Abstract: This paper presents a novel FPGA based method to implement a repeated squared-and-multiply algorithm in polynomial rings. The repeated square-and-multiply algorithm for exponentiation is ...

Algorithms have been used throughout the world’s civilizations to perform fundamental operations for thousands of years. However, discovering algorithms is highly challenging. Matrix multiplication is ...

The square-and-multiply algorithm is a widely used technique for efficient exponentiation, especially in cryptographic applications. While the algorithm offers a general-purpose solution with ...

Multiplication of two numbers is easy, right? At primary school we learn how to do long multiplication like this: Methods similar to this go back thousands of years, at least to the ancient Sumerians ...

This summer, battle lines were drawn over a simple math problem: 8 ÷ 2(2 + 2) = ? If you divide 8 by 2 first, you get 16, but if you multiply 2 by (2 + 2) first, you get 1. So, which answer is right?