Design of Hexi Cipher for Error Correction — Using Quasi Cyclic Partial Hexi Codes

Abstract

This paper presents a new cipher called the hexi cipher which makes use of a new class of codes called quasi cyclic partial hexi codes. This hexi cipher is a modification of the Advanced Encryption Standard (AES). It alters the mixed column operation of the AES and makes use of quasi cyclic partial hexi codes for error correction instead of the Maximum Distance Separable (MDS) code that has no error correcting capacity within the AES. The hexi cipher has the capacity to detect 99% of the errors and correct nearly 25% of the errors that occur, thus, it has a better error correcting capacity than existing error correcting ciphers.

Hexi McEliece Public Key Cryptosystem

“…Hexi codes and hexi polynomial codes were introduced along with other hexi codes in 2013 [14]. The definition of hexi field, hexi code and hexi polynomial code are recalled.…”

“…The operator '⊗' denotes multiplication modulo x 4 + x + 1 is given in Table 2. This operator '⊗' multiplication modulo x 4 + x + 1 was used in Mini AES in [27] and also described in [14]. This field is called as hexi field.…”

“…Some definitions are recalled from [14] to make this paper a self contained one. The Hamming metric of the hexi code is given in the following: …”

“…The public key cryptosystem is based on binary Goppa codes. Hexi codes were developed in 2013 for error correction in AES [14], further development of these codes is carried out in this paper. These codes are useful to create variants of the McEliece public key cryptosystem called the hexi McEliece public key cryptosystem and its variants.…”