Posted: July 14th, 2022

The Role that Prime Numbers Play in Cryptography

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1. Examine the role that prime numbers play in cryptography.
2. Conclude whether or not cryptology would be as effective without the use of prime numbers.
3. Provide a rationale for your response.
4. Use Internet references published within the past year.
The Role that Prime Numbers Play in Cryptography
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The Role that Prime Numbers Play in Cryptography
Examine the role that prime numbers play in cryptography.
Prime numbers are considered special, especially in cryptography. Prime numbers can easily be multiplied together, and other unique features of the numbers make them applicable in cryptography and number theory. Since it’s very fast to multiply two large prime numbers, it is computer-intensive to reverse or look for prime numbers from the results. The difficulty of reversing the equation is known as prime factorization (Childs, 2019). The challenge of factoring the numbers is key in cryptography, although it varies according to the numbers’ size. Cryptography depends on prime numbers, Especially the time it takes for an attacker to conduct prime factorization (Mohamad, Din, and Ahmad, 2021). It is difficult to factor the prime number used to decrypt a message, which is challenging practically. Factoring prime numbers are considered non-trivial because of the number’s uniqueness, especially being one, and themselves. What makes the cryptography algorithm strong is the prime number, where if a person could factor the numbers out, cryptography would not be effective anymore.
Not all crypto-systems use prime numbers; some crypto-systems do not use prime numbers in encryption. Symmetric encryption, also known as the secret key, does not involve prime numbers because the keys used in encrypting are the same used in decrypting. Also, it is not important to use prim numbers when encrypting for secrecy in RSA and DH because both the methods are considered inefficient. RSA uses the block cipher to encrypt secrecy, while DH uses secret keys, which is effective because the secret key does not disclose any secret information (Mohamad, Din, and Ahmad, 2021). On the other hand, asymmetric or public-key encryption does not require prime numbers. Still, cryptography is more secure when using prime numbers because it is challenging to factor out the numbers, hence providing security. The uniqueness of the prime numbers makes them effective in cryptography; hence cryptography would not be effective without prime numbers. Prime numbers become effective because it is difficult to find their products, hence used as a trapdoor tool. There are cryptosystems that do not make use of prime numbers; encryption in such cryptosystems does not include the use of prime numbers. Because the keys that are used for encrypting and decrypting in symmetric encryption are the same, this type of encryption does not require the use of prime numbers. Symmetric encryption is sometimes referred to as the secret key. Because RSA and DH are considered to be inefficient methods for encrypting data, it is not essential to make use of prim numbers when doing so in order to maintain confidentiality. RSA encrypts information using a block cipher, whereas DH employs secret keys, which is effective due to the fact that the secret key does not reveal any information that should be kept confidential (Mohamad, Din, and Ahmad, 2021). On the other hand, symmetric encryption uses prime numbers, while asymmetric encryption, often known as public-key encryption, does not. However, when prime numbers are used in cryptography, the level of security is increased because it is more difficult to factor out the numbers, which in turn provides security. The fact that prime numbers are each one of a kind makes them useful in cryptography; hence, the field of cryptography would be rendered useless in the absence of prime numbers. Because it is difficult to locate the products of prime numbers, prime numbers are powerful and are therefore utilized as a trapdoor tool.

The use of prime numbers in cryptography, especially in RS, can be challenging and faulty, especially in finding the prime numbers when the numbers are more than one hundred and thirty. Also, it is not advisable to use two numbers close together, wherein case the prime numbers are close to each other, one number can be used to factor the other through the Euler approach, hence not secure (Mohamad, Din, and Ahmad, 2021). On the other hand, the cryptography method can be broken down, especially after choosing unlucky numbers. Prime numbers are an essential part of cryptography because the computer can easily do and cannot undo them. The fact computers cannot figure out what prime numbers have been multiplied to get the super-large prime number used to encrypt data. The primary use of large prime numbers is because prime numbers are difficult to deal with, and prime-factor, hence an effective method for preventing breaches (Childs, 2019).

References
Childs, L. N. (2019). RSA cryptography and prime numbers. In Cryptology and Error Correction (pp. 135-151). Springer, Cham.
Mohamad, M. S. A., Din, R., & Ahmad, J. I. (2021). Research trends review on RSA scheme of asymmetric cryptography techniques. Bulletin of Electrical Engineering and Informatics, 10(1), 487-492.

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