General Number Field Sieve

The General Number Field Sieve (GNFS) is the most advanced algorithm for factoring large integers, especially those used in encryption. It works by translating the problem of breaking down a big number into smaller, more manageable pieces within complex mathematical structures called number fields. The process involves multiple steps: selecting polynomials, finding smooth numbers (numbers with small factors), and combining these results to uncover the original factors. GNFS’s complexity makes it computationally intensive and suitable mainly for very large numbers, like those used in modern cryptography, ensuring the security of digital communications.