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Given this encryption scheme: $\begin{align} c_1 &= E(k_2,E(k_1,(m_1\operatorname{xor}k)))\\ c_i &= E(k_2,E(k_1,(m_i\operatorname{xor}c_{i-1}))) \end{align}$

  1. Describe a known plaintext attack with a few input blocks where the attacker can discover the full key $(k,k_1,k_2)$ with approximately $2\cdot2^\ell$ runs of the encryption/decryption algorithm (do not care memory)

  2. Comment on the security of this mode of encryption as a potential way of strengthening DES with an increased key size.

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Welcome to crypto.se! Notice we have$\TeX$. Straight homework dump is discouraged, you should show what you have done (see this). The best I'll offer is hints: review what's known in a "known plaintext attack with a few input blocks", and the relation between these quantities. How many applications of $E$ are there between quantities that can be known? Have you studied an attack that works under these assumptions? Can you derive what's needed to apply just that attack? What's missing after that, and how do you get it? –  fgrieu Apr 26 at 13:33

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