6 Some Number Theoretic Algorithms

Number theory plays a prominent role in many areas of cryptography. In the simplest case, to develop a cryptosystem for an N letter alphabet, we consider the letters as integers modulo N. As described in Chapter 5, the integers modulo N form a ring called the modular ring _{N} and encryption is done using algebraic operations on this ring. The totality of operations within the various modular rings is called modular arithmetic. The encryption algorithms then apply number theoretic functions and use modular arithmetic on these integers. Hence encryption ...

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