# Question on recovering a key in the algorithm

Let $E$ be a block cipher that has block size and key size both equal to 64 bits. Let $E'$ be a block cipher that has 64-bit block size and is defined as follows:

For a 128 bits key $K \mathbin\Vert K'$ where $K$ and $K'$ are of 64 bits and a given 64-bit plaintext block $P$, we defined

$$E'_{(K,K')}(P)=E_K(P) \oplus K'$$

Suppose I can perform a brute force attack on $E$ to recover the key in a known plaintext attack. Can I recover the corresponding encryption key if I have access to more than one plaintext/ciphertext pair for $E'$? Why?

• I guess my goal is to obtain E(P), and get K via E(P). But I have difficulty in getting E(P). What should I do? Could you give me some hints? – KengoTokukawa Dec 8 '17 at 16:03
• Hint: Think about what "a brute force attack on $E$" actually involves. If you can do that, what else could you do? – Ilmari Karonen Dec 9 '17 at 2:51