Prime numbers are integers greater than 1 that can only be divided by 1 and themselves. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. This property makes prime numbers unique and highly significant in mathematics, particularly in cryptography. The use of prime numbers in cryptography is applied in encryption algorithms that are used to safeguard data security.
Cryptography is the science of studying methods to hide information or data so that only authorized parties can read it. Cryptography protects data from unauthorized access, ensuring the confidentiality, authenticity, and integrity of information. In today’s digital world, cryptography is used to secure communications, protect personal data, and ensure that online transactions remain safe. In cryptography, there is a concept of public keys and private keys. A public key is a key that can be freely distributed to anyone. This key is used to encrypt a message to be sent. Conversely, a private key is known only to its owner and is used to decrypt the received message.
The reason prime numbers are so useful in cryptography is due to the difficulty of factoring large numbers into their original prime factors. When two large prime numbers are multiplied, the result is a large number that is extremely difficult to break down into the two original primes. This difficulty underpins many modern encryption systems. One of the most famous encryption algorithms that use prime numbers is RSA (Rivest-Shamir-Adleman).
This algorithm is used to secure data in digital communication. The basic process in RSA involves selecting two large prime numbers, say p and q. These two prime numbers are then multiplied to produce n. This value of n will be used as part of the public key. Next, the value ϕ(n) is calculated as (p-1)×(q-1). A cryptographer then selects a value e that is relatively prime to ϕ(n). This value e also becomes part of the public key. To create the private key, the value d is calculated such that it satisfies the equation d×e=1 mod ϕ(n).
The RSA encryption process works by transforming the original message M into the encrypted message C using the formula C=Me mod n. This encrypted message can then be safely transmitted. To decrypt the message, the recipient uses the private key and the formula M=Cd mod n, which allows them to retrieve the original message M. The security of the RSA algorithm depends on the difficulty of factoring the large number n into its two original primes p and q. Without knowledge of p and q, it is very difficult to break the encryption and obtain the private key d.
Cryptographic applications that use prime numbers are vast and cover many aspects of our digital lives. For example, in online transactions, RSA encryption is used to protect credit card information and personal data during the payment process. Email services also use encryption to ensure that only the intended recipient can read the email content, maintaining communication privacy. Furthermore, end-to-end encryption is a feature of instant messaging programs like WhatsApp, which prevents third parties from reading the contents of conversations and only allows the sender and recipient to view them. Primes play an increasingly significant role in cryptography in this increasingly interconnected digital world. They facilitate safe communication and privacy online in addition to aiding in the protection of our financial and personal data.
The use of encryption technology in maintaining data security directly supports Sustainable Development Goal (SDG) number 9: Industry, Innovation and Infrastructure, specifically in terms of strengthening resilient information and communication technology infrastructure. Cryptography plays a role in ensuring secure technology systems, supporting digital innovation and protecting personal data in online communications, financial transactions and other digital applications. Moreover, by protecting personal information, cryptography also contributes to SDG number 16: Peace, Justice and Strong Institutions, by ensuring personal data security, privacy and transparency in digital systems, which are essential elements in realizing peaceful and inclusive societies.
Keywords: Cryptography, Prime Numbers, Encryption
Author: Kadek Wahyu Medalika Manik Segara
Editor: Endang Sulastri