I am generating large prime numbers to create a cyclic group for ElGamal encryption, I can specify the bit-length n but want to limit the size because this will ultimately allow me to limit the amount of data passed through external channels.
Also the data being protected has an extremely short time-value vector meaning after a short amount of time the data will become useless to anyone who might manage to decrypt or get access to it(Not sure if there is an official word for that).
What size of a prime number should be used for the cyclic group in this circumstance. The ElGamal keys themselves will also be highly temporary in this setup(can be thrown away almost immediately after a few messages). Is 2048 bit necessary?
Maybe another way of phrasing it:
How much time can
n bitlength of an ElGamal cipher-text (assuming the encrypted data is a large mostly random string) buy me(Assuming there is an attacker) before the attacker can potentially crack the encryption? What are some estimates for bitlength n as relating to crack time?