ABSTRACT
In this chapter, we will discuss some algebraic structures used in cryptography. Finite group, cyclic group, and finite field are some of the most important structures used in the design and analysis of cryptographic primitives. The well known RSA cryptosystem is defined over the group https://www.w3.org/1998/Math/MathML"> Z n ⋆ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315114590/68140701-3c0f-4366-b454-a08b0af79dfc/content/eq24.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , ElGamal cryptosystem is defined over the cyclic group https://www.w3.org/1998/Math/MathML"> Z p ⋆ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315114590/68140701-3c0f-4366-b454-a08b0af79dfc/content/eq25.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , and one of the popular symmetric key cryptosystem AES is defined over Galois field GF(28).
