Perfect Secrecy and Provable Security

Everyone knows that the one-time pad provides perfect security. But what does this mean? In this chapter, we make this concept precise. Also, we know that it is very difficult in practice to produce a truly random key for a one-time pad. In Section 2, we show quantitatively how biases in producing the key affect the security of the encryption. The topics of this chapter are part of the subject known as Provable Security. Rather than relying on intuition that a cryptosystem is secure, the goal is to isolate exactly what fundamental problems are the basis for its security. The result of Section 2 shows that the security of a one-time pad is based on the quality of the random number generator. In Section 7.5, we show that the security of the ElGamal Public key cryptosystem reduces to the difficulty of the Computational Diffie-Hellman problem, one of the fundamental problems related to discrete logarithms. In Section 8.6, we use the Random Oracle Model to relate the security of a simple cryptosystem to the non-invertibility of a oneway function. Since these fundamental problems have been well studied, it is easier to gauge the security levels of the cryptosystems.