Difference between Symmetric and Asymmetric. Is this answer correct, based on a written test? I asked the following question on a final exam:    


  Symmetric Ciphers (e.g. AES, DES, Blowfish) use up to 256 bit on the
  best case, which are considered strong against brute-force attacks. On
  the other hand, asymmetric cryptography (e.g. RSA, DSA, Elgamal) use a
  higher amount of bits (~2048). Explain the reason of the bit
  difference between Symmetric and Asymmetric Ciphers.


His answer was:


  Asymmetric Ciphers use more bits because generally it uses powers,
  which generates a bit increase. Additionally, Asymmetric Encryption
  requires more processing time than Symmetric, which leads to a higher
  cost on a bit level.


By “powers”, he meant “math powers”. He quotes the following from the internet to support his answer:


  "The algorithm is slow, since it uses math operations which have a high
  cost and works with big key sizes. Part of the problem is on the
  choice of the exponent"


And finally:


  "Although is not mathematically exact, the first operation could be
  accepted as linear since the number of operations is directly
  proportional to the size of both operands. On the other hand, the
  second operation is an exponential type because doubling the input
  size, the number of operations to make does not double, it increases
  exponentially in time."


Although the answer is here, I see that part of his statements are correct, but is he answering the question correctly?
I don't believe he is answering the right question.  You essentially asked "why are public keys so much larger than symmetric keys", and after his first sentence (which started to address the question, but was a bit vague), he tried to answer the distinct question "why are public key operations so much slower" (not that he got the details of that correct; his last sentence appeared to imply that public key operations take an exponential amount of time).