Extended DES algorithm to Galois Fields

Data Encryption Standard (DES) was initially considered a strong symmetric encryption algorithm, resistant to all known cryptographic attacks at that time [1]. But the short key used to encrypt data is a weakness of the algorithm. Increasing the data structure size and the key length are two recommended measures that ensure the strength of the encryption algorithm. The running-time is a constraint imposed to the design of the algorithm that restricts its applicability at a moment. Triple-DES (TDES) with 128-bit key will be considered as a candidate to Advanced Encryption Standard (AES) after 2020 when the technology is estimated to be sufficiently developed to run fast enough TDES [2]. Regarding the time, DES can be a good candidate to AES if it is applied on multi-bit symbols instead of bits. We propose an extension of DES algorithm to Galois Fields (GF), with an encryption key of at least 256-bit long. The substitution boxes (S-boxes) are the non-linear component of the algorithm that is decisive for its robustness. The design of multi-bit S-boxes is done using bijective polynomials defined on Galois Fields. DES-256 running on GF (16), with 4-bit symbols, is proposed and presented with all the details.