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A Course in Mathematical Cryptography by Gerhard Rosenberger, Martin Kreuzer, Benjamin Fine, Gilbert Baumslag

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5 Elementary Number Theoretic Techniques

5.1    Cryptography and Number Theory

Number theory plays a prominent role in many areas of cryptography. In the simplest case of applying a cryptosystem to an N letter alphabet, as explained in Chapter 1, we consider the letters as integers modulo N. The integers modulo N form a ring called the modular ring, N, and hence encryption is done within this ring. Operations within the various modular rings are called modular arithmetic. The encryption algorithms then apply number theoretic functions and use modular arithmetic on these integers. It follows that encryption maps on k-length-message units are functions ...

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