmetic. This modulo arithmetic is applied on real numbers, binary values and polynomial functions. The computation cost is based on how it works with minimum use of scarce resources like processor and memory We have implemented the determination of the multiplicative in-verse of a polynomial over GF(2(superscript p)) with minimum computational cost. The ”Extended Euclidean Algorithm” (EEA) has been demonstrated to work very well manually for integers and polynomials. However polynomial manipulation cannot be computerized directly. We have implemented the same by using simple bit wise shift and XOR operations. In small applications like smart cards, mo-bile devices and other small memory devices, this method works very well. To the best of our knowledge, the pro-posed algorithm seems to be the first, efficient and cost effective implementation of determining the multiplicative inverse of polynomials over GF(2(superscript p)) using computers. As this is a pioneering work, the results could not be compared with that of any previous work.

並列關鍵字

Advance encryption standard ； extended Euclidean algorithm ； multiplicative inverse