Cryptology is the use of algorithms and codes to enhance data security. The aim is to encrypt and decrypt messages to ensure that only the intended recipient understands them. Since it employs mathematical and computer skills, those intending to venture into it are usually uncertain whether they need more math or computer science skills.
So, is cryptography more math or computer science? Cryptography is not a subset of math or computer science; instead, it employs the principles from both subjects to aid in encryption and decryption of data for security reasons.
The skill requires equal knowledge in the two fields since they form the basis of most underlying concepts. Generally, cryptographers need a background in computer science, mathematics, information security, and other complex skills.
If you need to know what to expect when venturing into cryptography, this is the guide for you. We will explain whether cryptography needs math, what kind of math is used in cryptography, and whether cryptography uses pure math. Read on for these and more details.
Does Cryptography Need Math?
Mathematics is the foundation of most complex systems, including IT. Therefore, most professionals dealing with computer systems are proficient in math. However, does cryptography need math?
Mathematics forms the basis of cryptography. Therefore, you should be adept at math concepts and applications to pursue a cryptology career. It employs encryption and decryption of algorithms, all of which are mathematical models. If you don’t have a degree in mathematics, it is best to take a math course.
Otherwise, the course may seem too complex for you and strain you in the process. Besides, it would be best if you did more practice to perfect your math skills as you progress in learning the skill because you will often come across the mathematical concepts.
The ancient people of Egypt are the first documented to use cryptography. It was a complex message conveying what the recipient wanted to communicate. Other records show the Mesopotamia people hiding important pottery recipes in tablets. The skill has stood the test of time and evolved over the centuries to become the complex system we understand today by using math principles.
Currently, cryptography entails specially designed algorithms. Although it mostly deals with manipulating and creating keys, math is also a key component in dictating how both users send and receive the message.
These algorithms enhance data security such that other people cannot read the message unless they use the keys meant for the equation. The same principle applies to identity authentication and messages for enhanced security.
Therefore, having a mathematical background gives you an upper hand when learning cryptography or any other related skill. Professional cryptographers are talented in mathematics. Besides the creation and manipulation of algorithms, you need to understand the relation between digital signatures and cryptography.
Digital signatures enhance the key concepts of non-repudiation and confidentiality. These signatures are the mathematical form of representing the validity of a message. You will often apply math theories to verify statements using real number systems and algebraic structures.
In other cases, the course may go deeper, meaning that those with math or related degrees will understand better. You can expect linear algebra, differential equations, probability, calculus, and more in-depth mathematical concepts.
What Kind of Math Is Used in Cryptography?
The main reason why few people are venturing into cryptography is the fact that one needs to have a good understanding of various mathematical concepts. However, the silver lining is that it can be easy for you to grasp all the concepts when you understand the key areas you need in math.
Studying cryptography requires proficiency in various math concepts such as algebraic theory, probability, statistics, discrete math, algebraic geometry, complex analysis, number theory, algorithms, binary numbers, prime factorization, and other key areas. You may also need more knowledge about more complex topics if you are doing cryptography at an advanced level.
The key concept to consider is pure mathematics, which focuses on issues like number theory. Math also plays a role in applying cryptology aspects; hence, you need to be familiar with terms like data integrity, authentication, non-repudiation, and confidentiality.
To perfectly grasp modern cryptography, you need to understand all the foundational aspects of the skill. It emphasizes mathematics, which holds the theoretical and the hands-on part. It is vital to develop the essential tools to construct and analyze the current advanced cryptosystems, and the only way is to gain knowledge on basic mathematics.
The fundamental areas for cryptography include the classical Diffie-Hellmann system, discrete logarithms, RSA cryptosystems, digital signatures, binary numbers, big-O-notation, pseudo-random numbers, probability, and statistics, and other complex areas.
Without the elementary understanding of these essential topics, you may find it tasking to understand or even apply the concepts you learn in cryptography. For instance, the big-O-notation signifies the number of calculations used to run the system. At the same time, prime factorization employs multiplying two prime numbers when securing a public system.
You can also quickly generate random digit sequences using the pseudo-random algorithm. You may also learn the Birthday Problem concept, where you calculate the probability of individuals in a group sharing a birthday, which essentially determines other probabilities.
The most famous and widely used algorithm is the RSA, which is the basic tool in Bio Cryptography. It furthers biometric systems, centers around prime numbers, and helps generate keys for private and public systems on a large scale since it usually deals with bulky data. Lastly, we have the Diffie-Hellman (DH) algorithm, which is vital for securing data but doesn’t necessarily encrypt the ciphertext. Its main function is to find a way to send private and public keys.
Does Cryptography Use Pure Math?
A mathematical background is necessary to study the art of cryptography since algorithms require keys that are mathematically coded. Cryptology doesn’t use all the math concepts you previously studied but only employs particular relevant topics. We need to establish the exact kind of mathematics you need to comfortably and successfully study cryptography.
Cryptography requires not only pure math but also applicable mathematics and other fundamental related subjects like computer science. Other vital topics that will make your study a walk in the park include number theory, algebra, probability, and statistics, among others.
