coppersmith

The core difference between the batch NFS and Coppersmith is how relations on the rational side are handled.

The number field sieve came from independent efforts, started by ElGamal [6], Coppersmith et al [7], and Pollard [8].

Bernstein and Coppersmith suggested a method, based on lattice reduction, that reduces RSA keys to up to 1/3 of their size [5].

Because it wasn't Coppersmith who got rich off the telephone, it was Alexander Graham Bell and his investors, some 10 years later.

A related recent work is the Mersenne factorization factory [1], which also used Coppersmith in a clever way to save time on multiple related factorizations.

In reality, Don Coppersmith was right up there as well.

Tell that to Don Coppersmith or Daniel Bleichenbacher.

I don't think Coppersmith is a very good example here.

But it's virtually always as part of teams of otherwise well-established cryptography researchers, and it's clearly not of the same kind as say Joan Daemen or Daniel Bleichenbacher or Don Coppersmith or Philip Rogaway.

That number is commonly cited as a result of changes the NSA made to DES, which later suggested (and Don Coppersmith openly confirmed) they knew about differential cryptanalysis 20 years before Shamir published anything about it.

The Coppersmith–Winograd algorithm, on the other hand, is probably "strictly of theoretical interest" for the time being...

Here's the most astounding part to me: "[Rubin Xu] decided to use Coppersmith's Attack[1] to derive the private exponent.

The article on "Coppersmith%27s_Attack" against RSA, for example, is seemingly forced to cite a summary paper.

Similarly, there is a "discrete logarithm factory" method, based on Coppersmith's factorization factory, but that also has very large initial costs that make it not very attractive in practice.

So you can see that Coppersmith's GF(2^n) trick never factored into the number field sieve.

Generally the block Lanczos variant used in practice is Montgomery's [1], though, not Coppersmith's.

Coppersmith always comes into my head because of that thing Schneier wrote about him being the world's cleverest cryptanalyst in _Applied Cryptography_.