symmetric-key vs asymmetric-key encryption

Symmetric-key encryption (secret key encryption) is different from asymmetric key encryption (public key encryption) in that with symmetric-key encryption, one key is used for both encryption and decryption whereas with asymmetric key encryption, complementary keys are used for encryption (a public key) and decryption (a private key).
An example of symmetric-key encryption is Vernam cipher (one –time pad). It was considered secure because an attacker could only guess what the randomly generated key was because there was no frequency in the ciphertext. In order to crack the encrypted text, the attack could have possibly intercepted the key beforehand as it was being distributed from the sender to the receiver, as new keys are needed for every message. Symmetric key encryption has the advantage of being secure and fast but has the predicament of having to find ways to distribute new keys, which can be very tedious.
An example of an asymmetric-key algorithm is RSA, which uses modular arithmetic. It is secure because it is considered difficult to use the public key and modulus to find the private key. Yet as with integer factorization, with is considered computationally hard, there is no proof that it is in fact that difficult. The capability to crack RSA systems grow by 13-14 bits annually. Using asymmetric-key encryption has made key distribution simpler, but the encryption and decryption process slower, the larger keys are needed, and possible spoofing of public keys by attackers trying to pretend they are the sender or receiver.