This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.
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Springer
T. Rabin
Pushing the factoring boundary to 768 bits
IACR Crypto
Cryptology

Kleinjung, T., Aoki, K., Franke, J., Lenstra, A., Thomee, E., Bos, J., Gaudry, P., Kruppa, A., Montgomery, P. L., Osvik, D. A., te Riele, H., Timofeev, A.& Zimmermann, P. (2010). Factorization of a 768-bit RSA modulus. In T. Rabin (Ed.), Proceedings of Advances in Cryptology - CRYPTO 2010 2010 (pp. 333–350). Springer.