A research team from the University of California, San Diego (UCSD) and Inria Nancy/University of Lorraine made a significant breakthrough in cryptography this month. They demonstrated a new method that allows the forging of 1024-bit RSA signatures without needing to factor the public key—essentially, without finding the original two prime numbers used to create it. This discovery, named eNFS, has surprised the cybersecurity community, as it dramatically reduces the computational effort required to break this long-used key size. Traditionally, breaking an RSA key has been thought to depend on solving the difficult mathematical problem of factoring a large number. The eNFS method challenges this assumption by offering a more efficient approach. The eNFS method is inspired by earlier theoretical work from 2007 by researchers Joux, Naccache, and Thomé. It belongs to the family of Generalized Number Field Sieve (GNFS / SNFS) algorithms, which are typically used for numbers with special properties. This new method allows the forging of signatures with a computational complexity similar to the Special Number Field Sieve (SNFS), usually used for numbers with rare and weak structures. Instead of trying to factor the key directly, the algorithm uses temporary access to a "signature" or "plaintext decryption" oracle—essentially a service that can sign or decrypt data. This access allows the attacker to generate enough data to forge any signature offline, without ever recovering the private key or its prime factors. The attack requires only a short period of access to an RSA signature or decryption service that lacks modern security measures like masking or deterministic padding. During this phase, the attacker makes a minimal number of requests—232 in the experiment—to the oracle. Once this data is collected, the attacker can disconnect and generate any signature offline. Normally, factoring a 1024-bit RSA key would take between 500,000 and 1,000,000 CPU years. The eNFS method reduced this to just 1,380 CPU years for the precomputation phase, with generating new signatures taking only 180 CPU years. This was achieved using a standard university computing cluster, and the team used a real commercial hardware security module (HSM) as the oracle, showing that even supposedly secure components can be compromised. The implications of this research are significant. While the immediate impact on everyday internet users is currently limited, the demonstration shows that 1024-bit RSA keys are no longer secure and should be phased out. Web standards like those from the National Institute of Standards and Technology (NIST) have already discouraged their use in favor of larger keys like RSA-2048. Modern TLS implementations are not vulnerable to this specific attack because they avoid the types of oracles used. However, systems still using 1024-bit RSA keys or outdated signature schemes must be urgently updated to prevent potential security breaches. Cybersecurity experts now need to assess systems not only based on the theoretical difficulty of factoring numbers but also on how cryptographic services process and expose raw signatures.