A Cipher Based on Prefix Codes

A prefix code, a P-code, is a code where no codeword is a prefix of another codeword. In this paper, a symmetric cipher based on prefix codes is proposed. The simplicity of the design makes this cipher usable for Internet of Things applications. Our goal is to investigate the security of this cipher. A detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack. Specifically, in this regard we will find bounds on the number of minimal P-codes containing a binary word given in advance. Furthermore, the statistical attack is difficult to mount on such cryptosystem due to the attacker’s lack of information about the actual words used in the substitution mapping. The results of a statistical analysis of possible keys are also presented. It turns out that the distribution of the number of minimal P-codes over all binary words of a fixed length is Gaussian.

A New Coding Technique and Analysis of Trees

A message is encoded using one-time pad Cipher and Huffman coding with certain algorithm. Encoding process is done using a symmetric key known to sender and receiver. Then we get the encoded message as Ciphertext with a binary tree. Using the binary tree we form a prefix code of Huffman coding and we define a new labeling function of edge and vertex labeling. In this paper, we discuss the two methods of encoding algorithm and investigate Tree, Rooted trees, properties, theorem and Median of Huffman binary tree.

Characterizing classes of regular languages using prefix codes of bounded synchronization delay

This paper is motivated by the work of Schützenberger on codes with bounded synchronization delay. He was interested in characterizing those regular languages where groups in the syntactic monoid belong to a variety [Formula: see text]. On the language side he allowed the operations union, intersection, concatenation and modified Kleene-star involving a mapping of a prefix code of bounded synchronization delay to a group [Formula: see text], but no complementation. In our notation, this leads to the language classes [Formula: see text]. Our main result shows that [Formula: see text] coincides with the class of languages having syntactic monoids where all subgroups are in [Formula: see text]. We show that this statement holds for all varieties [Formula: see text] of finite groups, whereas Schützenberger proved this result for varieties [Formula: see text] containing Abelian groups, only. Our method shows the result for all [Formula: see text] simultaneously on finite and infinite words. Furthermore, we introduce the notion of local Rees extension which refers to a restricted type of the classical Rees extension. We give a decomposition of a monoid in terms of its groups and local Rees extensions. This gives a somewhat similar, but simpler decomposition than in the synthesis theorem of Rhodes and Allen. Moreover, we need a singly exponential number of operations, only. Finally, our decomposition yields an answer to a question in a recent paper of Almeida and Klíma about varieties that are closed under Rees extensions.

Structure and properties of strong prefix codes of pictures

A setX⊆ Σ** of pictures is a code if every picture over Σ is tilable in at most one way with pictures inX. The definition ofstrong prefix codeis introduced. The family of finite strong prefix codes is decidable and it has a polynomial time decoding algorithm. Maximality for finite strong prefix codes is also studied and related to the notion of completeness. We prove that any finite strong prefix code can be embedded in a unique maximal strong prefix code that has minimal size and cardinality. A complete characterization of the structure of maximal finite strong prefix codes completes the paper.

Research on 3D Modeling Method Based on Hybrid Octree Structure

With studying deeply of the three-dimensional modeling method, this paper proposed a hybrid data model which based on Octree,the four fork tree and NURBS. The characteristic of fast convergence of Octree is used to segment the 3D entity. Describe the irregular surface of entity by NURBS, and restructure the local mesh surface. The model uses the mixture data structure of Octree and four fork tree to restructure mesh surface gradually. The storage structure is the Octree structure type; establish Hash table based on octal prefix code. Finally, an experimental model system is designed by using OpenGL. The feasibility and effectiveness of the algorithm has been verified.

PREFIX PICTURE CODES: A DECIDABLE CLASS OF TWO-DIMENSIONAL CODES

A two-dimensional code of pictures is defined as a set X ⊆ Σ** such that any picture over Σ is tilable in at most one way with pictures in X. It is proved that in general it is undecidable whether a finite set of picture is a code. The subclass of prefix codes is introduced and it is proved that it is decidable whether a finite set of pictures is a prefix code. Further a polynomial time decoding algorithm for finite prefix codes is given. Maximality and completeness of finite prefix codes are studied.