Generalized Hermitian Codes over GF(2^r)

In this paper we studied generalization of Hermitian function field proposed by A.Garcia and H.Stichtenoth. We calculated a Weierstrass semigroup of the point at infinity for the case q=2, r>=3. It turned out that unlike Hermitian case, we have already three generators for the semigroup. We then applied this result to codes, constructed on generalized Hermitian function fields. Further, we applied results of C.Kirfel and R.Pellikaan to estimating a Feng-Rao designed distance for GH-codes, which improved on Goppa designed distance. Next, we studied the question of codes dual to GH-codes. We identified that the duals are also GH-codes and gave an explicit formula. We concluded with some computational results. In particular, a new record-giving [32,16,>=12]-code over GF(8) was presented

Towards a Better Understanding of the Semigroup Tree

In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which of the two types takes place in particular for well-known classes of semigroups. Also we study the question of what kind of chains appear in the tree and characterize the properties (like being (in)finite) thereof. We conclude with some thoughts that show how this study of the semigroup tree may help in solving the conjecture of Fibonacci-like behavior of the number of semigroups with given genus.Comment: 17 pages, 2 figure

A Note on the Injection Distance

Koetter and Kschischang showed in [R. Koetter and F.R. Kschischang, "Coding for Errors and Erasures in Random Network Coding," IEEE Trans. Inform. Theory, {54(8), 2008] that the network coding counterpart of Gabidulin codes performs asymptotically optimal with respect to the subspace distance. Recently, Silva and Kschischang introduced in [D. Silva and F.R. Kschischang, "On Metrics for Error Correction in Network Coding," To appear in IEEE Trans. Inform. Theory, ArXiv: 0805.3824v4[cs.IT], 2009] the injection distance to give a detailed picture of what happens in noncoherent network coding. We show that the above codes are also asymptotically optimal with respect to this distance

Obtaining and solving systems of equations in key variables only for the small variants of AES

This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we introduce a system of equations that naturally arises in the AES, and then eliminate all the intermediate variables via normal form reductions. The resulting system in key variables only is solved then. We also consider a possibility to apply our method in the meet-in-the-middle scenario especially with several plaintext/ciphertext pairs. We elaborate on the method further by looking for subsystems which contain fewer variables and are overdetermined, thus facilitating solving the large system

CyclicRainbow - A multivariate Signature Scheme with a Partially Cyclic Public Key based on Rainbow

Multivariate Cryptography is one of the alternatives to guarantee the security of communication in the post-quantum world. One major drawback of such schemes is the huge size of their keys. In \cite{PB10} Petzoldt et al. proposed a way how to reduce the public key size of the UOV scheme by a large factor. In this paper we extend this idea to the Rainbow signature scheme of Ding and Schmidt \cite{DS05}. By our construction it is possible to reduce he size of the public key by up to 62 \verb!%!

INFORMATION SPACE AND SOCIETY: EXPLORING NEGATIVE TRENDS, IDEOLOGICAL INFLUENCE, AND STRATEGIES FOR SUSTAINABLE DEVELOPMENT

Objective: The study aimed to identify ways to establish a secure environment that fosters the circulation of reliable information. This objective was pursued through enhancing the protection of the existing information infrastructure and ensuring its sustainable functioning, while also taking into account the impact of information confrontation on the escalation of interstate and intrastate conflicts. Methods: The study employs a comprehensive analysis of societal trends to understand the negative effects of information space on the development of destabilizing ideologies. By utilizing general scientific methods, including philosophical approaches and logical reasoning, the study aims to examine the problems of modern informatization in society and the activities of states and society in achieving sustainable development. Results: The study highlights the influence of information space on establishing conditions for public safety, personal security, and the security of critical sectors such as fuel and energy. It identifies the challenges involved in creating a secure information space and presents a viewpoint on the necessity of developing a unified information space that facilitates both educational and supervisory functions. Conclusion: The study's final conclusions emphasize the importance of mass information sources in providing quality information to individuals in social interactions. These sources play a crucial role in promoting socially beneficial behavior and establishing criteria for progressive development in societies and states. It also stresses the importance of increasing protection against potential threats that can harm individuals' lives, health, property, and personal data, as well as the social and psychological rehabilitation of those affected by modern threats

Selecting Parameters for the Rainbow Signature Scheme - Extended Version -

Multivariate public key cryptography is one of the main approaches to guarantee the security of communication in a post-quantum world. One of the most promising candidates in this area is the Rainbow signature scheme, which was first proposed by J. Ding and D. Schmidt in 2005. In this paper we develop a model of security for the Rainbow signature scheme. We use this model to find parameters for Rainbow over GF(16), GF(31) and GF(256) which, under certain assumptions, guarantee the security of the scheme for now and the near future

Selecting Parameters for Secure McEliece-based Cryptosystems

In 1994, P. Shor showed that quantum computers will be able to break cryptosystems based on integer factorization and on the discrete logarithm, e.g. RSA or ECC. Code-based crytosystems are promising alternatives to public key schemes based on these problems, and they are believed to be secure against quantum computer attacks. In this paper, we solve the problem of selecting optimal parameters for the McEliece cryptosystem that provide security until a given year and give detailed recommendations. Our analysis is based on the lower bound complexity estimates by Sendrier and Finiasz, and the security requirements model proposed by Lenstra and Verheul