## Paper Instructions

This paper is about Asymmetric Encryption specifically the RSA Algorithm. Even though this is a computer science topic, the paper is for a math class so the main focus of the paper is the math involved in Asymmetric Encryption with main emphasis in the RSA Algorithm.

· The paper should be 10-15 pages, double-spaced in 12 pt. font with one-inch margins.

· The paper should be written for an audience of your peers, i.e. for senior mathematics majors.

· There should be an introduction that informs the reader of where the paper will take them and a conclusion that summarizes the work.

· You should make clear what your own contribution to the topic is. That is, show how you relate or apply the material to an area of interest to you.

· Presentation and organization are major concerns.

· Style, grammar, and spelling are important and will be included in your grade.

· References must be cited within the paper.

· You should include complete bibliographic information, with several sources.

I included the 1st draft that is 6 pages. This is the feedback I received from my professor:

What you have so far makes sense, but I hoped to see more of the mathematics. Why are prime numbers used, and how? What does number theory have to do with the algorithm? I was also not clear on the difference between the public key and the private key. You call them “mathematically structured”; in what sense? You need to say a lot more about the mathematics behind the algorithm.

So the additional 5 pages need to be about the mathematics behind the algorithm.

RSA Algorithm Technique in Asymmetry Encryption

**Introduction**

Asymmetric encryption refers to a kind of encryption where two separate keys that are mathematically related are used to encrypt and decrypt data send across electronic media (Wang and Liu, 204). The encryption and decryption ensure that data sent from one source to another remain secure while in transit. It eliminates the possibility of data leakages or hacking by malicious computer experts. On the other hand, Rivest-Shamir-Adleman (RSA) algorithm is a type of asymmetric cryptographic algorithm used in the encryption and decryption of messages in modern computers (Zhou and Tang, 34). This algorithm provides much-needed security on data while on transit. It ensures that the security of the encrypted data is of high quality throughout the transmission. With advancements and the improvements in technology, there has been a higher need to keep data secure since many people have become experts in hacking computer systems and accessing data illegally for malicious reasons. Simple tasks on the internet such as communicating, playing games, and learning should be safeguarded to ensure that what an individual is doing cannot be accessed by any other person. Thus, encryption and decryption became the solution the much-sought answers to solve the 21^{st}-century problems in a world that acknowledges technology as the driving force. Therefore, this project will focus on asymmetric encryption with more emphasis on the RSA algorithm to keep the transfer of data between computer networks and the internet secure and safe.

**Why Asymmetry Encryption Is Crucial In Data Transmission**

Some people may wonder why the RSA algorithm and other asymmetric encryption are crucial in our modern society despite the many laws governing data transfer and ownership. The laws discourage sharing of data to a third party which might lead to a lawsuit. But as many people say, rules are created to be broken. The problem kicks someone unknown to the systems, breaks the systems, and gains illegal access to the data. This violates the laws, and in most cases, it can go unpunished because the real identity of the fugitive remains unknown. We have read and heard about rogue computer wizards who leave their organizations and become cybercriminals. These people are experts in computer programming and can hack people’s accounts and conduct other criminal activities. As such, it is done by some for fun, while others do it for financial reasons. Even if these people are caught and tried before the courts of laws, some of the damages caused by hacking and cracking of computer systems are so immersed to the extent that their effects remain for many years. An example is where an individual hacks an organization’s database and deletes its historical data. Such data can never be re-acquired and leaves a big hole in the organization’s history.

Therefore, this is why asymmetric encryption must be used to ensure these computer wizards cannot hack the systems and cause disruption to the smooth running of computer activities. To solve the problem, computer gurus have come up with secure data transfer systems where data can be shared without the risk of being hacked. Individuals and organizations have resolved to use asymmetric encryption to secure their communication lines and systems by encrypting data uniquely and sending it through the required system. Thus, data encryptions through various mathematical algorithms such as RSA are essential in ensuring that data in transit does not fall into the wrong hands (Zhou and Tang, 36). Data security is the first line of defense against any possible attack on an organization’s operations. An organization that cannot guarantee data security to its members or customers is not worth operating in the public domain.

