My point was essentially that key-length could have unintended side-effects.
E.g. if you were to have some rainbow table approach, e.g. in theory larger key size would mean more possible key combinations, meaning more expensive space complexity, and harder-to-crack keys. Factoring a key is not necessary if you already know the factors, a hashtable has O(log(N)) complexity. If you implement some custom FPGA hardware and a nice database its not too difficult to imagine some specialized operation storing off generated public keys to their corresponding private key pairs, and the power costs are rather low.
Of course due to combinatorics the size of this output space is rather large, despite the fact that the distribution of primes shrinks as they grow larger, but the argument is about factoring a single number, not about efficiently computing primes and their common multiples. Counter to the article, it completely obviates the need to hide your power bill, as you can cache every single computation from the past 30+ years...
To bring it back to what I was saying, the difficulty of brute-forcing RSA (or other schemes) is potentially irrelevant to the cost of obtaining a solution, and higher bit-length key-pairs offer some hedge against that possibility. It seems pretty relevant to the question "how secure is RSA" to me.
My point was essentially that key-length could have unintended side-effects.
E.g. if you were to have some rainbow table approach, e.g. in theory larger key size would mean more possible key combinations, meaning more expensive space complexity, and harder-to-crack keys. Factoring a key is not necessary if you already know the factors, a hashtable has O(log(N)) complexity. If you implement some custom FPGA hardware and a nice database its not too difficult to imagine some specialized operation storing off generated public keys to their corresponding private key pairs, and the power costs are rather low.
Of course due to combinatorics the size of this output space is rather large, despite the fact that the distribution of primes shrinks as they grow larger, but the argument is about factoring a single number, not about efficiently computing primes and their common multiples. Counter to the article, it completely obviates the need to hide your power bill, as you can cache every single computation from the past 30+ years...
To bring it back to what I was saying, the difficulty of brute-forcing RSA (or other schemes) is potentially irrelevant to the cost of obtaining a solution, and higher bit-length key-pairs offer some hedge against that possibility. It seems pretty relevant to the question "how secure is RSA" to me.