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This chapter provides a brief overview of some cryptographic concepts that will be expanded on later in this book. Cryptography is a complex art, though, and it cannot be adequately explained in a short chapter like this. There are many good books that give a solid background in cryptography that you're strongly encouraged to read. A good place to start is Cryptography and Data Security by Dorothy Denning, and Applied Cryptography by Bruce Schneier.
There are important and fascinating protocols and problems that were not covered here. For instance, the zero knowledge proof: where one party proves to another that she knows some information without actually divulging the information. Another one-way function that was not discussed is the knapsack problem. Like the discrete logarithm problem, the knapsack problem can be used to construct public key cryptosystems. Other, more complicated, key exchanges also exist, like the Encrypted Key Exchange (EKE). There are even attacks against the cryptographic tools that IPSec uses, like the Birthday Attacks against hash functions. This attack takes its name from the observation that if you are in a room with only 182 other people, the chances are even that one of those persons has the same birthday as you. If there is a room of only 23 people, the chances are even that there are two people in the room that share the same birthday. This in spite of the fact that there are 365 (sometimes 366) days in the year! The birthday paradox affects hashing algorithms because it illustrates the statistical probability of finding two random inputs that will hash to the same digest i.e., in finding a collision. If the digest from a hash algorithm is n bits in length, finding two distinct messages that hash to the same digest would take O(2n/2) operations.
Cryptography is probably as old as speech but it continually evolves to solve new, interesting, and critically important problems of today and tomorrow.
Top IPSec (2nd Edition) ISBN: 013046189X
EAN: 2147483647 Year: 2004
Pages: 76 Authors: Naganand Doraswamy, Dan Harkins
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