What is the non-linear function that made DES cryptography so strong?

What is the non-linear function that made DES cryptography so strong?

• Trick question, DES is fully linear
• Swapping 4 bytes (left and right) after every round
• Expansion & Contraction algorithms
• 16 rounds of S-Box lookups 

 

EXPLANATION

The genius of Horst Feisel's cipher was in the use S-Boxes for a non-linear lookup function based on the bit values of the ciphertext within each round. Operating on only 1/2 the ciphertext per round, the 48 expanded bits are chopped into 6-bit inputs across the 8 S-Boxes, with each 6-bit input performing a row/table lookup to yield 4 bits of output.  Without this non-linear function, DES would have been linear, and thus very weak.
This design is even more impressive when you consider that the process ran the same forwards and backwards for encrypt/decrypt, and was optimized for hardware.  While met with great suspicion when introduced, the Data Encryption Standard proved worthy of the trust provided it, weathering every attack except Moore's Law and time, which ultimately led to its obsolescence due to brute force attacks.  40 years later, the field of cryptography, and the fabric of the Internet and digital commerce, owes much to the knowledge we gained regarding cryptanalysis and ciphers from this legacy

SOURCE

https://en.wikipedia.org/wiki/Data_Encryption_Standard#The_Feistel_.28F.29_function