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February 9, 2017

# Tutorial: Math For Computer Science Security

February 9, 2017

By: xorinsomnia

February 9, 2017

**Hello, Cybrarians!**Today we will continue our discussion about Security, as mentioned in Introduction to Computer Science Security, math is the core of security, and as I promised I will try to make this part as simple as possible. Before we start our discussion, I'd like to mention that during this tutorial, you will figure out that there are two categories of required math and they depend on the branches of Cryptographic studies:

- Classic Cryptography require some basic mathematics operation (addition, subtraction, etc..) as we will see in Caesar Cipher,
- On the other-hand, Modern Cryptography requires an advanced level of mathematics (function, log, factorization, etc...) as we will see on (RSA algorithm, HASH, etc..)

- Basic Math
- Advanced Math

*Basic math corresponding to classic cryptography, hence for the sake of simplicity, I will mention the name of mechanism and a brief of it, till the cryptography part done.*

**Basic Math:****Caesar Cipher:**In the

*Caesar cipher*(based on simple addition or subtraction a.k.a substitution), the English alphabet consists of 26 letters A = 1, B= 2, C = 3, etc... . In order to apply the

*Caesar cipher*mechanism, you need to shift every letter by 3 positions in the alphabet.

- For encryption, you need to shift the letter 3 positions to the left (Addition)
*Ex.1*suppose we have word (cybrary) to encrypt it we recall caesar cipher

so (Plain Text: ABCDEFGHIJKLMNOPQRSTUVWXYZ Adding 3 to every letter will give us the cipher text Cipher Text: DEFGHIJKLMNOPQRSTUVWXYZABC **cybrary**) will be (**fbeudub**)

- For decryption, you just need to reverse the previous operation by shifting the letter 3 positions to the right(subtraction)
*Ex.1*suppose we have word (VHFXULWB) we want to decrypt it we recall caesar cipher

so (Cipher Text: DEFGHIJKLMNOPQRSTUVWXYZABC Subtracting 3 from every letter will give us the plain text Plain Text: ABCDEFGHIJKLMNOPQRSTUVWXYZ **VHFXULWB**) will be (**SECURITY**)

*which is similar to cipher text.Thank you*

**substitution cipher**