1 Basic Ideas of Cryptography

1.1  Mathematical Cryptography

The subject of this book is mathematical cryptography. By this we mean the mathematics involved in cryptographic protocols. We will define, and make precise, all these terms as we proceed. As the field has expanded, using both commutative and non-commutative algebraic objects as cryptographic platforms, we felt that a book describing and explaining all these mathematical methods would be of considerable value.

Cryptography or cryptology is loosely the science of encrypting and decrypting secret codes, and the related task of breaking or uncovering secret codes. The science of cryptography touches on many other disciplines, both within mathematics and computer science and in engineering. ...

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