On application of algebraic geometry codes of L-construction in copy protection | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 44. DOI: 10.17223/20710410/44/6

Traceability schemes which are applied to the broadcast encryption can prevent unauthorized parties from accessing the distributed data. In a traceability scheme, a distributor encrypts the data and gives each authorized user a unique key suit to decrypt the data. This suit uniquely identifies the recipient and therefore allows the tracing of the source of an unauthorized redistribution. A widely used approach to the constructing good traceability scheme is the use of error-correcting codes with a suitable minimum distance and efficient decoding algorithms. The paper deals with the usage of algebraic geometry codes (AG-codes) of L-construction and Sudan - Guruswami list decoding algorithms in these schemes. We suggest the problem of constructing traceability AG-codes and obtain sufficient conditions for applying them. Let C C Fq^' be the algebraic geometry code constructed using curve of genus g and divisor of degree a. Firstly, if c д/п/а, then C is a traceability code when the number 1, then C can be we obtain several is possible to use of attackers is a maximum of c. Secondly, if a > log_q N + g - used to build traceability schemes maintaining N users. Finally, cumbersome bounds on the number of intruders within which it Sudan - Guruswami hard- and soft- decision list decoding algorithms for tracing the unauthorized redistribution source. Based on these derived conditions and some other lemmas, the algorithm for suitable one-point AG-code construction is presented. The algorithm can be polynomially reduced to the Riemann - Roch space basis construction problem. Much attention is given to the algorithm validity and its sample execution. Besides, the paper gives a brief description of AG-codes and Sudan - Guruswami hard- and soft- decision list decoding algorithms.