Simultaneous Encryption using Linear Block Channel Coding Part1

Posted by CRYPTOcrat | Encryption | Sunday 5 October 2008 6:38 pm

This article is authored by Rohit Pandharkar a fellow CRYPTOcrat.  Rohit is currently pursuing his under graduate studies at College of Engineering Pune. He has great interests in Cryptography, Mathematics and at this early stage has already published couple of research papers related to Cryptography.

You can find more information about Rohit on his LI Profile.


Channel coding is an error-control method used for providing robust data transmission through imperfect channels by adding redundancy to the data. Two vital classes of such coding techniques are: block and convolutional. In this article, we will be focusing on the Linear Block Coding and its use for encryption in this work.

The attempts at simultaneous source coding and encryption mainly involved exploitation of the freedom involved in the compression algorithms. Chung-E Wang [1], [2] has worked extensively in the area of Cryptography in data Compression, and has delved into the possibilities of exploiting the freedom in the source coding algorithmic for the sake of encryption.

Need to use Channel Coding for Encryption:

We opt for channel coding as a better point of infusing encryption as compared to the source coding because of the following reasons:

Limitations of infusing secrecy when simultaneously compressing.

A) Limitations due to reduction in Redundancy

The Source Coding Algorithms by default decrease the redundancy in the original dta, whereas channel coding techniques increase the redundancy. The more the redundancy, the more the secrecy can be infused according to Shannon.Hence, Channel Coding is a better choice for simultaneous encryption.

B) Limitation on the length of the key

Length of the key is an important factor in determining the strength of encryption. Longer lengths of keys help preventing the brute force and chosen plain text attacks.

In Huffman coding:,the limit on using joint compression and encryption approach is that, the key length cannot be more than the number of parent nodes present in the tree. And hence maximum key length is dependent on Message characteristics and prefix coding scenario. This restraint is related to

1. Number of symbols

2. Probability distribution of the symbols

However, as shown in the further work, the encryption using channel coding can have a key matrix of n*n dimensions, and hence has better key length strength.

Combining ‘Channel’ Coding and Encryption without using freedom:

Considering the relations established by Shannon between source coding and encryption, and looking at the possibility of exploiting the freedom in the source coding algorithms, we look for alternative possibilities for simultaneous channel coding and encryption without using the freedom within the algorithms.

In this article, we present a Matrix-based method for simultaneous Encryption and channel coding using Linear Block Codes. The method presented is different from the previous attempts by others so far for simultaneous coding and encryption in that it does not use the freedom or choice involved in the coding algorithms. It essentially uses a key matrix to add an encryption layer on the code-word matrix. The original code-word matrix is recovered by nullifying the encryption layer at the receiving end. This needs special Key Matrix design. The design considerations for this key matrix are elaborated and the encryption procedure is explained with the help of an example for the (6,3) Linear Block Code.

To be continued in the next part.

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