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Most of the codes that have an algebraic decoding algorithm are derived from the Reed Solomon codes. They are obtained by taking equivalent codes, for example the generalized Reed Solomon codes, or by using the so-called subfield subcode method, which leads to Alternant codes and Goppa codes over the underlying prime field, or over some intermediate subfield. The main advantages of these constr...

Security is an important issue related to the storage and communication of data and information. In data and information security, cryptography and steganography are two of the most common security techniques. On one hand, there is cryptography, which is the secret communication between two parties by message scrambling on the sender’s side and message unscrambling on the receiver’s side so tha...

This thesis studies the implications of using public key cryptographic primitives that are based in, or map to, the multiplicative group of finite fields with small extension degree. A central observation is that the multiplicative group of extension fields essentially decomposes as a product of algebraic tori, whose properties allow for improved communication efficiency. Part I of this thesis ...

Chapter 4 (Encryption Steps: Polygraphic Substitution and Coding) extends the preceding chapter by polygraphic ciphers, introducing bigraphic and trigraphic substitution and tomographic methods. As in the preceding chapter, there is a theoretical description of each method as well as a detailed explanation of the single steps of calculation using a concrete cipher as an example. These examples ...

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We discuss the general theoretical ideas of the possibility using cryptosystems based on the partial differential equations (PDE) and the role of inverse scattering problem for the cryptanalysis as the possible way to the postquantum cipher scheme. An application of the nonlinear Schrödinger equation and optical fibre technology in cryptology is presented.

1Department of Computer Science and Electrical Engineering, University of Missouri-Kansas City, Kansas City MO 64110, USA 2Department of Information and Computer Science, Park University, Parkville, MO 64152, USA 3State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing 10049, P.R. China 4Key Laboratory of Network Security and Cryptology, Fujian ...

Cryptology and computers have a long common history; in fact, some of the early computers were created as cryptanalytic tools. The development of faster and widely deployed computers also had a great impact on cryptology, allowing modern cryptography to become a practical tool. Today, both computers and cryptology are not only practical, but they have became ubiquitous tools. In truth, computin...