Generally, you need a strong knowledge of computer science, pure mathematics, and information security to start your career. You may also require information about programming, networking, and computer architecture to ace everything up for you.
Pure math can help advance and develop more complex encryptions with enhanced security to guard against cybercrimes. Notably, math is the foundation you need to build a career in cryptanalysis.
Decrypting and encrypting data is a complex process such that you require knowledge in other disciplines, not only computer systems. However, surface knowledge may be enough to learn the basics of cryptography, but you may need more than that if you want a deeper understanding and hands-on experience.
A wealth of knowledge in pure mathematics will etch a place for you in the job market and guarantee a lucrative salary in employment regardless of whether you work for the public or private sector. On the contrary, you may not have a lot of qualifications, but, instead, have a strong interest and high drive to succeed in the field, qualities which will go a long way in learning and polishing the skill. Having basic knowledge as an employer is also vital to enable you to question certain processes.
Data encryption and decryption is a fascinating course that you can enjoy learning and will never regret investing your time and resources taking it. Don’t be discouraged by the fact that the subject requires prior understanding or pure mathematics. The good thing is you don’t need to have studied the subject at a very advanced level.
Having a degree, master’s, or even Ph.D. in the key subjects you need for cryptography will only give you an upper hand by enabling you to grasp certain theories and know-how and when to apply them.
An added advantage is that your training period may be shorter than for another learner starting from scratch. The subject is quite bulky; hence, it may take a beginner approximately two years. However, those with background knowledge can take a few months to become professional cryptanalysts. Furthermore, it would be best to review some pure mathematics topics you are likely to deal with.
For instance, you will come across a concept like the Diffie-Hellman algorithm, which uses a secured path to pass private and public keys in asymmetric cryptology. Secondly, RSA algorithms will help you generate keys using prime numbers, and Big-O-Notation will assist in understanding what calculations you need to execute a certain algorithm. Finally, the Birthday problem in pure mathematics deals with probabilities to determine certain events in cryptography.
Does Cryptography Need Computer Science?
Computer science integrates theory and application using computers for engineering, mathematics, artificial intelligence, algorithms, software, and hardware development. Therefore, we aim to determine whether these two sciences are connected in any way.
Cryptographers need knowledge in computer science to understand how computers work in encrypting and decrypting data. All information coded through cryptography needs safe transportation through computer networks, which is where these two sciences complement each other.
The two work collectively to enhance the understanding and implementation of non-disclosure, verification, data integrity, and non-repudiation to secure computer systems. In essence, once the cryptographer develops a ciphertext, it will require a computer system to ensure that the message reaches the intended recipient without being hijacked by cybercriminals.
First, confidentiality ensures that the information sent should only be accessed by the intended user who will then decipher the original data. With the help of cryptographic equipment, any unauthorized person is shut out from accessing the computer networks.
Similarly, the non-repudiation principle ensures that the data stays authentic such that there will always be evidence of successful communication between the recipient and the sender. Therefore, it ensures that all the involved parties take responsibility for their actions.
Furthermore, verification factors (mathematical algorithms and protocols) always guarantee that the computer network knows the identity of the sender and audience, which helps in the authentication process. Finally, data honesty in cryptography assures that the information you send, and the network system are always protected, and no one can compromise your data.
What Education Do You Need To Be a Cryptographer?
Undoubtedly, cryptography is one of the most competitive skills in the job market, especially now that the world is going digital. Therefore, many professionals are adding it to their skill sets. As a beginner, you would want to know what it takes to be an expert cryptographer.
The most important education you need to kick start your career in cryptology is computer science, pure mathematics, or computer engineering. You can also pursue it with a degree in any other related course. It wouldn’t harm to do a refresher course if you did the subjects at an elementary level.
However, an undergraduate degree is preferable since you will have the foundation and background of the key cryptography aspects, which are computer science and mathematics.
Although a degree will suffice to launch your career, you can get experience in the field and pursue your master’s to perfect your expertise. A higher education level will make you stand out more and give you a more competitive edge. We usually advise those talented in mathematics to pursue cryptography.
You will need it in encryption and decryption of ciphers and algorithms, which require a strong background in math. The best cryptographers are either exceptionally good in mathematics or practiced a lot and took refresher classes.
To establish your career, you need at least a bachelor’s degree in the key areas. You can also further go for a master’s or Ph.D. for a better advantage over other applicants. Besides a higher education level, some companies may require you to have a wealth of experience. You can find an internship to polish your skill sets and work in different sectors to gain more practice.
Expect to work for private and public sectors and be dedicated, hardworking, and committed to handling bulky data. You can also get a sensitive role like helping to secure government data when dealing with national security matters.
All professional cryptographers will tell you that cryptography isn’t for the faint-hearted. The algorithms used are pretty complex and exceptional, and the only way to understand them better is to have background knowledge in mathematics, computer science, or a related field. It may be tasking for you to start from scratch.
Relatively, it may also take you a long time to understand how and when to implement the algorithms fully. Remember that you will ensure the safe conveying of sensitive information; therefore, you need to be fully involved in getting it right. It is wise to have a high affinity for computer science and mathematics to grasp and apply the concepts.