On Advanced Encryption Standard and S-boxes

Abstract

ryptography plays a fundamental role in the security of data transmission. After the early stages of cryptography i.e. in the Egyptians times, four thousand years before till the 2nd world war, cryptography played a prominent role in the 20th century. Nevertheless, post-World War II, the development of a variety of crypto analysis techniques weakened cryptography of the earlier stages. Accordingly, these techniques break the codes and different algorithms that were secure in the early stages. In 1970’s Horst Feistel created a cipher at IBM called the Feistel Cipher and then in 1997 the US National Bureau of Standards (NBS) published a cipher named Data Encryption Standard (DES) [3]. This Cipher was considered to be the best secure algorithm till 1997. It uses a key of length 56-bit which was very small as shown by recent distributed key search exercise [14]. When DES was nearing its end, the US National Institute of Science and Technology (NIST) issued a call for an algorithm which was highly secure, simple and fast called the “Advanced Encryption Standard (AES)”. The NIST shortlisted five algorithms, out of which Rijndael algorithm [18] was chosen as an AES. It is a 128-bit block cipher that accepts keys of length 128-bit, 192-bit and 256-bit. This was designed to overcome the issues of secure communication especially on platforms like ATM networks, High Definition Television (HDTV) and Integrated Services Digital Network (ISDN) (see [21]). Among shortlisted algorithms proposed for Advanced Encryption Standard (AES), the Serpent Algorithm [1] is also included. For Serpent Algorithm, initially S-boxes are taken from DES that resulted in Serpent-0 [13], a more secure Algorithm than triple-DES [13] having a key size of length 192 or 256 bits, presented at the 5th international workshop on Fast Software Encryption [4]. After this, Serpent-1 [1] was designed which used new and stronger S-boxes (taken from DES S-boxes) with a different key schedule in order to resist different attacks like differential [4] and linear [2]. Like Rijndael, Serpent Algorithm was also designed to encrypt a 128-bit block by using keys of length 128-bit, 192-bit or 256-bit. It was especially designed for intel-based chips. Nowadays it is used in folder locks like “Folder Lock Professional”, Dropbox file security [23] etc. There are different ways to modify these algorithms e.g. using Substitution boxes (Sboxes) of good quality depending on their nonlinearity. Furthermore, it also depends on the number of rounds and key schedule.

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On the lines of AES S-box, different S-boxes were constructed over finite Galois fields 𝐹2𝑚,𝑚 = 2,3,4,5,6,7,8, such as residue prime S-box [12], perfect nonlinear S-box [16], Gray S-box [22], APA S-box and S8 AES S-box [11]. In our proposed Algorithm (Modified Serpent Algorithm), unlike the Serpent-0 and Serpent-1, we used 4 × 4 S-boxes constructed from a commutative chain ring whose each entry is a byte [19]. Splitting the given key into just two vectors, we calculated approximately half of the pre-keys as compared to Serpent Algorithm [1]. Moreover, the pre-keys calculated in our proposed algorithm are different from those calculated in Serpent Algorithm. For the proposed Modified Serpent Cipher in this study use the same ideas for bit slice implementation of cipher [3] like Serpent-1. Furthermore, unlike the DES that gains extra speed by encrypting 64 different blocks in parallel, each single block of the Serpent Algorithm in this study is efficiently encrypted by bit slicing and hence there is no need of changes for gaining extra speed. The Serpent Algorithm S-boxes are limited to hexadecimal numbers (i.e. both the domain and range are confined to 16 numbers) while in our modified procedure the 4 × 4 S-box has the property that it take elements from commutative chain ring 𝑅8 = ℤ2[𝑥] <𝑥8> = 𝔽2 + 𝑥𝔽2 + 𝑥2𝔽2 + 𝑥3𝔽2 + 𝑥4𝔽2 + 𝑥5𝔽2 + 𝑥6𝔽2 + 𝑥7𝔽2 having 512 elements, and results again in 𝑅8. This property extends the security of Modified Serpent Algorithm. Using less number of rounds and dealing with 64-bits at a time make the algorithm fast, whereas the main drawback of the Serpent algorithm is its less speed as compared to