Factoring in birth day attacks and all that, with 256-bit elliptic curve cryptography, what is the maximum number of accounts that are secure? It isn't 2^256 since then any time you generate a random number you find a used account. Birth day paradox and all that, what is the upper limit of how many accounts Ethereum actually supports? (Not at all factoring in transactions per second limits, just asking from a cryptography PoV. )
Cross posted this to a cryptography site too. Somewhere around a trillion trillion accounts.
(accounts)^2/2^bitsize/2 = 2^(log2(accounts)*2-bitsize-1), with a trillion trillion accounts probability of a collision becomes 10^-30, requires something like a billion seconds to find a collision when using all compute power on Earth, if I got that right. https://crypto.stackexchange.com/questions/85861/cryptographic-limit-to-total-accounts-in-secp256k1/85868#85868