The Number Field Sieve is an advanced algorithm used for integer factorization, particularly effective for large numbers. It operates by finding a number field and a polynomial that help in identifying smooth numbers, which are integers that factor completely over a small set of prime numbers. This method is especially useful for numbers with hundreds of digits. This algorithm is one of the fastest known for factoring large integers, surpassing earlier methods like the Quadratic Sieve. It plays a significant role in cryptography, as many encryption systems, such as those based on RSA, rely on the difficulty of factoring large numbers for security.