Which background is more suitable to study "Cryptography"

Question

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE .

Recently I have started learning "Cryptography" .But there are many definitions involved here like polynomial time algorithm,time complexity etc.

My question is it all right for a student in Pure Mathematics to study Cryptography or as time progresses I will eventually fall out of place and lose interest in this subject.

Is Cryptography more suitable for computer science graduates or it does not matter which background a student is from to study this?

Please share your thoughts here as i am still in my early days and may help to change the subject if necessary before it is too late

Cryptography is vast, it would be helpful to describe in more detail what kind of material you are studying (or, even better, what the assigned textbook is, if any). For example, is it a course in the foundations (one-way functions, pseudorandomness, etc.), a more standard "intro to cryptography course" where you study classical ciphers, Diffie-Hellman, RSA, or something else? — fkraiem, Jul 22 '15 at 16:45
Whether you will lose interest is a very personal question that takes a lot more data than you have given to answer. It can happen, but so can the opposite (you discover your true destination is breaking ciphers). Whenever you learn a discipline, getting bored is always a possibility, and the only way to tell is to try it out. — darij grinberg, Jul 22 '15 at 16:59
@fkraiem; I have to study classical ciphers,symmetric,public key crypto etc — Learnmore, Jul 22 '15 at 17:22
@Learnmore Dear OP, Did you end up choosing cryptography as your career? — SARTHAK GUPTA, Jan 02 '25 at 21:43

hexaflexagonal · Accepted Answer · 2015-07-22T16:57:12.640

As a computer science student who took a graduate course (albeit an introductory one) in cryptography last semester, I found myself pulling from my knowledge of number theory immensely more than I did from my knowledge of computer science. The field today is a highly mathematical one, with current state-of-the-art systems reliant on number theoretical subjects like discrete logarithms, prime factorization, and elliptic curves. Emerging techniques center around even more mathematical subjects, such as the hardness of lattice basis reduction. In fact, I think that pure math students will on average have an easier time learning cryptography than computer science students.

Even though you are not currently familiar with the meaning of terms like "polynomial time algorithm," you should be able to grasp time complexity very quickly as a student of pure mathematics. You will need to become familiar with algorithm design, but that will come naturally as you study.

In short, go for it! Almost everyone will come in lacking some sort of background knowledge regardless of what they studied, but if you are motivated then you should be able to pick up the slack without much trouble.

I feel I should go for it from your comments ;+1;any books for me — Learnmore, Jul 22 '15 at 17:25
Hoffstein, Pipher, and Silverman (who are themselves pioneers in the field) have written the excellent and accessible An Introduction to Mathematical Cryptography. As a student of pure mathematics, you will be able to skip a lot of the material (e.g. there are subsections dedicated to introducing rings, groups, and fields) and jump straight into the cryptography itself. Admittedly, it's the only introductory cryptography text I've ever used, but I do not hesitate at all in recommending it. — hexaflexagonal, Jul 22 '15 at 17:34

score 6 · Answer 2 · answered Jul 22 '15 at 16:41

In a sense, both of your ideas (computer science and pure mathematics) are both correct for what might be suitable for cryptography. RSA encryption is based on abstract algebra concepts, and also the computer science belief that factoring integers is hard unless on a quantum computer. You can read about RSA online, there's plenty of references and if you know abstract algebra it's not that hard. Similarly, mathematical (theoretical) computer science as well as more pure math like combinatorics and number theory can play a huge role in cryptography. Who knows what crazy problem from combinatorics or number theory or algebra will lead to the next latest and greatest cryptography system where de-crypting is equivalent to solving the original math problem instance and the problem is NP-complete?

thank you very much +1;can suggest some books for me which are more inclined towards having pure maths as background? — Learnmore, Jul 22 '15 at 17:25

score 4 · Answer 3 · answered Jul 22 '15 at 22:14

Much of cryptography today works on grounds of abstract algebra (and number theory). Clearly to show that some encryption technique has a corresponding decryption one requires proof, that is math. But that is just a small part of cryptography. The recent most talked about problems with cryptographic systems have been programming errors, disregard of the theory and existing practical experiences, blatant misuse of the theory or of the programs, and other "human", not "technical" or "theoretical" problems. I'd suggest you take a peek at the classic "Security Engineering" by Anderson (the link is to the free full set of PDFs for the chapters, I liked it so much I bought it on paper...), it shows a much wider scenery (one I find much more relevant in actual practice).

Which background is more suitable to study "Cryptography"

3 Answers3