Lenstra elliptic-curve factorization
Lenstra elliptic-curve factorization is a technique for solving an equation called a "diophantine equation". A diophantine equation is a type of equation that has two or more variables, and these variables can represent numbers. The Lenstra elliptic-curve factorization technique uses curves, called elliptic curves, to help solve these equations.
To understand how this works, first imagine drawing a line on a piece of paper. This line is like an equation that has two variables. If we try to draw another line on the same paper, our goal is to try to make it so that the two lines intersect-- which means that they have the same values of the variables.
Elliptic curves work the same way. An elliptic curve is a special kind of equation, like the line on the paper, that has two variables. We try to use these equations to find the intersection point of two curves, which means that they have the same values of the two variables. With Lenstra elliptic-curve factorization, we can use these two equations to solve for the two variables and this can help us solve the diophantine equation.
To understand how this works, first imagine drawing a line on a piece of paper. This line is like an equation that has two variables. If we try to draw another line on the same paper, our goal is to try to make it so that the two lines intersect-- which means that they have the same values of the variables.
Elliptic curves work the same way. An elliptic curve is a special kind of equation, like the line on the paper, that has two variables. We try to use these equations to find the intersection point of two curves, which means that they have the same values of the two variables. With Lenstra elliptic-curve factorization, we can use these two equations to solve for the two variables and this can help us solve the diophantine equation.