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"
"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?