Nowadays most communications are done by utilizing digital transmission mechanisms. The security of this digital information transmitted through different communication systems is quite important. The secrecy of digital data is one of the burning topics of the digitally developed world. There exist many traditional algorithms in the literature to provide methods for robust communication. The most important and recent modern block cipher named the advanced encryption standard (AES) is one of the extensively utilized encryption schemes with binary based. AES is a succession of four fundamental steps: round key, sub-byte, shift row, and mix column. In this work, we will provide an innovative methodology for extending the AES in a Galois field with any characteristic

It is critical to keep secret multimedia material out of the hands of unauthorized parties. Content, music, still images, liveliness, and video are all examples of the interactive media material. Multimedia security is used to protect these compounds. This is done using cryptographic techniques. These plans foster communication security, robbery, and refugee protection. Encryption is made more difficult by image size [

There are four sections in this research article. The basic notions are discussed in segment 2. The suggested scheme along with examples is now discussed in Section 3. Lastly, we have concluded the section.

A Galois field is a finite field with finite order. The Galois field has an order of prime or an exponent of prime,

Now we describe the structure of

As in

The elements of

There are three sets of assertions or propositions that we will refer to as ternary logic

Consider, if

Implication

Negation

Conjunction

Disjunction

The system

The outcomes in

1 | 1 | 2 | 1 | 1 | 1 | 1 |

1 | 0 | 2 | 0 | 1 | 0 | 0 |

1 | 2 | 2 | 2 | 1 | 2 | 2 |

0 | 1 | 0 | 0 | 1 | 1 | 0 |

0 | 0 | 0 | 0 | 0 | 1 | 1 |

0 | 2 | 0 | 2 | 0 | 0 | 0 |

2 | 1 | 1 | 2 | 1 | 1 | 2 |

2 | 0 | 1 | 2 | 0 | 1 | 0 |

2 | 2 | 1 | 2 | 2 | 1 | 1 |

Unary functions are defined as those in which there is only one solution, and this is the case when

0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |

1 | 0 | 0 | 0 | 2 | 2 | 2 | 1 | 1 | 1 | 0 |

2 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 |

1 | 0 | 0 | 2 | 2 | 2 | 1 | 1 | 1 | 0 | 0 |

2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 | 0 | 2 | 1 |

0 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | |||

1 | 0 | 2 | 2 | 2 | 1 | 1 | 1 | |||

2 | 0 | 2 | 1 | 0 | 2 | 1 | 0 |

By utilizing this process, we can calculate

An affine transformation

As a result, S-box structure is described as

This is the required structure for the S-Box design created on

S-box is the main non-linear component of the block cipher, which increase the confusion in the algorithm, therefore it must be strong and highly resistant to cryptanalytic attacks. Here we define a new approach to constructing a strong Substitution box. We define a map

In the context of symmetric algorithms, AES is referred to as a “block cipher.” Commercial systems, such as Microsoft’s Windows, use it regularly (IPsec, the internet Skype, the IEEE 802.11i, and TLS). AES is referred to as AES-128, AES-192, or AES-256 depending on the size of the key employed in the encryption of the information being protected. Depending on the size of the key, the data matrix has 10, 12, or 14 rounds.

Other than binary qualities, we’ve mostly made use of the extension field in this section. To begin, we must expand the block cipher’s nonlinear S-box component to include features 3 and 5, as well as shift row, mix column, and round key. Here we define AES on the plaintext and key of 8-rits with two rounds of encryption, but in general, we can use the desired length of key and plaintext. The round of encryption can also be increased. The working strides of the proposed generalized AES are shown in

A substitution box can be constructed by using the map

The S-box changes to the following value when input values are inserted into the expression (see

0 | 1 | 2 | |
---|---|---|---|

0 | 22 | 20 | 00 |

1 | 21 | 02 | 10 |

2 | 01 | 11 | 12 |

The inverse S-box, as shown in the

0 | 1 | 2 | |
---|---|---|---|

0 | 02 | 20 | 11 |

1 | 12 | 21 | 22 |

2 | 01 | 10 | 00 |

Suppose the plaintext of 8-rits be

Now we divide this 8-rits plaintext into 4 parts, each consisting of 2-rits

The following matrix can be used to represent the simple text:

Assume the key be of equal length as plaintext i.e., 8-rits

The following is a matrix representation of the key:

First, we add a key matrix in the plaintext matrix

The first step is to do the sub-byte conversion to each element of the matrix

After shifting the components in the matrix

Consider a matrix for the mix column’s operation.

