RSA – Part 2/2

The question that many people keep asking is (How does the RSA cipher work?). In fact, RSA cipher consists of three basic steps, where you need to have at least some basic mathematical concepts knowledge.

  1. The modulo operator.
  2. Euler’s totient function.
  3. Euler-Fermat theorem.


First, you need to keep in mind the following concepts, since you will be using them continuously in Cryptography, especially RSA operation.

  • Integer numbers: Simply any number/whole number and is not a fraction. For example, (0, 1, 2, 3, 4, 5 and more). Sometimes they are called natural numbers.
  • Fraction number: is a way of expressing a number that is a ratio of two integers. Usually fraction numbers are part of a whole or something. For example, 1/2, 1/8 and more.
  • Prime numbers: any number that is divisible only by itself and 1. For example, (2, 3, 5, 7, 11 and more).
  • Factor numbers: are the numbers we multiply to get another number. For example, the factors of 15 are 3 and 5. In addition, some numbers have more than one factorisation or more than one way to do the factoring. For example, the factors of 12 could be (1×12), (2×6) or (3×4). Remember: any number that can only be factored as 1 times itself is called “Prime”.
  • Modulo operation: in this modulo operation, we are interested in the remainder (r) left over from the division with an integer number. For example, 16 1 mod 5. As a real-life example, 5 university students have ordered a large pizza. The pizza has arrived with 16 slides, where every student will eat 3 slides; and eventually 1 extra slide will remain (this slide is what we are after the reminder). Note: the modulo operation sign is “”. See the figures below for more details:





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