Broadcast encryption is a data distribution protocol which can prevent malefactor parties from unauthorized accessing or copying the distributed data. It is widely used in distributed storage and network data protection schemes. To block the so-called coalition attacks on the protocol, classes of error-correcting codes with special properties are used, namely c-FP and c-TA properties. We study the problem of evaluating the lower and the upper boundaries on coalition power, within which the algebraic geometry codes possess these properties. Earlier, these boundaries were calculated for single-point algebraic-geometric codes on curves of the general form. Now, we clarified these boundaries for single-point codes on curves of a special form; in particular, for codes on curves on which there are many equivalence classes after factorization by equality of the corresponding points coordinates relation.
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- Title The attackers power boundaries for traceability of algebraic geometric codes on special curves
- Headline The attackers power boundaries for traceability of algebraic geometric codes on special curves
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 53
- Date:
- DOI 10.17223/20710410/53/4
Keywords
broadcast encryption, frameproof codes, algebraic geometry codes, traceability codesAuthors
References
Hoholdt T., van Lint J.H., and Pellikaan R. Algebraic geometry codes // Handbook of Coding Theory / V. S. Pless, W. C. Huffman, and R. A. Brualdi (eds.). V. 1. Amsterdam: Elsevier, 1998. P.871-961.
Цфасман М. А, Влэдуц С. Г., Ногин Д. Ю. Алгеброгеометрические коды. Основные понятия. М.: МЦНМО, 2003.
Noskov I. and Bezzateev S. Traceability schemes usings finite geometry // 10th Intern. Congress ICUMT. Moscow, Russia, 2018. P. 1-5.
Ge G., Ma J., and Shangguan Ch. New results for traitor tracing schemes. https://arxiv.org/abs/1610.07719.
Chee Y. M. and Zhang X. Improved constructions of frameproof codes // IEEE Trans. Inform. Theory. 2012. V. 58. No. 8. P. 5449-5453.
Ge G. and Shangguan Ch. Good traceability codes do exist. https://arxiv.org/abs/1601.04810v1.
Safavi-Naini R. and Wang Y. New results on frame-proof codes and traceability schemes // IEEE Trans. Inform. Theory. 2001. V. 47. No. 7. P.3029-3033.
Fernandez M. Codes with traceability properties and the Silverberg - Staddon - Walker conjecture // XVI Intern. Symp. “Problems of Redundancy in Information and Control Systems”. Moscow, Russia, 2019. Plenary lecture.
Moreira J., Fernandez M., and Soriano M. On the relationship between the traceability properties of Reed - Solomon codes // Adv. Math. Commun. 2012. V. 6. No.4. P.467-478.
Кабатянский Г. A. Идентифицирующие коды и их обобщения // Проблемы передачи информации. 2019. Т. 55. №3. С. 93-105.
Zagumennov D., Deundyak V., Gufan A. and Mkrtichan V. Algebraic geometry codes for special broadcast encryption schemes in telecommunication nets // Proc. MWENT. Moscow, Russia, 2020. P. 1-6.
Barg A. and Kabatiansky G. A class of I.P.P. codes with efficient identification // J. Complexity. 2004. V. 20. Iss. 2-3. P. 137-147.
Деундяк В. М., Загуменнов Д. В. Исследование свойств АГ-кодов как кодов для защиты от копирования // Моделирование и анализ информационных систем. 2020. Т. 27. № 1. С.22-38.
Pellikaan R. and Wu X.-W. List decoding of q-ary Reed - Muller codes // IEEE Trans. Inform. Theory. 2004. V. 50. No. 4. P.679-682.
Fernandez M., Cotrina J., Soriano M., and Domingo N. A note about the traceability properties of linear codes // LNCS. 2007. V. 4817. P. 251-258.
Деундяк В.М., Евпак C. А., Мкртичян В. В. Исследование свойств q-ичных помехоустойчивых кодов Рида - Маллера как кодов для защиты от копирования // Проблемы передачи информации. 2015. Т. 51. №4. С. 99-111.
Guruswami V. and Sudan M. Improved decoding of Reed-Solomon and algebraic-geometric codes // Foundations of Computer Science. Palo Alto: IEEE, 1998. P. 28-37.
Ma Y. and Ding Y. Reed - Solomon codes as traceability codes with an efficient tracing algorithm // 8th Intern. Conf. Signal Processing. Guilin, China, 2006. V. 4. https://ieeexplore.ieee.org/document/4129649.
Деундяк В. М., Мкртичян В. В. Исследование границ применения схемы защиты информации, основанной на PC-кодах // Дискретный анализ и исследование операций. 2011. Т. 18. №3. С. 21-38.
Загуменнов Д. В., Мкртичян В. В. О применимости алгеброгеометрических кодов L-конструкции как кодов защиты от копирования // Прикладная дискретная математика. 2019. №44. С. 67-93.
Staddon J. N., Stinson D. R., and Wei R. Combinatorial properties of frameproof and traceability codes // IEEE Trans. Inform. Theory. 2001. V. 47. No. 3. P. 1042-1049.
Stinson D. R. and Wei R. Combinatorial properties and constructions of traceability schemes and frameproof codes // SIAM J. Discr. Math. 1998. V. 11. Iss. 1. P. 41-53.
Chor B., Fiat A., and Naor M. Tracing traitors // LNCS. 1994. V. 839. P.257-270.
Silverberg A., Staddon J., and Walker J. Applications of list decoding to tracing traitors // IEEE Trans. Inform. Theory. 2003. V. 49. No. 5. P. 1312-1318.
Fiat A. and Naor M. Broadcast encryption // LNCS. 1994. V. 773. P.480-491.
The attackers power boundaries for traceability of algebraic geometric codes on special curves | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2021. № 53. DOI: 10.17223/20710410/53/4
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