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Is there a way of preventing meet-in-the-middle attack when using double-encryption?

pf flag

Let's suppose I encrypt something with AES-256 two times using 2 different keys wanting to achieve 512-bits of security. I know that this scheme will in fact give me only 257-bits of encryption strength due to Meet-in-the-middle attack.

Is there a lightweight method of preventing this without having to encrypt three times for achieving twice the strength of a single key?

I have been thinking on adding a XOR operation between two encryption operations, of course a block of random bits. Does this prevent a Meet-in-the-middle attack in double-encryption?

fgrieu avatar
ng flag
So you are asking if the block cipher defined by $\mathrm E((K_1,K_2,K_3),P)=E(K_3,(K_2\oplus E(K_1,P)))$ is vulnerable to MitM. Hint; assume $\mathrm E((K_1,K_2,K_3),P_1)=C_1$ and $\mathrm E((K_1,K_2,K_3),P_2)=C_2$. Find a relation between $P_1,C_1,P_2,C_2,K_1,K_3$ (involving $E$ and associated decryption $D$) independent of $K_2$.
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