Currently, any organization, company, or institution swears by the use of computer technology to ensure the backup and exchange of data. Academic data of the students of the DRC are for the most part stored on physical supports. As the process of digitization of the latter is at an advanced stage, we have an obligation to anticipate potential problems related to the digitization of sensitive data that would be subject to attacks and multifaceted threats and therefore vulnerable in the future. The topic of this article is therefore the security of academic data of all involved students throughout the DRC. This paper is based on the design and implementation of encryption algorithms for computer data stored or exchanged across various transmission networks using the RSA and Christopher Hill encryption algorithms [6]. Since the latter uses a certain number of theoretical concepts in their cryptosystems, a brief overview of this would provide an entry point into the tools and methods used.

Given the problems of managing the circulation of information on the network, we, teachers and computer security enthusiasts, found it urgent to look for a security mechanism for the data transiting on the web, especially in the digital platform of higher and university education in the Democratic Republic of the Congo.

To achieve our objectives, we resorted to symmetric encryption using the C. Hill algorithm and asymmetric encryption using the RSA algorithm.

Several methods are used to encode and decode information. These methods are developing in parallel with the constant evolution of computer software and tools for intercepting information for or from a third person. Among the commonly used methods, we will mention the symmetric encryption which is known as the secret key algorithm. It is a unique decoding method that must be provided to the recipient before the message can be decoded [7]. On the other hand, asymmetric encryption uses two different keys, public and private, that are mathematically related and therefore interdependent to some extent. Specifically, the keys consist only of large numbers that have been paired together but not identical. In view of the above, we will implement two sets of cryptographic algorithms, one based on the Hill Symmetric cryptosystem and the other based on the RSA cryptosystem.

The first crypto system developed is made with the Hill algorithm which uses an n*n matrix as key and an n*m matrix as encrypted text, where the m is variable depending on the encrypted text. The second one was done with the RSA algorithm using prime numbers encoded on 512 bits. Since these will be used to secure academic data, we will nuance these two approaches by using the listings sowed on the encryption interfaces.

1) Example: Here is the text to be encrypted with C. Hill’s algorithm in Figure 1.

L’informatique prend aujourd’hui.

The numerical result in matrix form is:

The randomly selected key matrix is as follows in Figure 2.

The result of the encryption in an encrypted matrix in Figure 3.

The result of the original text encryption transformed into a matrix is presented below in Figure 4.

This way of presenting numerical result shows only that the matrices were used [8]. We have just finished the encryption with the algorithm of C. Hill, then decryption will follow. In every decryption, one uses encrypted result. For this case, we will use the encrypted matrix then search for the inverse of the key matrix which will be multplied to obtain a clear matrix (Transformed into a source text). With these two matrices (the first obtained after encryption and the second from the key matrix), we can decrypt the message without any problems.

a) First Matrix

This figure is the same as Figure 4.

This one in a numerical matrix:

This figure is also the same as Figure 3.

b) Second Matrix in Figure 5

At this level, the decryption consists of multiplying the second matrix by the first (key matrix inverse to encrypted matrix) in order to come back to the initial matrix that will be the clear text. The result is the following in Figure 6.

2) Example of the RSA algorithm

The RSA algorithm is an asymmetric cryptography algorithm; this means that it uses a public key and a private key (i.e. two different, mathematically linked keys). As their names suggest, a public key is shared publicly, while a private key is secret and must not be shared with anyone.

Principle of this algorithm

1) Key generation

The RSA works from two prime numbers, which we will call p and q. These two numbers must be very large, because they are the keystone of our encryption. Today, we use keys from 128 to more than 1024 bits, which represents decimal numbers from 38 to more than 308 digits! Once these two numbers are determined, let’s multiply them. We note n the product n = p × q, and (p − 1) × (q − 1).

Let us now look for a number e (less than (p − 1) × (q − 1)), which must necessarily be prime with (p − 1) × (q − 1).

Let us then compute the inverse of e modulo (p − 1) × (q − 1)), which we will note d.

d ≡ e − 1 mod ( ( p − 1 ) ( q − 1 ) )

The couple (e, n) is the public key, and (d, n) is the private key.

2) Encryption and decryption

To encrypt a number, you just have to put it to the power e. The remainder modulo n represents the number once encrypted.

Encrypted message = Be encrypted message ^e mod n

To decrypt, we use the same operation, but to the power of d:

Be encrypted message = Encrypted message ^d mod n

Once e, d and n are computed, we can destroy p, q and ((p − 1)(q − 1)), which are not necessary to encrypt and decrypt. Even worse, the private key d can be computed very quickly from p and q, so these numbers should not be kept.

Note: In general, the private key is then encrypted using symmetric encryption. This makes it possible to keep it in a safe way, because the key used by the symmetrical encryption does not have to be transmitted, and thus does not risk to be intercepted. At our level, we have applied this algorithm with other more complex aspects, as demonstrated in the following lines. We now focus on the data stored in the database management system. The RSA encryption algorithm is used to secure the identifiers [9]. First, the generation of random numbers encoded on 512 bits gives the result shown in the listing below. Since the RSA algorithm uses prime numbers, we have developed a tool to generate them randomly as much as we can. Its interface is in Figure 7.

