Lenstra elliptic-curve factorization

Lenstra's elliptic-curve factorization method is an algorithm used to find the prime factors of large numbers. It uses properties of elliptic curves—special mathematical structures—to detect factors more efficiently than traditional methods. By selecting random elliptic curves and performing calculations modulo the number to factor, the algorithm often finds a non-trivial divisor when certain calculations "break down." This approach is especially effective for numbers with small to medium-sized prime factors and has become an important tool in computational number theory and cryptography, helping to break down complex encryption by revealing their underlying prime components.