Mathematics for Cryptography?

vegetaholic

I see all security certs have objective related to cryptography.I have few questions regarding:

1)What Maths I should know for cryptography?
2)Should I really need to know mathematics for cryptography or I only need to know
structure of cryptography or how crypto-system works?

I know maths which will help me writing exploits and brute-force attacks.

I have little mathematics background.I know matrix,a little number theory,sets , logic,groups,
curve fitting,a bit of calculus.That's all.

I know Keatron you will take care of my problem. :P

best regards,
Vegeta

Schluep

I am not a cryptography expert by any means, but hopefully this will answer your question and peak your curiosity at the same time .

Unless you are planning to write cryptographic algorithms or perform cryptanalysis you like will not have much need to be heavily involved with the mathmatic aspect. Unless you plan to be a math expert and spend a lot of time with things such as frequency analysis a basic understanding is usually sufficient for Security purposes.

For any information related to Cryptography when it comes to InfoSec is knowing which algorithms have inherent flaws or weak keys that should be avoided. Knowing which algorithms are the strongest and their recommended key lengths is the most important thing to know. Also, Cryptography can be used for different purposes, such as Integrity, Confidentiality, or Non-Repudiation. Some devices needing encryption such as cell phones do not have the same processing capability of a PC. Do you need an entire communication channel to be encrypted or simply a credit card number exchanged over the internet? All of these factors will weigh into the decision and having a basic understanding of the algorithms available and how they work will be needed to make that decision.

As an example from a mathmatical example consider RSA. If you do any reading on RSA you will see that the math is basic factorization of numbers (with padding). It is very easy to understand for people not heavily involved in mathmatics. You don't even need to know how to factor numbers in order to use the algorithm successfully however as the software handles it for you. It is very easy to understand, but very difficult to break since the numbers used are very large using our current processing capability. Keys are typically 1024 or 2048 bits for safe use with RSA. As processing power increases the keys need to become longer. If you used RSA with a 256 bit key most personal computers today are certainly capable of cracking it. If someone finds a highly effective way for a computer to factor large numbers the entire algorithm will essentially be broken. You may want to read about TWIRL and the ability it could have (or already has) for a government or large organization to crack even 1024 bit keys on RSA in a short period of time if built.

As you study cryptography you will see several different methods being used such as Factoring, Elliptical Curves, Discrete Logarithms, and more. Cryptography will obviously continue to evolve with things such as Quantum Computing which can be used to possibly break many of the encryption methods we use today or even the use of Quantum Mechanics when applied to the transmission if light in a Fiber Optic line that was not previously possible. Personally I think it is amazing to see how far things have come already from simply substituting characters. The most important thing to understand with cryptography is that every algorithm/key combination can be cracked, it is only a matter of how long it will take. The goal is to make the time period so long that there is no point in attempting to crack it using our current processing power.