## 5. Algebraic Structure

Modern encryption algorithms such as DES, AES, Rivest–Shamir–Adleman (RSA), and ElGamal, to name a few, are based on algebraic structures such as group theory and field theory as well as number theory. We will begin with a set S, with a finite number of elements and a binary operation (∗) defined between any two elements of the set:

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That is, if a and b  S, then a∗b  S. This is important because it implies that the set is closed under the binary operation. We have seen that the message space is finite, and we want to make sure that any algebraic operation on the message space satisfies the closure property. Hence, we ...

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