A two part cryptography question:

a) A DES cipher takes a 56-bit long key. An attacker has a computing machine that performs 1/10 of a trillion (10^11) DES decryptions per second. What is the average time required, in hours, for the attacker to brute force search for the key to break the DES cipher?

b) Suppose the decryption takes the same processing time for DES and an ideal block cipher. How long should the key be for the ideal block cipher to have greater resistance against a brute force attacker?