Basic Concepts
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This chapter describes some basic concepts of cryptography:
 What is cryptography?
 Functions.
 Encryptions.
Cryptography
Cryptography  The study of techniques related to all aspects of data security.
The word "cryptography" is derived from the ancient Greek words "kryptos" (hidden)
and "graphia" (writing).
Some aspects of data security:
 Confidentiality  Keeping data secret.
 Data Integrity  Ensuring data has not been altered.
 Entity Authentication  Identifying parties involved.
 Data Origin Authentication  Identifying the data origin.
Cryptanalysis  The study of techniques to defeat cryptographic techniques.
Function
Function  Two sets of elements, X and Y, and a rule, f, which
assigns to each element in X, to one element in Y. A function is denoted as
f: X > Y.
Domain  The set of elements, X, in the above definition.
Codomain  The set of elements, Y, in the above definition.
If x is element in X, and y is the element in Y assigned to x by a function f,
y is called the image of x, and denoted as y = f(x).
If y = f(x), x is called a preimage of y.
Image of Function  The set of all elements in Y which has at least one
preimage in X.
11 Function  A function that satisfies that "if x <> y, then f(x) <> f(y)".
No two elements in the domain will have the same image for a 11 function.
Bijection  A 11 function that satisfies that "image of f is Y".
Inverses Function  The function g of a bijection f that satisfies that
"if y = f(x), then x = g(y)".
Oneway Function  A bijection that satisfies that "the computation of its
inverse function is very hard, and close to infeasible".
Trapdoor Oneway Function  A oneway function that satisfies that
"the computation of its inverse function becomes feasible, if additional information
is given".
Permutation  A bijection that satisfies "f: X > X".
Involution  A permutation that satisfies that "inverse function of f is f".
(Continued on next part...)
Part:
1
2
