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You suggested ECC over RSA, implying that ECC offers greater security than RSA in the context of easy prime factorization. ECC's security relies on the hardness of the discrete logarithm. Yet, both prime factorization and the discrete logarithm are both special cases of the hidden subgroup problem over an Abelian group. In short, cracking RSA means cracking ECC, too.

Am I wrong? Were you just joking?

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@tptacek

> I believe you to be wrong about the idea that tenably factoring 1024 or 2048 bit moduli implies a solution to the elliptic curve discrete modulus problem

Probably. This mathy stuff is way over my head. I'm just repeating what I read in Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer [1] published by Peter W. Shor on behalf of AT&T Research in 1995. Supposedly his proof is valid, predicated on the existence of quantum computers. Quantum computers actually exist [insert epistemological joke here].

[1] https://arxiv.org/abs/quant-ph/9508027v2

You are talking about quantum attacks, whereas tptacek is talking about classical attacks.

If I understand your argument properly, then I believe you to be wrong about the idea that tenably factoring 1024 or 2048 bit moduli implies a solution to the elliptic curve discrete modulus problem, yes.

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