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Is Cryptography Math, Or Computer Science?

Cryptography or cryptology is an approach that involves using codes and mathematical algorithms to secure information and communication. While not explicitly a digital field — we have been employing ciphers and encryption techniques for ages — cryptographic methods are now used extensively online to maintain the integrity of the web. 

Information security / cryptography aims to help organizations and individuals to secure and pass sensitive information across the various insecure platforms to the intended recipients, without any other person gaining access to it.

So, since cryptography makes use of code and mathematical algorithms to secure data, is it primarily mathematics, or is it computer science?

Cryptography is neither math nor computer science alone. Instead, it’s a process that embodies three major subjects: computer science, pure mathematics, and information security. That said, some of the important topics in digital cryptography include number theory, software architecture, networking, and programming.

The Importance of Encryption and the Growth of Information Security Careers

With the advancement in technology, the internet has now become a great platform to facilitate a host of activities, including social interaction, shopping, and making payments online. For instance, studies showed that e-commerce sales gained about $861.12 billion in 2020 alone in the US. However, none of these transactions would have been possible if not for the cryptography (encryption and decryption) algorithms that prevent hackers from intercepting the transactions.

Cryptography involves complex processes to secure data. One of them is “defining and analyzing” encryption and decryption algorithms and protocols. Digital cryptography also requires being written in software and embedded in even larger software before it can work. So, it requires the knowledge of both math and computer science, as one alone isn’t enough to make it work. In the rest of this post, I’ll be further sharing with you everything that you need to know about cryptography, and which path to take: computer science, or pure mathematics.

Is Cryptography Math, Or Computer Science?

If you have a background in Mathematics, are you better prepared to study cryptography than someone with a computer science background?

Although cryptography embodies more concepts from mathematics, the fact remains that it won’t be able to work without the knowledge of computer science. As we all know, cryptography is the process of securing information and communication with the help of codes and mathematical algorithms.

Mathematical algorithms are utilized in cryptography for data encryption, authentication, and digital signatures. However, it’s worth noting that without binding cryptographic keys to user identities, there is no way you can enable the algorithms. This is where the building of Public key infrastructure (PKI) systems comes into the scene – a process that requires the knowledge of computer science.

Is Cryptography A Math?

Pure mathematics is the basis for cryptography. As such, modern cryptography heavily depends on some of its theories, such as number theory. Even at that, you need to understand that this doesn’t make cryptography math alone, as it also embodies computer science and information security.

In cryptography, there are a couple of terms that you need to get familiar with to understand its mathematical aspect. These terms, which include confidentiality, authentication, non-repudiation, and data integrity, also helps to understand how mathematical algorithms work in cryptology.

Let’s have a quick look at the list of some of the key mathematical topics involved in cryptography:

  • The Diffie-Hellman algorithm
  • RSA algorithm
  • Birthday problem – requires knowledge of probability
  • Binary numbers
  • Pseudo-random number generation
  • Prime factorization
  • Big-O-Notation
  • Number theory
  • Algebra and set

Is Cryptography A Computer Science?

Cryptography is a science of securing information and communication from being accessed by unauthorized people (cybercriminals). Although pure mathematics form the basis of cryptography, the process also relies heavily on computer science. In cryptography, there’s a need to convert data to hidden codes to be able to transmit it over a public network. This is one of the applications of computer science knowledge in cryptography.

I mentioned earlier that confidentiality, authentication, non-repudiation, and data integrity are the major cryptology terms that enable us to understand the math behind the process. These terms also help to understand how to use cryptography to secure computer systems.

For instance, confidentiality means information must only be accessed by authorized parties. Data integrity means that data must be preserved throughout the encryption. As for non-repudiation, it means nobody is capable of denying a transaction on computer network systems. 

Furthermore, authentication means the mathematical algorithms must confirm the identity of the sender and recipient of the information.

Yes, computer science plays an integral role in cryptography.

What Kind Of Math Is Used In Mathematics?

Earlier, I mentioned that cryptography embodies pure mathematics. I listed a few mathematical topics that you’ll likely come across if you’re planning to learn cryptography. They include the Diffie-Hellman algorithm, RSA algorithm, Birthday problem, binary numbers, pseudo-random number generation, prime factorization, Big-O-Notation, number theory, and Algebra.

Speaking of Big-O-Notation, it’s an important mathematical notation that helps in terms of expressing the computational difficulty of certain algorithms. In simple terms, the notation helps to understand the number of calculations required to execute specific algorithms in cryptography.

Furthermore, the Diffie-Hellman algorithm is used in asymmetric cryptology to find solutions for passing both public and private keys package through a secured path.

The RSA algorithm requires the use of prime numbers to generate keys: both the public keys and the private keys; these keys are what helps in the encryption and decryption of information and communication.

The Birthday problem is another kind of mathematics used in cryptography. The problem involves showing how probable it is for many people in a group to have the same birthday, and it is utilized to give a detailed explanation of other phenomena in cryptography.

Another mathematics in cryptography is the pseudo-random number generation. These are algorithms that help to come up with random number sequences, used in cryptography.

What Education Is Needed To Become A Cryptographer?

As a cryptographer, you can always work in various organizations, including the private sector. You can also be hired by the government to help secure data and national interests.

The field today is a highly mathematical one, with current systems dependent on theoretical subjects like discrete logarithms, prime factorization, and elliptic curves. Emerging techniques rely on even more mathematical subjects, such as the hardness of lattice basis reduction. Pure mathematics will on average better prepare someone for learning cryptography, than will computer science.

If you have no background in computer science, you will need to become familiar with algorithm design, but that will come naturally as you study.

What education is required to start a career in cryptography?

Depending on which aspect of cryptography you’re interested in, the three major education degrees required to pursue your career are computer engineering, computer science, and pure mathematics. In case you have a degree in related courses, you can also start a career in cryptography. You might also be interested in Is Cryptography Hard to Learn?

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