Mathematics is the queen of the sciences, and number theory is the queen of mathematics. Frequently, she deigns to assist astronomy and other of the natural sciences, but primacy is due her under all circumstances.

—–Carl Friedrich Gauss

**Why do we need a** book on cryptography whose principal focus is the arithmetic of whole numbers—the integers—and its application to computer programming? Is this not a rather insignificant subject in comparison to the important problems with which computer science generally involves itself? So long as one confines oneself to the range of numbers that can be represented by the standard numerical types of a programming language, arithmetic is a rather simple affair, and the familiar ...

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