Security guarantees in cryptography typically rely on the computational hardness of solving mathematical problems, as well as the assumption that implementations properly generate values. In this talk, I will discuss several examples of large-scale computations for cryptanalysis of real-world systems, including large factoring and discrete log computations with the number field sieve, data analysis of cryptographic data from Internet-wide scans, and lattice-based cryptanalyses. These problems and algorithms all have quite different structures and pose interesting challenges when run at large scale.
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