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I'm an undergraduate student at Kaplan University and one of my projects in my Algebra class is to be able to identify two concepts that we've learned thus far and how they might apply towards my major which is IT Security/Computer Forensics. I'm struggling because I can easily see how some of the formulas, graphs, etc. apply to something like accounting or nursing; but I'm just not making the connection to IT Security. Partly because this is new field of study for me and I'm just not sure where to begin.


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closed as off topic by GdD, Rory Alsop Mar 4 '13 at 19:55

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The way you've asked your question is very localized and very open ended; that is a bad fit for SEC:SE. Could you revise the question so that the answsers are (1) objective and (2) useful to a wider audience? –  Mark C. Wallace Mar 4 '13 at 16:42
If you learned about groups or finite fields, you should look into asymmetric crypto. –  CodesInChaos Mar 4 '13 at 17:39
Closing as off topic, as per 2 flags and a vote to close. Not a Stack Exchange suitable question, I'm afraid. –  Rory Alsop Mar 4 '13 at 19:56

3 Answers 3

Well, exponents are a big deal in IT security, especially powers of two. The "strength" of most cryptographic secrets is based on how many bits of entropy they contain, which for most purposes is simplified to the maximum number of bits of the secret (the length of the key, hash, IV, salt, etc). The number of possible combinations of N bits is 2N.

Most ciphers are based on bitwise arithmetic or modulo division, which are interesting but not usually core concepts of a college algebra class.

It would be helpful for you to give us a short list of the things you've learned in your algebra class so far. We could then tell you how they're used.

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I can see quite a few ways that it's applicable:

  • Algebra involves a lot of problem solving, since you have to identify the problem, the variables involved, and decide upon the best tool(s) to target that problem. This kind of thought process is critical to most security jobs.
  • If you're going to do pretty much any cryptography theory, you're going to need to know some basic algebra. Cryptography is very deeply grounded in mathematics.
  • A lot of security jobs involve some sort of programming or scripting, which algebra applies to, both in terms of direct mathematics and inherent problem solving requirements.

If you're looking for individual types of mathematics that are applicable:

  • The properties of primes are exploited as part of RSA, to perform asymmetric cryptography.
  • Statistical entropy calculations are used as a crude measure of "randomness", which may be useful in detecting spam produced by Markov chain generators and other such random schemes.
  • Set theory is often utilised in identifying traffic correlations and building filters for "bad traffic".
  • Vulnerability scoring systems often use algebraic models to produce a single value score, based on input score values for a variety of categories.
  • Cryptanalysis is highly reliant on the field of probability to identify situations where a bias can be detected and exploited.
  • Learning algorithms can employ mathematical models of brain neurons to match patterns with high accuracy, even if the sample data changes in a subtle way. This is useful for spam filters, traffic filters (IDS / IPS), malware detection, etc.

Of course, these are just a few shallow examples. What's really applicable depends on what kind of things are on your course.

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Cryptography uses a lot of algebra (basic algebra, and... less basic algebra). You can use a lot of cryptography in IT Security, and there is a lot of IT Security that you cannot do without cryptography.

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