![]() Based on this reduction, we speed up the NTT and propose faster, multi-purpose algorithms. We present a new modular reduction technique that is tailored for the special moduli required by the NTT. It is commonly used in cryptographic schemes that are based on the hardness of the Ring Learning With Errors (R-LWE) problem to efficiently implement modular polynomial multiplication. This app also does not contain any links to other apps or the web.The Number Theoretic Transform (NTT) provides efficient algorithms for cyclic and nega-cyclic convolutions, which have many applications in computer arithmetic, e.g., for multiplying large integers and large degree polynomials. This app has no ads or in-app purchases and it does not transmit any data during the operation of the app. New ideas to make this app better are welcome. Some of the other 40 iDevBooks math apps are Column Addition, Long Multiplication, Long Division, Column Subtraction, Visual Multiplication Table, Partial Differences Subtraction, Partial Quotients Division, Partial Sums Addition, Decimal Rounding, etc. IDevBooks math apps have been reviewed and endorsed by, ,, Teachers with Apps, and other respected sites and organizations. There are 3 different themes: black, gray and gold The operands for the current operation can be highlighted The current operation for each step can be hidden The multiplicand can have up to 5 digits If the user presses the wrong button the answer will appear above the keyboard but it will not move. The correct answer will fly to the right place. In the steps the user will multiply or add. The Lattice Multiplication app allows the user to solve a lattice multiplication problem step by step and animates all the steps. Fibonacci presented both the current standard long multiplication and also an originally Indian method called lattice multiplication, which is faster and more compact for working with larger numbers. Ancient Indians and Chinese originally invented some of the algorithms. In this groundbreaking book Fibonacci presented many algorithms for working with Arabic numerals. The method was introduced to Europe in 1202 in Fibonacci's Liber Abaci. All the multiplications are done first and then the additions. A lattice (a grid) guides the calculation. Lattice multiplication is algorithmically equivalent to long multiplication. I am so glad to have come across this great educational tool!" Being able to adjust the level of difficulty to suit their needs is also very motivating for the students. They also provide individualized feedback to each student, with an immediacy that is not always possible through pencil and paper practice. "The math apps by Esa Helttula allow students to practice and reinforce the specific computation strategies taught in class, with as much or as little scaffolding as necessary. ![]() Rita Zeni, Ecole Sandy Hill Elementary, Abbotsford, BC, Canada: It makes multiplying large numbers easier, and allows you to see it all visually" "This was one form of multiplication that I’d never done before, but the app taught me very clearly. The user can solve custom and random multiplication problems with small and large numbers. The app is very easy to use and it has an intuitive interface with customizable colors and other settings. Solving lattice multiplication problems is also excellent times tables practice. This app can be used to teach and study the ancient lattice multiplication method.
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