Topic
Division (mathematics)
About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.
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TL;DR: A new algorithm based on a pattern matching technique for computing multiplication and division in GF(2/sup m/) is presented and an efficient systolic architecture is described for implementing the algorithm which can produce a new result every clock cycle and the multiplication anddivision operations can be interleaved.
Abstract: Finite or Galois fields are used in numerous applications like error correcting codes, digital signal processing and cryptography. The design of efficient methods for Galois field arithmetic such as multiplication and division is critical for these applications. A new algorithm based on a pattern matching technique for computing multiplication and division in GF(2/sup m/) is presented. An efficient systolic architecture is described for implementing the algorithm which can produce a new result every clock cycle and the multiplication and division operations can be interleaved. The architecture has been implemented using 2- mu m CMOS technology. The chip yields a computational rate of 33.3 million multiplications/divisions per second. >
35 citations
35 citations
Patent•
09 Jan 1998
TL;DR: In this article, a modulo exponentiation of polynomials is done by repeated squaring and shifting, and a division circuit built on a linear feedback shift register is provided to perform an efficient modulo squaring of poynomials.
Abstract: Method and apparatus for efficiently producing a delayed version of a maximum length sequence output from a linear feedback shift register. Polynomial (vector) exponentiation is performed instead of matrix exponentiation to calculate the mask coefficients which yield the delayed sequence from the linear feedback shift register. Polynomial (vector) operations are much simpler and faster than the corresponding matrix operations and require substantially less circuitry and computational effort. Modulo exponentiation of polynomials is done by repeated squaring and shifting, and a division circuit built on a linear feedback shift register is provided to perform an efficient modulo squaring of polynomials.
35 citations
Journal Article•
35 citations
TL;DR: This work presents a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics and provides an analytical approximation for the resulting numerically challenging convolution integral.
35 citations