How does not knowing the factors of a large number hide information?
How have we not run out of numbers used to generate private and public keys? There's only so many prime numbers that exist within a 2048-bit number space. And the larger the number the less likely it is to be a prime.
When 2048-bits become unsafe do we just go to something like 4096-bits? Is that the name of the game? Just increase keep increasing the key size? What's the downside, that it takes more time to legitimately use these keys every time you want to encrypt and decrypt a message?
When i'm generating a private key, am I finding two huge prime numbers then multiplying them together to get an even bigger number that takes people a long time to figure out what the two prime factors are?
Obviously there are some fundamental mathematical concepts that I'm not getting that make these questions seem rather stupid.
How have we not run out of numbers used to generate private and public keys? There's only so many prime numbers that exist within a 2048-bit number space. And the larger the number the less likely it is to be a prime.
When 2048-bits become unsafe do we just go to something like 4096-bits? Is that the name of the game? Just increase keep increasing the key size? What's the downside, that it takes more time to legitimately use these keys every time you want to encrypt and decrypt a message?
When i'm generating a private key, am I finding two huge prime numbers then multiplying them together to get an even bigger number that takes people a long time to figure out what the two prime factors are?
Obviously there are some fundamental mathematical concepts that I'm not getting that make these questions seem rather stupid.
