Are "deterrent" algorithms like NFS and Coppersmith's algorithm actually used in practice?

Published: 13/08/2017
Are "deterrent" algorithms like NFS and Coppersmith's algorithm actually used in practice?
Source: CRYPTO.STACKEXCHANGE.COM

It seems like there are a lot of algorithms in number theory which I would classify as "deterrent" algorithms -- for example the various number field sieves for factoring, Coppersmith's algorithm for discrete logarithm -- which effectively serve as a benchmark for the cost of attacking a cryptographic protocol. They have immense value to society by justifying minimum bit sizes needed to make at

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