**How Asymmetric Encryption Operates**

All asymmetric encryptions apply the same basic principle in securing the transmission of data over computer systems. They make use of mathematical instructions, which are used to generate operations for encrypting and decrypting data. There are two main mathematically structured keys used to encrypt and decrypt data. These keys are the public key and private key (Hoffstein et al., 159). The public key process data on the entry point to encrypt it, while the private key process data at the exit point to decrypt it into readable form. There are various mathematical algorithms in use today in the quest to keep data secure. These algorithms include the RSA, Elliptical Wave Algorithm, and Diffie Hellman algorithm (Zhou and Tang, 37). Even though they almost serve the same purpose of encrypting and decrypting data for security purposes, the most preferable and secure algorithm is the RSA. However, it also depends on the workload of an organization the sensitivity of its operations. Some organizations, such as the defense, need to keep their data more secure because it concerns the security of the entire country. Thus, they are advised to use the RSA algorithm with is better suited for such tasks. Other organizations, such as social media, have little privacy and my not need a higher degree of data security. However, the data should still be kept secure and free from data miners.

RSA works in a unique way, making it more preferable and efficient in encrypting and decrypting data in different organizations. In simpler terms, a computer wizard creates a public key that offers different individuals the opportunity to data that is encrypted and send it to a certain system, like the organization’s system. Once the data has reached its desired system, it cannot be accessed by unauthorized persons. The only way to make the data accessible is by using a private key to decrypt it. Unless an individual holds the private key, they will not be able to access the data. Hence, this is how the RSA protects people from cybercriminals who try to access their data, such as bank account details. It is the most reliable technique to protect data and ensure the security of information in most organizations.

Specifically, in the RSA algorithm, the private keys are made using prime numbers. The Public keys encrypt these prime numbers and transfer them from one point to another as a coded message (Çavuşoğlu et al., 658). Special computer programs convey the coded message to the receiving network on the other end, where special computer programs conduct a conversion from the coded cyphertext into a plain text that any literate person can read. The public key structure is usually created to ensure a safe transfer of data by the cipher and public keys. It comprises different components which enable it to transfer the codes securely. For example, it has a registration authority, a certificate authority, a digital certificate, and a database to collect and distribute digital certificates from the approved authority. Through this process, the asymmetric encryption in the RSA algorithm overcomes the tribulations that were once witnessed in symmetric encryption (Çavuşoğlu et al., 660). In the latter encryption, some unauthorized people could access the data in transit by faulting one of the programs involved. However, the asymmetric cryptography applied in the RSA algorithm ensures that the only message decrypted is the plaintext carried by the public key.

To decrypt the message, the two people sharing it must exchange the public keys and code names so that the one receiving the coded cipher gains access to the password encrypting the plaintext. This process ensures that data cannot leak to unauthorized people or that those who try to hack the system fail because they have no access to the required credentials. In our daily lives, we witness the importance of asymmetric encryption in our transactions. For example, online money transfers use this kind of system to ensure that it is only the account owner or someone with the owner’s credentials can transfer money from the account. Cryptocurrency platforms such as Bitcoin use this type of encryption to restrict only the wallet to transact safely over the internet. A more common example is when people browse the internet. When you search for something by visiting the HTTPS in your computer, the host browser link to the required webpage through asymmetric encryption, ensuring that no other person can interfere with your browsing activities. Therefore, asymmetric cryptography is an important aspect of our daily lives.

**Asymmetric Encryption Subsidiaries**

To make asymmetric encryption a success, it must function through other programs that will facilitate the secure transfer of data from one user to another. Besides, many rogue computer wizards have doubled their efforts to hack the current encryption procedures and illegally access other people’s data. Thus, system developers are coming up with ways to architecture the encryption techniques to ensure better security measures that cannot be cracked or breached. According to Cavusoghu et al. (656), one way to make encryption stronger is by integrating the complex chaos theory into its development. The system designers use the chaos-based hybrid RSA (CSR) encoding technique to incorporate RSA and RNA algorithms in simultaneous use, whose outcome is highly secure and unbreachable encryption that can securely transmit data across different networks.

