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What is Cryptography?

According to the Oxford English Dictionary, cryptography is, “A secret manner of writing … intelligible only to those possessing the key; also anything written in this way. Generally, the art of writing or solving ciphers.” A secret code used in cryptography is a cipher. The process of using a cipher to turn a plain document into a secret text is encryption, and the reverse process is decryption.

Cryptography is an ancient subject that has changed a lot throughout the years. To quote Wikipedia: “In modern times, cryptography is considered to be a branch of both mathematics and computer science.” At one time, the subject was mainly a linguistic one, the key concern being the ability to recognize words and make words unrecognizable with a simple cipher. Today, thanks to computers, the subject is very mathematical with the ciphers involved drawing from computer science and number theory.

The introduction of computers has changed the face of encryption. Historically encryption was done by hand with a pencil (or pen) and paper. A typical modern personal computer will be able to perform around 5 billion “operations” per second. This processing power coupled with its widespread use has changed the face of encryption.

People who want to enter the career field of cryptography must first earn an undergraduate degree in computer science, mathematics or a related subject. These disciplines teach the logic, quantitative, and technical skills needed to make and break complex computerized codes. Many cryptographers support military defense systems that require interaction with foreign communication signals. Researched based cryptographers have advanced degrees in information security or network engineering with specializations in cryptography and/or cryptology.

The complex mathematical formula used to convert ‘plain text’ to ‘cipher text’ is known as ‘algorithm.’

One university’s College of Criminal Justice offers a Bachelor of Science in Applied Mathematics with two concentrations: Data Science and Cryptology. The Data Science concentration presents the principles of data representation, big data management, and statistical modeling. Students learn to use modern computing techniques to reveal hidden causal and temporal relationships within large data sets. Cryptology  is the science of both personal and institutional data security. Students learn to secure information, maintain data integrity, authenticity, and non-reputability.

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During this program, you will apply the principles of mathematical proof and deductive logic to prove appropriate mathematical statements or create counterexamples with the context of the real number axioms and the axioms defining various algebraic structures. In other words, this is a math-intensive degree. Some of the classes include calculus, linear algebra, probability & mathematical statistics, and differential equations.

Understand the Differences

  • Cryptography: Writing hidden messages
  • Cryptanalysis: Analyzing hidden messages
  • Cryptology: Reading hidden messages

It is rare to find an undergraduate program devoted to cryptography. Most of the courses in the subject are embedded in computer science or cybersecurity curricula. If you opt for the computer science route, you will encounter mathematics. These may include geometrical algorithms, algebraic algorithms, and probability in computing. All useful to become a cryptographer.

There are more opportunities for a master’s degree to broaden your knowledge of cryptography. One example is a Master of Science in Cyber Security Engineering. As a student, you will become versed in the challenges and problems of secure operating systems, secure applications, secure networking, database security, and privacy, use of cryptography and key management. One of the courses in Applied Cryptography offers an intensive overview of cryptography for practitioners, historical perspective on early systems, number theoretic foundations of modern-day cryptosystems and basic cryptanalysis. This program is light on math.

It is definitely beneficial to include mathematics in your studies at the bachelor and graduate levels. This will provide the comprehension of algorithms. For example, the RSA, named after Rivest, Shamir, and Adelman who first described the algorithm in 1977. It is the first example of an algorithm for public key cryptography. It also solves the problem of authentication with public key systems. A user of RSA creates and then publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers must be kept secret.

It is evident that to understand the nuances of cryptography, you will need to be proficient at math. In addition to algorithms, you will likely study digital signatures, which are a practical application of cryptography. Digital signatures are signatures applied digitally. They enforce the concepts of authentication, non-repudiation, and confidentiality. Wikipedia defines digital signatures the following way: “A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or documents.” (Digital Signature 2016)

Manually signing a document and transferring it to different locations is time-consuming. This time lag might not bode well for either the customer or the client. By digitally signing the documents, the business transaction is completed on time.

For future cryptographers still in high school, it is advisable to take as many algebra classes as possible.

Additional Resources: 

What Degree do I need to be a Cryptanalyst?

What is a Degree in Mathematics?

What is the difference between a Computer Science and Computer Engineering degree?