A Course in Mathematical Cryptography

9 Basic Concepts from Group Theory

9.1 Groups and Group Theory

Up to this point we have been using algebraic objects arising from number theory, such as the modular rings _n and elliptic curve groups, to do encryption. These objects are all commutative and hence we can call the type of encryption we have already done as commutative cryptography. In an effort to improve upon cryptographic security, non-commutative cryptography was introduced. Non-commutative cryptography is essentially group based cryptography. In group based cryptography, non-abelian groups and their properties are used in encryption and decryption. There are two primary sources ...