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I know that 3DES was considered to increase the strength of DES from 56-bit to 112-bit (now considered 80-bit) by using 3 DES keys and doing DES-Encrypt(DES-Decrypt(DES-Encrypt(plain-text, key1), key2), key3).

What would the cryptographic strength be if someone made 3x 3DES keys and did 3DES-Encrypt(3DES-Decrypt(3DES-Encrypt(plain-text, key1), key2), key3) to create 3DES-squared?

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Assuming that each of the 3DES keys is 174-bits (i.e. 3x 56-bit keys), then the security would be 280-bits. There is a meet-in-the-middle attack on a sufficiently large number of matched plain and cipher texts to guarantee a unique solution (8 blocks of matched plain and cipher should suffice). One can then exhaust 4 DES operations in the forward direction (EDED) and match against 5 DES operations in the reverse direction (DEDED).

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  • $\begingroup$ OP asks about 56*3*3 key sizes. $\endgroup$
    – kelalaka
    Commented Aug 4 at 16:19
  • $\begingroup$ @kelalaka Many thanks; now updated. $\endgroup$
    – Daniel S
    Commented Aug 4 at 16:55
  • $\begingroup$ IMHO, this should be HW. Since no one cares 3DES(-squared). $\endgroup$
    – kelalaka
    Commented Aug 9 at 13:24

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