The success of asymmetric encryption similarly depends on the complexity of mathematics behind its algorithms. Different approaches exist that can be taken to enhance encryption techniques by use of modern cryptography. This cryptography has a unique mathematic principle for designing the public key cryptographic signature and cryptosystem mechanisms (Hoffstein et al., 157). Mathematical tools are used to assess any encryptions’ security status before coding and sending data across the networks. The fundamental mathematical tools used are the basic linear algebra and strategies from the number theory. These tools, probabilities are made and implemented and improved over time to suit the current situation’s data transmission needs. Thus, the RSA algorithm depends on these mathematical tools to make it a more secure way of transmitting data without the risk of being cracked by outsiders.

**Enhancing the Asymmetric Encryption**

Hackers and other cybercriminals keep getting smarter day in day out. In the same way, encryption developers have to advance their skills and techniques to protect people from falling victims to these cybercriminals. One way of enhancing the system is by accelerating the RSA algorithm’s application in transferring data between communication networks (Nagar and Alshamma, 56). This can be achieved through conducting a modification of the keys used in the data transmission. The modification is determined by the software used in developing the keys. In the RSA algorithm, the enhancement is executed using a unique technique coded in a C # language called RSA Interaction Server Protocol (Nagar and Alshamma, 58). This protocol controls all the doorways involved in RSA-Key Generations to meet the demands of a particular problem in an organization. Therefore, through enhancing and rectifying any loopholes in the encryption process, an organization can keep its data secure and away from malicious people.

Another way of enhancing asymmetric encryption is through DNA computing techniques (Wang and Zhang, 312). These techniques relate to different fields and can effectively solve seemingly complex unrelated problems. In this case, the encryption concepts make it impossible for an individual to decipher the message by simply encoding the letters used. A modern approach has to be applied to explain how cryptography functions in DNA computing and conveying messages safely. This renders the message being relayed almost impossible to decipher while on transit, making organization systems extremely secure.

**Conclusion**

The encryption and decryption of data are the foundation of the secure transmission of data. However, organizations have to do more than just encrypting and decrypting data by making the transmission more secure. The use of complex encryption programs and techniques such as the RSA algorithm adds more security features to the system, making it very difficult for third parties to access the data. Thus, understanding the importance of asymmetric encryption and various mathematical algorithms’ functionality will enable individuals and organizations to enjoy a secure transmission of data. It makes our lives more comfortable as people know that their day-to-day online activities are well guarded. Further, organizations that deal with highly classified data such as the defense department, the banking systems, and the healthcare department should be keener on their encryptions algorithms.

Works Cited

Çavuşoğlu, Ünal, et al. “The design and implementation of hybrid RSA algorithm use a novel chaos-based RNG.” *Chaos, Solitons & Fractals* 104 (2017): 655-667.

Hoffstein, Jeffrey, et al. *An introduction to mathematical cryptography*. Vol. 1. New York: Springer, 2008.

Nagar, Sami A., and Saad Alshamma. “High-speed implementation of RSA algorithm with modified keys exchange.” *2012 6th International Conference on Sciences of Electronics, Technologies of Information and Telecommunications (SETIT)*. IEEE, 2012.

Wang, Suli, and Ganlai Liu. “File encryption and decryption system based on RSA algorithm.” *2011 International Conference on Computational and Information Sciences*. IEEE, 2011.

Wang, Xing, and Qiang Zhang. “DNA computing-based cryptography.” *2009 Fourth International on Conference on Bio-Inspired Computing*. IEEE, 2009.

Zhou, Xin, and Xiaofei Tang. “Research and implementation of RSA algorithm for encryption and decryption.” *Proceedings of 2011 6th international forum on strategic technology*. Vol. 2. IEEE, 2011.

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