cryptography - what method or technique is used to generate a random key and public key required in randomized hybrid encryption technique? -

i want use hybrid encryption technique involves combination of aes technique rsa technique encrypting block of data.since technique involves generation of random key encrypting data using aes algorithm , random key encrpyted public key using rsa algorithm. confused algorithm used here generate random key public key. single key generation algorithm used generate both random key public key?? or 2 different methods should use generating these keys??? please clear confusion giving suitable solution.

public / private key pairs related mathematically, , require different algorithm generate them. have specific properties, why need such large key (1024 bits or more) have secure key.

symmetric ciphers such aes use shorter keys because cipher not rely on specific mathematical properties of key itself. that's why can security 128-bit key aes.

typically, architecture you're describing uses aes one-time random session key encrypt bulk data, , private key encrypts aes session key. public/private key pair generated ahead of time , used multiple messages. session key changes message-to-message. (that's basic idea behind pgp, recall.)

if don't understand differences between these elements , how they're used, might suggest rely on already-proven software such gpg, pgp or libraries based on them?