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On the Properties of Algebraic Geometric Codes as Copy Protection Codes

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Abstract

Traceability schemes that are applied to broadcast encryption can prevent unauthorized parties from accessing the distributed data. In a traceability scheme, a distributor broadcasts the encrypted data and gives each authorized user a unique key and identifying word from the selected error-correcting code for decrypting. The following attack is possible in these schemes: groups of c malicious users join into coalitions and gain illegal access to the data by combining their keys and identifying codewords to obtain a pirate key and codeword. To prevent this type of attack, classes of error-correcting codes with special c-FP and c-TA properties are used. In particular, c-FP codes are codes that make direct compromise of scrupulous users impossible and c-TA codes are codes that make it possible to identify one of the attackers. We are considering the problem of evaluating the lower and the upper boundaries on c, within which the L-construction algebraic geometric codes have the corresponding properties. In the case of codes on an arbitrary curve, the lower bound for the c-TA property was obtained earlier; in this paper, the lower bound for the c-FP property was constructed. In the case of curves with one infinite point, the upper bounds for the value of c are obtained for both c-FP and c-TA properties. During our work, we have proven an auxiliary lemma and the proof contains an explicit way to build a coalition and a pirate-identifying vector. Methods and principles presented in the lemma can be important for analyzing broadcast encryption schemes’ robustness. Also, the c-FP and c-TA boundaries’ monotonicity by subcodes are proven.

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Correspondence to V. M. Deundyak or D. V. Zagumennov.

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Translated by K. Gumerov

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Deundyak, V.M., Zagumennov, D.V. On the Properties of Algebraic Geometric Codes as Copy Protection Codes. Aut. Control Comp. Sci. 55, 795–808 (2021). https://doi.org/10.3103/S014641162107021X

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  • DOI: https://doi.org/10.3103/S014641162107021X

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