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Block ciphers cryptanalysis is serious challenge specially with the existing of the powerful block ciphers that require massive number of plaintext-ciphertext pairs to perform a successful attack. Algebraic attack is superior among different attack types as it does require the smallest number of such pairs. On the other hand, the equations describe the input/output relations should be in hand to execute the algebraic attack. In this paper, we present the method of collecting the input/output algebraic equations for 2-key simplified 3-DES as a miniature example of the 2-key 3-DES. The simplified DES has similar structure and characteristics to DES with the privilege of using smaller parameters than DES. Also, we prove that the complementation property of DES can be used to double the number of obtained algebraic equations for 3-DES variants and consequently decreasing the required number of plaintext-ciphertext pairs. Finally, we compared the expected number of obtained equations and variables in both 2-key simplified 3-DES and 2-key 3-DES.

Extracting algebraic equations of the 2-key simplified 3-DES for algebraic cryptanalysis