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In other words, it is easier to crack single RSA key by utilizing modern factorization problem solve techniques than build a database and find matching key.Д®C keys rely on different mathematical problem and their key space literally equals to full space (say, ECDSA 256-bit will get you up to 2^256 possible keys and it is still huge). Here is a thread that explains the keyspace for 4096-bi RSA asymmetric key. The database will be extremely huge and its population with known keys will take centuries.Key generation is still computationally expensive and fast key generation will require expensive hardware (clusters, arrays, suporcomputers).Then, is it in theory, possible to have a huge database of all known public keys and keep randomly generating key pairs and checking against the database if any of them match Yes, they will match, because they are tightly related to each other.

If by co-incidence my public key that is generated is the same as a public key of someone else. And for Bitcoin addresses, which run the secp256k1 key through a (net) 160-bit hash, it is quite possible someone will find a duplicate within not too many millenia, though probably not within your lifetime (or mine). For the commonly used ~256-bit curves (secp256r1, secp256k1, X25519/Ed25519) the universe does contain enough energy to break some reasonable number of keys, though the Earth doesn't. Both of these are astronomically unlikely - literally so if you used all the energy in the universe the chance of hitting any target is still much less than the chance of your house being hit by dozens of independent asteroids within one second.Д®ven for RSA 2048, which is much more common today, you improve from 1/2^1005 to 1/2^980 - still not enough to matter.Д®CC, on the other hand, is much smaller because it isn't subject to math-structure attacks like RSA. storing it on paper cards in an old-style library catalog would be costly.ДЄs per the link in Crypt32's answer, the chance that a randomly generated RSA 4096 key matches a particular target is about 1 in 2^4070 with 2^25 targets, it improves to about 1 in 2^4045. This is not large at all for modern database systems and computers, although e.g. They reported 12 million in 2012 adding a generous allowance for growth and rounding up, call it about 32 million (2^25).

This takes some work and a bit of time, but is quite possible. How many known keys there are depends on who does the knowing, but if consider available from public servers on the Internet, several projects have collected more or less all SSL/TLS and/or SSH keys on public Internet servers for various kinds of investigations see for one good example.

Breaking any key from a set by random guessing is indeed 'easier' than breaking a specific key, but not enough to make a difference.

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