A lot of security services such as confidentiality, integrity, authentication, and non-repudiation can be provided by using cryptographic algorithms.[1]

• Confidentiality

Confidentiality serves the purpose that information is not revealed to unauthorized entities. Confidentiality is accomplished by transforming the understandable information to a state that is unintelligible except by authorized entities. This transformation mechanism is called encryption. The decryption of unintelligible data is performed to restore it to its original state. Both symmetric and asymmetric algorithms can provide encryption. Confidentiality is not only important for data at rest but also for the network communication data.

• Data Integrity

Integrity is the mechanism that assures that the data has not been altered in an unapproved way. The integrity of data is maintained at the creation, transmission, and storage phases. Alteration of data includes insertion, deletion, and substitution breaches. Digital signatures and message authentication codes (MAC) are the cryptographic mechanisms that can be used to notice both intentional & accidental alterations.

• Authentication

Source and Integrity authentication. Source authentication assures the identity of the entity that originally generated the information. Integrity authentication validates that data has not been modified and the integrity of data is protected.

• Non-Repudiation

Non-repudiation is the guarantee that no one can deny a transaction. The terminology of non-repudiation is frequently used for digital signatures and email messages. When a data hashing algorithm is combined with public/private keys, data origination authentication can be achieved. The well-known technique of data origin authentication is using digital certificates.
Cryptographic algorithms can be categorized into three classes: Hash functions, Symmetric, and Asymmetric algorithms.
The proper approach to incorporate security services for applications and protocols dealing with data security is the use of cryptographic methods. A lot of public/open source and proprietary algorithms are available. The document “NIST Special Publication 800-57 Part 1 Revision 4” provides background information and establishes frameworks to support appropriate decisions when selecting and using cryptographic mechanisms.[2]
The issue of information security is extremely complex and at the same time complicated. The main objective of the protection measures in a system is the elimination of the possibilities of accidental or willful destruction of the information, as well as of their unauthorized consultation. In the case of a computer system, the problem becomes even more complicated when the data needs to be protected but at the same time made available to the users.
Prevention objectives can be achieved by encrypting information, an effective solution when storing or transmitting data is done through unsafe environments. Detection objectives are achieved if specific protocols are used, in conjunction with cryptographic methods, which ensure the exchange of messages between the entities of the respective computing system.
The encryption gives protection to the information transmitted for the channels being listened to or intercepted. For this purpose, the transmitter chooses an encryption algorithm and a key, which it communicates to the receiver by secure means, for example, by post or courier. Modern cryptography protects data transmitted over high-speed lines and stored in computers.
Cryptography pursues two main objectives:
- protection or confidentiality (preventing unauthorized disclosure of information transmitted or stored);
- authenticity or integrity (preventing unauthorized data changes) protected information.
NBS (National Bureau of Standards - US) has published the requirements for the encryption algorithm standard, which refers to:

• must provide a high level of security;

•  must be fully public, with complete specifications and easy to understand;

• the security of the algorithm should be fully concentrated in the key strength and not in the algorithm itself;

•  must be available to all users;

•  must be flexible, it can be adapted to different types of applications;

• the implementation of the algorithm in electronic devices should be cheap;

• must be efficient;

• provide for the possibility of validating the algorithm;

• the algorithm and the devices used by it can be exported.

 
A cryptographic system has the following components [2]:
- clear text message space, {M};
- message space in encrypted text, {C};
- keyspace, {K};
- family of encryption transformations, ; where 
- family of decryption transformations, ; where 
Each encryption / decryption transformation is defined by an encryption algorithm respectively decryption.
 
In the specialized literature are used:

•  symmetric method

Within these methods, the basic feature is to ensure the secretion of the coding key, on the one hand, and the uniqueness of the coding/decoding key, on the other. In other words, the encryption key is the same for decoding the message, ie:  
                                                     the encryption operation
              the decryption operation
in which the same key K is used. Function E represents the encryption operation (Encode) and D the decryption operation (Decode).
With these methods, data protection and authentication can be ensured.

•  asymmetric  methods

The concept of asymmetric cryptosystem was introduced by Diffie and Hellman [3]
The proposed encryption method consists in the use of the two processes, of coding and decoding, of two keys for the specific operation. This method is also called public-key encryption.
In these cryptosystems, every user A has a public encryption transformation and a secret decryption transformation, which cannot be obtained from the public encryption transformation, as follows:
                                                    the encryption operation
             the decryption operation
 
The mechanism is shown in figure 1

Figure 1. The asymmetric mechanism

 
With these methods, data protection, and authentication can be ensured, according to the following schemes:
Either two users, A and B, who perform a coded message exchange, user A sends a coded message to user B, as follows:
-  A will encode the message using the public key of user B;
-  B will decode the message transmitted by user A, using his secret key.
 
1. For the protection of information the coding scheme is:
A:  encryption: , where     P_B represents the public key of user B
B: decryption: , where S_B represents the secret key of user B, with which the decoding is performed. It is mandatory to keep it secret and protected.
 
2. To authenticate the information the schema is:
A:   sign information:   , where  S_A represents the secret key of user A
B:  verify signature: , where  P_A represents the public key of user A, with which the decoding is performed, and which is kept secret.
 
In this case, the confidentiality of the respective information cannot be guaranteed.
 
3. For the protection and authentication of information the scheme is:
A: encryption: , where S_A represents the secret key of user A, and P_B the public key of user B.
B: decryption: , where, P_A and S_A are the public and secret keys of user A;  P_B and S_B are  the public and secret keys of user B, with which the authentication and protection of information is carried out.

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[1] https://www.cryptomathic.com/news-events/blog/differences-between-hash-functions-symmetric-asymmetric-algorithms
[2] https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-57pt1r4.pdf