Use the Chinese remainder theorem to evaluate x from the following simultaneous congruences:

x ≡ 1 (mod 2);
x ≡ 2 (mod 3);
x ≡ 3 (mod 5).

Calculate gcd(14526, 2568).

(c) Compare and contrast Advanced Encryption Standard (AES) to Data Encryption Standard (DES). For each of the following elements of DES, indicate the comparable element in AES or explain why it is not needed in AES:

• XOR of subkey material with the input to the f function
• XOR of the f function output with the left half of the block
• The f function
• Permutation P 
• Swapping of halves of the block