Methods for Monitoring and Diagnosing Data in the Residue Class

This article proposes a method for monitoring and diagnosing the information provided in the residue class. These methods are based on the use of orthogonal bases for complete base system residue class, as well as a set of projections of number by modules. A concrete example is given of data monitoring and diagnostics in residue class for built-in computer funds the transmission and processing of digital information (data) with a single¬byte bit grid. Use of the proposed methods will make it possible to simplify technical procedure for monitoring and diagnosing the data presented to residue class, as well as to increase promptness of this procedure.

[1]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[2]  K R Venugopal,et al.  Implementation of Public Key Crypto Processor with Probabilistic Encryption on FPGA for Nodes in Wireless Sensor Networks , 2018, 2018 9th International Conference on Computing, Communication and Networking Technologies (ICCCNT).

[3]  Stefan Mangard,et al.  Arithmetic logic units with high error detection rates to counteract fault attacks , 2011, 2011 Design, Automation & Test in Europe.

[4]  V. Krasnobayev.  Method for Realization of Transformations in Public-Key Cryptography , 2007 .

[5]  D.I. Popov,et al.  Development of Algorithm for Control and Correction of Errors of Digital Signals, Represented in System of Residual Classes , 2018, 2018 International Russian Automation Conference (RusAutoCon).

[6]  Alexandr Kuznetsov,et al.  Methods for Comparing Numbers in Non-Positional Notation of Residual Classes , 2019, CMIS.

[7]  Thanos Stouraitis,et al.  Grouped-moduli residue number systems for fast signal processing , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[8]  K. Liang,et al.  Irregular repeat accumulate low-density parity-check codes based on residue class pair , 2017, 2017 IEEE 9th International Conference on Communication Software and Networks (ICCSN).

[9]  Alexandr Kuznetsov,et al.  Code-based key encapsulation mechanisms for post-quantum standardization , 2018, 2018 IEEE 9th International Conference on Dependable Systems, Services and Technologies (DESSERT).

[10]  Alina Yanko,et al.  Method of Error Control of the Information Presented in the Modular Number System , 2018, 2018 International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T).

[11]  V. Krasnobayev,et al.  A Method for Arithmetic Comparison of Data Represented in a Residue Number System , 2016 .

[12]  Alexandr Kuznetsov,et al.  ON HIDING DATA INTO THE STRUCTURE OF THE FAT FAMILY FILE SYSTEM , 2019 .

[13]  V. A. Krasnobayev,et al.  A Method for Increasing the Reliability of Verification of Data Represented in a Residue Number System , 2014 .

[14]  Chong-Dao Lee.  Decoding Quadratic Residue Codes Based on Bivariate Weak-Locator Polynomials , 2018, 2018 13th APCA International Conference on Control and Soft Computing (CONTROLO).

[15]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[16]  K. Navi,et al.  Efficient Class of Redundant Residue Number System , 2007, 2007 IEEE International Symposium on Intelligent Signal Processing.

[17]  Y.N. Kocherov,et al.  Development of an Antinoise Method of Data Sharing Based on the Application of a Two-Step-Up System of Residual Classes , 2018, 2018 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon).

[18]  Ivan Gorbenko,et al.  Examining a possibility to use and the benefits of post-quantum algorithms dependent on the conditions of their application , 2017 .

[19]  Mikolaj Karpinski,et al.  Advanced method of factorization of multi-bit numbers based on Fermat's theorem in the system of residual classes , 2016, 2016 16th International Conference on Control, Automation and Systems (ICCAS).

[20]  Alexandr Kuznetsov,et al.  Construction of cascade codes in the frequency domain , 2017, 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T).

[21]  I. Shparlinski,et al.  Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients , 2014, 1408.4515.

[22]  Mona B. Musa.  On Some Double Circulant Binary Extended Quadratic Residue Codes , 2008, IEEE Transactions on Information Theory.

[23]  Gennian Ge,et al.  A Unified Approach to Whiteman's and Ding-Helleseth's Generalized Cyclotomy Over Residue Class Rings , 2014, IEEE Transactions on Information Theory.

[24]  Christian Gehrmann,et al.  Fast authentication codes based on random polynomial residue classes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[25]  Rainer Steinwandt,et al.  A Redundant Representation of GF(q^n) for Designing Arithmetic Circuits , 2003, IEEE Trans. Computers.

[26]  Ray C. C. Cheung,et al.  Zero collision attack and its countermeasures on Residue Number System multipliers , 2014, 2014 International Symposium on Integrated Circuits (ISIC).

[27]  I Ya Akushskiy,et al.  Machine Arithmetic in Residual Classes , 1981 .

[28]  Xu An Wang,et al.  New Construction of PVPKE Scheme Based on Signed Quadratic Residues , 2013, 2013 5th International Conference on Intelligent Networking and Collaborative Systems.

[29]  Piero Maestrini,et al.  Error Correcting Properties of Redundant Residue Number Systems , 1973, IEEE Transactions on Computers.

[30]  Israel Koren,et al.  A note on error detection in an RSA architecture by means of residue codes , 2006, 12th IEEE International On-Line Testing Symposium (IOLTS'06).

[31]  Alexandr Kuznetsov,et al.  Method of Data Control in the Residue Classes , 2019, CMIS.

[32]  A. Skavantzos,et al.  Novel residue arithmetic processors for high speed digital signal processing , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[33]  Alexandr Kuznetsov,et al.  Improved Method of Determining the Alternative Set of Numbers in Residue Number System , 2018 .

[34]  Lina Zhang.  Cyclic Codes over Polynomial Residue Class Rings , 2010, 2010 International Conference on Electrical and Control Engineering.

[35]  Alexandr Kuznetsov,et al.  STUDIES ON STATISTICAL ANALYSIS AND PERFORMANCE EVALUATION FOR SOME STREAM CIPHERS , 2019, International Journal of Computing.

[36]  Danna Zhou,et al.  d. , 1934, Microbial pathogenesis.