| Abstract: | n this thesis, a randomly dynamic cryptosystem is proposed. The processes are composed of two major parts. The first is a process of encoding and the other is encrypting. The process of encoding can be applied alone, without encrypting process.
Originally, there is a codebook, called original codebook. The original codebook is transformed with homogeneous transformations into some business codebooks, each one is different from the others. Each business has one such unique business codebook. A business has many users. Each user has one unique codebook which is again transformed from the business codebook with a homogeneous transformation, which is called fixed codebook. Once a custom wants to make a plaintext into a ciphertext, that fixed codebook is again transformed into a floating codebook with a random time function. So every time, the floating codebook is different.
Accordingly, the floating codebook is used to transform the plaintext from ordinary language words or sentences into codes. Because such codes are not easy to solve, it is already to be transmitted and accepted as the ciphertext.
The codes are further encrypted with a protocol which randomly creates a function for transforming the codes into the ciphertext. Such function may also be the homogeneous transformation with some augments which are provided by the fixed codebook with a protocol. Clearly, the fixed codebook is again used to release its subset with a protocol. Such a subset contains a series of codes and to be used as the augments. In this way the codes are transformed into more complex ciphertext.
At the receiver?s end, a key is received. Combine this key and the ciphertext, nothing but some codes are obtained. Again, the receiver has his own fixed codebook. With this fixed codebook, the above codes can be transformed to be the plaintext.
This article supposes the hackers can steal everything via the network. When the ciphertext and the key are intercepted by the hacker, the hacker can not solve it because the hacker does not have the fixed codebook of the receiver?s, which is never appeared in the network. In this article, a condition of a ciphertext sender may be the hacker to peep the fixed codebook of the receiver?s is discussed.
This article proposes the three principles of encryption, namely: 1, without knowing what to find, 2, without knowing where to find or the space is too huge to search, and 3, how many to find.
The encoding process has a huge sample space as large as . The encrypting process provides infinite possibility for adopting homogeneous transformations and possibilities in the augments. Therefore the principle 2 is satisfied.
In the method proposed, the ciphertext is nothing but 1 and 0?s. Without the protocol, an attacker can do nothing. No matter how hard he tries, what he can have is nothing but codes. Without the codebook, an attacker does not know even he get the correct codes. Hence the principle1 is satisfied.
We may adopt some mathematical method such as simultaneous equations to make an attacker can not but have to solve all the codes in a same time. This is also called the effect of avalanche. Firstly, the attacker should know the number of equations in a set of simultaneous equations. Suppose there are 100 sets of codes in the codes, the possibilities of partition is . The hacker doesn?t know the 100 and , the principle 3 is satisfied.
In performing the homogeneous transformations, Euler?s rotations are suggested. Further, this article suggests the possibility of onion structure of the codebook. In this way it is possible to have integer computation, actually permutation. Each set code in the codes is a triple ordered pair. Each component of the triple ordered pair shall be permuted during transformation. Or to keep the performance of the homogeneous transformations, Euler?s rotations are still hold. Each shell of the onion rotates independently with a pole of rotation. |
