# Foundations of Coding: Compression, Encryption, Error Correction

# Foundations of Coding: Compression, Encryption, Error Correction

## Jean-Guillaume Dumas, Jean-Louis Roch, Éric Tannier, Sébastien Varrette

Language: English

Pages: 450

ISBN: B00STERUWA

Format: PDF / Kindle (mobi) / ePub

**Offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations**

This book offers a comprehensive introduction to the fundamental structures and applications of a wide range of contemporary coding operations. This text focuses on the ways to structure information so that its transmission will be in the safest, quickest, and most efficient and error-free manner possible. All coding operations are covered in a single framework, with initial chapters addressing early

mathematical models and algorithmic developments which led to the structure of code. After discussing the general foundations of code, chapters proceed to cover individual topics such as notions of compression, cryptography, detection, and correction codes. Both classical coding theories and the most cutting-edge models are addressed, along with helpful exercises of varying complexities to enhance comprehension.

Foundations of Coding: Compression, Encryption,Error-Correction is an invaluable resource for understanding the various ways information is structured for its secure and reliable transmission in the 21st-century world.

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parameters of the code are the size k of the input blocks, the size n of the output blocks, the number of blocks m, and the polynomials. To simplify this presentation, we are going to explain the mechanisms of a convolutional code encoding all bits of the source message one by one, that is, . Thus, one considers n generator polynomials of maximum degree m. The source is represented by an infinite sequence of bits . The bits of negative index are considered to be null to indicate the beginning

correspondence table. This works as a human fingerprint, which does not enable one to reconstitute the other characteristics of an individual but which enables one to identify him. Hash functions are particularly useful in cryptography. They notably enable one to decrease the amount of information to be encrypted. If the image of x by the hash function is called the fingerprint of x, one can – for example – encrypt only the fingerprint. Moreover, they enable one to set up electronic signature

Figure 1.17 Miyaguchi–Preneel construction Function g adapts the construction to the size of the key of the encryption function E. Hence, one has . Galois hashing Another popular hash function is GHASH, for Galois hashing, which uses multiplication in the field with elements and Horner scheme. The idea is to choose an element h of where the field is usually build as polynomials modulo 2 and modulo the primitive polynomial . Then, a message m is cut into blocks of bits and each block is

breaking this system is in this way only 100 times more difficult than breaking the simple DES (and not times more difficult as one might have expected using two keys). Indeed, the “meet-in-the-middle” attack uses a fast sort to break the double DES with almost no computation overhead with respect to breaking the simple DES: Compute all possible encryptions of a given message M. Sort the with a fast sort in steps. There are approximately operations. Compute all possible decryptions of C with a

of each line even if these are not the exact values that are used in practice. The receiver can then check that each line is in the format “ ,” with an integer thatprovides the number of consecutive bits and the color of these bits. In particular, the condition must be respected and the colors must be alternated. Thus, a modification or the loss of one bit is easily detected as soon as this format is not respected. All error detection and correction principles, which will be closely studied in