By successively multiplying the

In the end, when we combine these two columns into a single matrix, we obtain

By using the recent key

Therefore, the key becomes

By adding the key

We obtain the following as the matrix

Shift row is applied to the matrix

There is no mix column in the last round

The following procedure can be used to produce the key:

Therefore, the key becomes

The encrypted message is

The encrypted data can be decrypted by utilizing the reverse process of encryption.

For decryption, the key matrix

After key subtraction inverse shift row is applied to the matrix

After applying inverse shift row, inverse sub-byte transformation is applied by using inverse S-box

Now we subtract the key of round 2 i.e.,

In the inverse mix column, we take the inverse of the matrix

After multiplying the columns of the matrix

After putting these columns together in a matrix,

After utilizing the inverse shift row on the matrix, which is obtained after the inverse mix column,

After utilizing inverse Sub-byte transformation by using inverse S-box, we get

Finally, we subtract the initial key from the matrix

Finally, the recovered message is

A substitution box can be constructed by using the map

Now consider the matrices for this expression be

As a result, we acquire output values by adding input values into the above formula, the required S-box is given in

0 | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|

0 | 00 | 12 | 32 | 11 | 34 |

1 | 13 | 40 | 31 | 04 | 22 |

2 | 41 | 03 | 24 | 42 | 21 |

3 | 10 | 14 | 20 | 23 | 01 |

4 | 44 | 43 | 02 | 30 | 33 |

The inverse S-box is shown below in

0 | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|

0 | 00 | 34 | 42 | 21 | 13 |

1 | 30 | 03 | 01 | 10 | 31 |

2 | 32 | 24 | 14 | 33 | 22 |

3 | 43 | 12 | 02 | 44 | 04 |

4 | 11 | 20 | 23 | 41 | 40 |

Consider the plaintext of 8-rits be

Now we divide this 8-rits plaintext into 4 parts, each consisting of 2-rits

The following is a matrix representation of the plain text

Assume the key be of equal length as plaintext i.e., 8-rits

Using the matrix form, the key may be expressed as follows:

First, we add a key matrix in the plaintext matrix

Initially, we utilize the S-box transformation to all components of the matrix

After employing the shift row to the components of the matrix

Consider a matrix for the mix column’s operation.

This is the result of multiplying each column of the matrix

Combining these two columns into one matrix yields the following result:

By using the recent key

Therefore, the key becomes

By adding the key

We obtain the following as the matrix

By implementing shift row on the matrix

In the last round, there is no mix column.

Keys can be produced in the following way:

Therefore, the key becomes

The encrypted message is

The encrypted text can be decrypted by utilizing the reverse process of encryption.

For decryption, the key matrix

After key subtraction inverse shift row is applied to the matrix

After applying inverse shift row, inverse sub-byte transformation is applied by using inverse S-box

Now we subtract the key of round 2 i.e.,

In the inverse mix column, we take the inverse of the matrix

After multiplying the columns of the matrix

After combining these columns in one matrix

After utilizing the inverse shift row on the matrix, which is obtained after the inverse mix column,

After employing inverse Sub-byte transformation by using inverse S-box, we get

Finally, we subtract the initial key from the matrix

Finally, the recovered message is

In this paper, we have defined a generalization of AES which gives better results to increase the security of the algorithm. This modifies AES as a complex mathematical structure which is utilizing the composition of two affine nonlinear functions instead of one affine Boolean function as in the case of standard AES. Moreover, the use of different characteristics other than the binary is one of the thought-provoking problems of cryptography. As a result, brute force attacks fail on the modified AES due to increasing the number of possibilities to find the key. The use of ternary and quinary characteristic finite field is yet not used in the development of AES structure. We have utilized ternary and quinary characteristic fields to design a new mathematical foundation for modified AES. The implementation of the generalized AES on hardware is one of the challenging problems for future interests. The designed structure can be utilized for audio and video encryption as well.

This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project Number (PNURSP2022R87), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.