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The Laws of Cryptography with Java Code.

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There are excellent technical treatises on cryptography along with a number of popular books. In these notes I am trying to find a middle ground, a ``gentle'' introduction to selected topics in cryptography without avoiding the mathematics. The material is aimed at undergraduate computer science students, but I hope it will be accessible and of interest to many others. The idea is to cover a limited number of topics carefully, with clear explanations and illustrative Java implementations.

The emphasis is on the underlying systems and their theory, rather than on details of the use of systems already implemented. For example, the notes present material on the RSA cryptosystem, its theory and a Java implementation, but there is no discussion of a commercial implementation such as PGP (``Pretty Good Privacy'').

The reader should not actively dislike mathematics, although the amount and difficulty of the mathematics requirements vary. One of my goals is to cover the necessary mathematics without hiding details, but also without requiring material from an undergraduate mathematics degree.

The notes contain ``maxims'' or ``laws'' designed to emphasize important points, sometimes in an amusing way -- hence the title of the overall work.

I refer interested readers to the book: Handbook of Applied Cryptography, by Menezes, van Oorschot, and Vanstone (CRC Press, 1997). That work gives a comprehensive survey of the whole field, leaving many details to technical articles that the handbook refers to. The work presents ``techniques and algorithms of greatest interest to the current practitioner''. In contrast, my work is more ideosyncratic, occasionally presenting odd material that current users would avoid.

The Java programs that accompany these notes are demonstration implementations to help readers and students understand the concepts. I have kept the code simple to further this goal, rather than strive for code that could be included into commercial or open source projects, which would require far longer and more complex code (and be much harder for me to write). The complexities then would get in the way of understanding. Readers need some familiarity with programming and with Java to understand these programs.

The book also contains various tables of values along with sample or ``toy'' calculations. In every case I've found it easier and quicker to write Java programs to generate this material rather than to do the calculations by hand.

A one-semester course in cryptography might cover the following material (I will be amending this list as the present work progresses):

• Section I.1 ``Cryptographers' Favorites''.
• Section I.2 ``Cryptographers' Favorite Algorithms''.
• Section I.3 ``Coding and Information Theory''.
• Section I.4 ``Visualizing Channel Capacity'' (at least the diagram illustrating Shannon's Noisy Coding Theorem).
• Section I.8 ``Verhoeff's Decimal Error Detection'', along with enough material from Section I.7 to understand this section. (This topic serves to introduce students to an unusual algebraic structure, namely the non-commutative dihedral group with ten elements, to prepare them for later more demanding topics, including especially the field used by the Advanced Encryption Standard (AES).)

• Section II.1 ``Introduction to Cryptography'', covered quickly as an easy read.
• Section II.2 ``The One-Time Pad '', also covered quickly as an easy read.
• Section II.3 ``Conventional Block Cipher Cryptosystems''.

• Section III.1 ``Public Key Distribution Systems''.
• Section III.2 ``Public Key Cryptography''.
• Section III.3 ``The RSA Cryptosystem ''.

• Section IV.1 ``Traditional Random Number Generators''.
• Section IV.2 ``Perfect Random Number Generators''.
• Section IV.3 ``Random Number From Chaos Theory''.

• Section V.1 ``Introduction to the AES'', and important new system.
• Section V.2 ``The Finite Field GF(256)'', hard mathematics which might appeal because of the immediate application.
• Sections V.3 -- V.6 the rest of the AES algorithm.

• Section VI.1 ``Hash Functions''.

• Section VIII.4 `` Threshold Schemes''.

The author would like to thank his mother for giving birth to him, but can't think of anyone else to thank at this time.