USD$75 解 RSA 512bits

Cryptology ePrint Archive 上面剛好是 2015 年編號 1000 號的論文:「Factoring as a Service」。透過 Amazon EC2 服務以及 CADO-NFS 的幫助,四小時內就可以解出 512bits RSA,而如同作者說的,雖然已經很不安全了,但在許多地方仍然被使用著:

The difficulty of integer factorization is fundamental to modern cryptographic security using RSA encryption and signatures. Although a 512-bit RSA modulus was first factored in 1999, 512-bit RSA remains surprisingly common in practice across many cryptographic protocols. Popular understanding of the difficulty of 512-bit factorization does not seem to have kept pace with developments in computing power. In this paper, we optimize the CADO-NFS and Msieve implementations of the number field sieve for use on the Amazon Elastic Compute Cloud platform, allowing a non-expert to factor 512-bit RSA public keys in under four hours for $75. We go on to survey the RSA key sizes used in popular protocols, finding hundreds or thousands of deployed 512-bit RSA keys in DNSSEC, HTTPS, IMAP, POP3, SMTP, DKIM, SSH, and PGP.

另外也有專案網站:「Factoring as a Service」,程式碼也有放上 GitHub:「Factoring as a Service」。

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