Is Cryptography Math or Computer Science: Unraveling the Interdisciplinary Field

Introduction:

Cryptography, this foundational pillar of secure communication, is often perceived as an encompassing specialty that intersects both mathematics and computer science. This article delves into the intricate relationship between these disciplines, exploring how cryptography is both mathematically founded and practically applied through computer science.

The Mathematics Behind Cryptography

Theoretical Foundations:

Cryptography relies heavily on mathematical concepts such as number theory, algebra, and probability. For example, public-key cryptography is based on the mathematical difficulty of factoring large prime numbers. This theoretical underpinning forms the backbone of cryptographic algorithms and protocols, ensuring the security of information in digital communication.

Algorithms:

Many cryptographic algorithms are developed using mathematical principles. For instance, elliptic curve cryptography utilizes the properties of elliptic curves in algebra. These mathematical tools provide the necessary framework for secure and efficient cryptographic mechanisms.

The Computer Science of Cryptography

Implementation:

Cryptography is implemented in software and hardware, requiring a deep understanding of algorithms, data structures, and programming. Software engineers and security experts design and develop cryptographic systems that can be integrated into various IT platforms and networks, ensuring secure access and communication.

Security Analysis:

Computer science provides essential tools for analyzing the security of cryptographic systems. This includes complexity theory and computational models, which help in understanding the robustness of cryptographic algorithms against potential attacks.

Protocols:

The development of secure communication protocols like SSL/TLS involves principles from both computer science and cryptography. These protocols ensure secure data transmission over digital networks, making them a critical component of modern cybersecurity infrastructure.

Conclusion

In summary, cryptography is fundamentally rooted in mathematics, but it is applied and implemented through computer science. The two fields work together to create secure systems for information protection. This interplay highlights the critical importance of both disciplines in ensuring the confidentiality, integrity, and availability of digital information.

Does It Matter?

First things first, “computer science” is a horrible misnomer. It isn’t and never was a science; instead, it is a field of engineering, primarily focused on constructing useful things, heavily reliant on several disciplines within applied mathematics.

The field of cryptography is essentially divided into two separate fields:

Theoretical Cryptography: Responsible for the mathematical underpinning of cryptography—the algorithms themselves. This side is what is taught at most universities and it is very much a field within mathematics. The theoretical cryptologists get most of the fame and accolades, but the applied cryptologists, who are more focused on practical implementation, often eclipse them both in number and budgets. Applied Cryptography: Concerned with the implementation and integration of cryptographic tools into larger software projects, mostly used to provide secure communication. Practitioners are mostly software engineers who have become specialists in security.

The jargon and language used in these fields have become so different that they have essentially become two different fields.

Final Thoughts

The division between theoretical and applied cryptography highlights the dual nature of this field. While the fundamental concepts and algorithms are rooted in mathematics, the practical application and integration of these concepts require a strong foundation in computer science. This interplay underscores the critical importance of both disciplines in the advancement of cryptographic technology and cybersecurity.