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2

First property says- If you consider a 6-bit Inpput Difference(Difference means XOR in case of DES).i.e 6-bit binary number which is the xor of two inputs(obviously both 6 bits).When you enter both of these inputs to Sbox and get two outputs each of 4 bits and xor the outputs what you get is called Output Difference. Total 64 inputs are possible hence 32 ...

5

It is of course possible to write DES or any block cipher as a system of non-linear equations involving the plaintext bits, the ciphertext bits, and the key bits, which hold with probability 1. In principle, cracking the cipher would then merely involve collecting enough linearly independent equations (e.g. from a couple different known plaintexts) and then ...

4

The S-Boxes are lossy. They map 6-bit inputs to 4-bit outputs, so for a given 4-bit output there are several possible inputs. Considering that there are 8 S-boxes, that's 16 bits of information lost per round, or 256 bits for all 16 rounds. It's much easier to exhaustively search the 56-bit keyspace than try to work backwards against that kind of information ...

44

That value 0E329232EA6D0D73 was found by brute force. I would be surprised if there was a significantly better method: that would be tantamount to a cryptanalytic break of DES, very different from the few we know. A sketch of the brute force method (with details about parallelization omitted) goes: for each $K$ of 64 bits among the $2^{56}$ valid DES keys ...

0

Also, differential attacks can be useful in the design of a cipher to strike the right balance between performance (e.g., number of rounds) and security. Let's assume DES initially had 10 rounds and the designers performed a differential attack on that setup. They would have found that 10 rounds were not buying enough resistance against that type of attack ...

3

Anyone who begins to develop an attack on primitive XYZ is probably not aware beforehand of what the computational complexity of their attack will turn out to be. Then, the attack is developed and computational complexity becomes known. Just because DES isn't broken by the attack in question does not mean no other ciphers will be. And just because the ...

3

Differential cryptanalysis is a very powerful technique that permitted highly practical attacks on many ciphers that were not designed to resist it (e.g. FEAL-4). DES, as it turns out, was designed to be pretty resistant to it, which is why it requires an essentially impractical amount of chosen plaintexts to implement a differential attack on DES. ...

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