Cryptology ePrint Archive paper 2026/2131 (“Forging 1024-bit RSA signatures in nearly SNFS time”; Laura Shea, Miro Haller, Adam Suhl, Nadia Heninger, Emmanuel Thomé) and Ars Technica (Dan Goodin, 24 September 2026) describe a classical-computing signature-forgery method that breaks RSA without factoring the modulus — building on an under-appreciated 2007 Joux–Naccache–Thomé oracle algorithm. Practical demonstration: forging against deprecated 1024-bit RSA took a handful of months on an academic CPU cluster, far below nation-scale GNFS factoring estimates for that size.

Authors and independent cryptographers (quoted in Ars) stress widely deployed RSA-2048+ implementations remain practically safe for now, but the result is a conceptual break from the long-held “RSA security ≈ factoring hardness” assumption and further argues against any remaining 1024-bit RSA. Peer review pending. (sources: IACR ePrint 2026/2131; Ars Technica)

Correction (01 Nov 2026): the card is now dated 22 September 2026, when the paper was approved on the Cryptology ePrint Archive (received 20 September), instead of 24 September, the date of Ars Technica's coverage. (source: IACR ePrint 2026/2131)