We now analyze the security of DES double encryption (2DES) by doing a cost-estimate: 2DES(x) = DESK₂(DESK₁ (x))

1. First, let us assume a pure key search without any memory usage. For this purpose, the whole key space spanned by K₁ and K₂ has to be searched. How much does a key-search machine for breaking 2DES (worst case) in 1 week cost? In this case, assume ASICs which can perform 10⁷ keys per second at a cost of $5 per IC. Furthermore, assume an overhead of 50% for building the key search machine.