TABLE OF CONTENTS A major problem when designing cryptosystems is how to define and measure the exact security of the system. A scientific study of the security of cryptosystems started with the work of Claude Shannon [1]. Shannon is also famous for being the first person to propose the use of Boolean algebra to analyze digital circuits, creating what is now called logical switching. In Shannon's later work, "A Mathematical Theory of Communication" [2], outlining what we now know as information theory, he described the measurement of information by binary digits representing yes-no alternatives, the fundamental basis of today's telecommunications.
What was most impressive is that, believe or not, Shannon did prove that a cipher proposed by Gilbert Vernan, a researcher at AT&T, is a perfect encryption scheme, secure even against all powerful adversaries. This scheme is known as the one-time pad. For simplicity, we will describe the one-time pad for binary messages {0, 1}. Suppose that both the sender and the receiver possess a copy of a random sequence of 0's and 1's (the key). The sender, Alice, can encode a message by combining the message and the key using the exclusive-OR operation bitwise. An exclusive-OR operation, or XOR, will be denoted by the symbol + and is characterized by the following relations: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0. In general words, when the two terms of the XOR operation are equal,...
