Rapid Estimation of the Entropy of Long Codes with Dependent Bits on Low-Power, Low-Bit Microcontrollers (Review of Literature on Reducing the Dimension of a Problem)

Abstract

Introduction. The aim of the work is to reduce the requirements for bit depth and processor performance of a trusted computing environment when estimating the entropy of long codes with dependent bits. Materials and Methods. Testing procedures recommended by the Russia national standards are used. The transition from the analysis of ordinary long codes to Hamming distances between random Alien codes and the Own image code is used. Results. It is shown that the transition to the presentation of data by the normal distribution law in the space of Hamming distances makes the relationship between mathematical expectation and entropy almost linear. Low-bit tables are constructed that relate the first statistical moments of the distribution of Hamming distances to the entropy of long codes. In calculations, the correlation index of the digits of the studied codes can vary widely. Discussion and Conclusion. The calculation of the mathematical expectation and standard deviation is easily feasible on low-discharge low-power microcontrollers. The use of the synthesized tables makes it possible to pass easily from the lower statistical moments of the Hamming distances to the entropy of long codes. The task of calculating entropy is accelerated many times in comparison with Shannon’s procedures and becomes feasible on cheap low-bit processors.