Factorization of a 768-Bit RSA Modulus

By T. Kleinjung, Kazumaro Aoki, J. Franke, A. Lenstra, Emmanuel Thomé, Joppe W. Bos, P. Gaudry, A. Kruppa, P. L. Montgomery, Dag Arne Osvik and 3 more. Annual International Cryptology Conference, 2010

506 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Information Systems

View Paper: https://www.semanticscholar.org/paper/db55b938d8c957cdb2af21ce91627403afb7db4a

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Citations in the corpus

Analysis of the HTTPS certificate ecosystem (2013, unknown): “large distributed computing efforts [20].”
Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice (2015, unknown): “3We would lower the smoothness bounds compared to the parameters in [29].”
A Review on the Use of Blockchain for the Internet of Things (2018, background): “A 2048-bit key is the minimum size considered secure, since 768-bit and 1024-bit RSA implementations were broken in 2010 [109], [110].”
Toward the first quantum simulation with quantum speedup (2017, background): “of RSA-768 that was achieved classically in 2009 (36).”
The First Collision for Full SHA-1 (2017, background): “The number of single instructions to have been executed is estimated to be of the order of 2(67) [22](6).”
Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices (2012, background): “No one has been publicly known to factor a well-generated 1024-bit RSA modulus; the largest known factored modulus is 768 bits, which was announced in December 2009 after a multi-year distributed-computing effort [28].”
How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2019, background): “The best published academic record is the factorization of a 768 bit RSA modulus in 2009, see [44] for details.”
Accountable Virtual Machines (2010, background): “In December 2009, factoring a 768-bit number took almost 2,000 OpteronCPU years [3], so this key length should be safe for gaming purposes for some time to come.”
Formal certification of code-based cryptographic proofs (2009, methodology): “1993] is currently the most efficient way of factoring large composite integers like RSA moduli; it has been used to factor several RSA moduli from the RSA Factoring Challenge, including the 512-bit RSA-155 number and the largest (non-special) integer factored with a general-purpose algorithm, the 7”
Quantum algorithms: an overview (2015, unknown): “As a more speci(cid:12)c comparison than the above asymptotic runtimes, in 2010 Kleinjung et al. [57] reported classical factorisation of a 768-bit number, using hundreds of modern computers over a period of two years, with a total computational e(cid:11)ort of (cid:24) 10 20 operations.”