The tool that we have created allows to generate randomly coded prime numbers on 512 bits, it is the first RSA tool that we implemented. It generates the numbers p, q, and e. The generated numbers are:

Numbers of the capture:

p = 171423785473521206284128400968069563514322955840589422284823             025493472541823410634011604497963291624434855358467026774334             51768521881334928097448674126813997

q = 335908331699656042571935046859611459129412410880368139860155           248333276438946086211114058264044903159716953148206936059137           83617344190008542990496397710666557

e = 960466691299657440890727557958375040243325870483982156548763           893411555256332192751165565972028678115234761573945379216762           19119844670842244023877763801759877

Suppose we want to encrypt 65 which is the ASCII value of A. To begin with we need to calculate the value of n which is the product of p and q. Then calculate (p − 1)(q − 1).

n = 575826777920502404431124967283521690715726393197842077648265           666166568712315613822711737906855092641318870121538155559039           147344443125260510490572366339777441557608867798006325258029           450412761026445488325714606523492010645310759155796269464670           141765871839950343680658581653689838997451205055168843586693           627398329

( p − 1 ) ( q − 1 ) = 57582677792050240443112496728352169071572639319784207764826566       61665687123156138227117379068550926413188701215381555590391473       44443125260510490572366339777390824397150480281439651684667644       65876207195165361885030899418326263586107884658495210386556505       2361535162829991185370342603611585133711697755641621789917776

Having already n and e we can then generate the public key which is the couple formed by n and e, and from the public key we can encrypt the message.

Encrypted message = be encrypted message exponent e modulo n

Be encrypted message = 65

e = 960466691299657440890727557958375040243325870483982156548763           893411555256332192751165565972028678115234761573945379216762           1911984467084224402387776380175987

n = 575826777920502404431124967283521690715726393197842077648265           666166568712315613822711737906855092641318870121538155559039           147344443125260510490572366339777441557608867798006325258029           450412761026445488325714606523492010645310759155796269464670           141765871839950343680658581653689838997451205055168843586693           627398329

Encryptedmessage = 45551297184769508546973079307976137216164034195612314837870913       48361355704607818436159611440674523922053553949920277408847809       23165365746220165759474995244726525240964927536246190868532357       35526800813878375581774840600766739827300466036772794497449569       125022346751012772341288313150998718572707493450633648969022

With the previous example, we find that if Mr. Bob sends message A to Alice with RSA encryption using the above parameters, Alice will receive 45551297184769508546973079307976137216164034195612314837870913483613557046078184361596114406745239220535539499202774088478092316536574622016575947499524472652524096492753624619086853235735526800813878375581774840600766739827300466036772794497449569125022346751012772341288313150998718572707493450633648969022 instead of A, as for her to decrypt the message if she has the private key. In the following part we will show how to decrypt the message.

Before decrypting the message in RSA, we need to calculate the value of d, which is the inverse of e modulo (p − 1)(q − 1).

d = 770310650716094684905263403650319109705367415620859422729266             185743414560946120644604519772368027323956964506786031689161             149204317703603543474263464168753022251193366280111700542310             118172050956687595721698308163374076552396504072499466513651             806670296581175855788692893718291049182384305707470088978135             83621805

With the value of d, we can generate the private key which is the couple n and d.

So to decrypt the message, we use the following formula:

Having the necessary information n, d we can find the clear message which is the starting message.

After making all the calculations, the clear message is: 65. In sum, we have just presented two tools (cryptographic systems), the first is based on symmetric encryption while the second is based on asymmetric encryption. The first one implements the Hill algorithm which is based on matrices, which allowed us to rely on the transformation of the entered text into a matrix and the second one implements the encryption which is based on prime numbers, we used prime numbers encoded on 512 bits. In computer security, the more we think about increasing the bits of the prime numbers to be encrypted, the more the security of the information increases.

We managed to deploy two crypto systems that use symmetric and asymmetric encryption respectively. The first one used Hill’s algorithm while the second implemented RSA’s. Let us now note the particularities and nuances constraints of the two implemented algorithms.

For the algorithm designed based on Hill’s crypto system:

1) The text to be encrypted of n characters;

2) The invertible square matrix;

3) The matrix determinant must be > 0;

4) The number of rows in the encrypted matrix depends on the columns of the key, while the number of columns is the resultant of the length of the text to be encrypted and the number of columns in the key if the former is a multiple of the latter;

5) The encrypted text converted into an ASII code value is transformed into a matrix according to the key matrix;

6) The product of the key matrix and the text to be encrypted.

For the algorithm based on the RSA cryptosystem:

1) The recovery of the ASCII value of each character in the text to be encrypted;

2) Triggering the concatenation procedure of the found ASCII values;

3) The created function returns the concatenated ASCII codes;

4) The transformation of the returned value into Big Integer;

5) The use of the exponent e modulo n;

6) The encrypted message is saved in the database.

The major and main part of our work consisted of the implementation of encryption and decryption algorithms which consist in securing all the information and/or data exchanged on the network including the academic data of the students.

In addition to these algorithms, we have implemented tools to encrypt information using symmetric and asymmetric algorithms. Initially, these tools are used to demonstrate what we have achieved, and then we will use some of these features in all the computer systems we implement. This will ensure the security of information that will be stored in the database management systems, while controlling unauthorized access and availability of data on our servers.