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ALGEBRAIC MANIPULATION DETECTION CODES WITH PERFECT NONLINEAR FUNCTIONS UNDER NON-UNIFORM DISTRIBUTION

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Classical methods of error detection are not efficient when an attacker controls the process of error injection. Nowadays the problem of providing high level of security for cryptographic systems, secret sharing schemes, flash memories and other communications, computation and storage systems is central to information security. To solve this problem the algebraic manipulation detection (AMD) codes have been proposed by Cramer at EUROCRYPT 2008. AMD codes represent a new class of nonlinear error detection codes which minimize the maximum of error masking probability. The paper presents the findings on behavior research of perfect nonlinear functions used in algebraic manipulation codes when the input distribution is not uniform. This research gives the detail review of behavior of perfect nonlinear functions and the maximum of error masking probability in case of different irreducible polynomials used for AMD codes. The received measurements can be used for selection of coding function that can be the most suitable for encoding information in specific situation such as given distribution of input codewords, irreducible polynomial and other parameters. The paper highlights the cases of parameter changing in coding system which do not change the error masking probability distribution or the changes are insignificant. These cases can be used to modify designs without reducing the stability of the entire integrity system to algebraic attacks that gives the possibility to customize the system for practical needs. Such parameters as the distribution of input codewords are also considered. They have an adverse effect on the stability of the system to algebraic manipulations. Changes in the input codeword distribution should be monitored in the integrity system, and additional transformations for input codewords should be used for security reasons or the encoding function within the integrity system should be changed.

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