Geodesic
Blakley type secret sharing scheme based on the intersection of subspaces
Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 1, pp. 13-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the problem of constructing a secret sharing schemes permitting to replace any subset of participants with new participants so that new secret shares may be calculated only for the newly added members, and secret shares of others participants do not change. Using the theory of error-correcting codes we construct protocols of separation and recovery of the secret. In order to study the permissible domains of parameters of this secret sharing scheme the new characteristics of linear code is introduced and explored. We implement the proposed scheme for some linear codes as examples. 
@article{MVK_2017_8_1_a2,
     author = {Yu. V. Kosolapov},
     title = {Blakley type secret sharing scheme based on the intersection of subspaces},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {13--30},
     year = {2017},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2017_8_1_a2/}
}
TY  - JOUR
AU  - Yu. V. Kosolapov
TI  - Blakley type secret sharing scheme based on the intersection of subspaces
JO  - Matematičeskie voprosy kriptografii
PY  - 2017
SP  - 13
EP  - 30
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2017_8_1_a2/
LA  - ru
ID  - MVK_2017_8_1_a2
ER  - 
%0 Journal Article
%A Yu. V. Kosolapov
%T Blakley type secret sharing scheme based on the intersection of subspaces
%J Matematičeskie voprosy kriptografii
%D 2017
%P 13-30
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2017_8_1_a2/
%G ru
%F MVK_2017_8_1_a2
Yu. V. Kosolapov. Blakley type secret sharing scheme based on the intersection of subspaces. Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 1, pp. 13-30. http://geodesic.mathdoc.fr/item/MVK_2017_8_1_a2/

[1] Cramer R., Damgard I., Maurer U., “General secure multi-party computation from any linear secret-sharing scheme”, EUROCRYPT 2000, Lect. Notes Comput. Sci., 1807, 2000, 316–334 | DOI | MR | Zbl

[2] Chen H., Cramer R., Goldwasser S., Haan R., Vaikuntanathan V., “Secure computation from random error correcting codes”, EUROCRYPT 2007, Lect. Notes Comput. Sci., 4515, 2007, 291–310 | DOI | MR | Zbl

[3] Pogorelov B. A., Sachkov V. N., Slovar kriptograficheskikh terminov, MTsNMO, M., 2006, 91 pp.

[4] Shamir A., “How to share a secret”, Comm. ACM, 22:11 (1979), 612–613 | DOI | MR | Zbl

[5] Blakley G. R., “Safeguarding cryptographic keys”, AFIPS Conf. Proc., 48, 1979, 313–317

[6] Brickell E. F., “Some ideal secret sharing schemes”, EUROCRYPT'89, Lect. Notes Comput. Sci., 434, 1989, 468–475 | DOI | MR

[7] Blakley G. R., Kabatianski G. A., “Linear algebra approach to secret sharing schemes”, Error Control, Cryptology, and Speech Compression, Lect. Notes Comput. Sci., 829, 1994, 33–40 | DOI | MR

[8] Dijk M., “A linear construction of perfect secret sharing schemes”, EUROCRYPT'94, Lect. Notes Comput. Sci., 950, 1994, 23–34 | DOI | MR

[9] Ozarov L. H., Wyner A. D., “Wire-tap channel II”, Bell Labs Techn. J., 63:10 (1984), 2135–2157 | DOI

[10] Deundyak V. M., Kosolapov Yu. V., “Ob odnom metode snyatiya neopredelennosti v kanale s pomekhami v sluchae primeneniya kodovogo zashumleniya”, Izv. YuFU. Tekhn. nauki, 2014, 197–208

[11] Sendrier N., “Finding the permutation between equivalent linear codes: the support splitting algorithm”, IEEE Trans. Inf. Theory, 46:4 (2000), 1193–1203 | DOI | MR | Zbl

[12] Forney G. D., “Dimension/length profiles and Trellis complexity of linear block codes”, IEEE Trans. Inf. Theory, 40:6 (1994), 1741–1752 | DOI | MR | Zbl

[13] Deundyak V. M., Maevskii A. E., Mogilevskaya N. S., Metody pomekhoustoichivoi zaschity dannykh, YuFU, Rostov-n/D, 2014, 308 pp.

[14] Wei V. K., “Generalized Hamming weights for linear codes”, IEEE Trans. Inf. Theory, 37:5 (1991), 1412–1418 | DOI | MR | Zbl

[15] Dodunekov S. M., Landgev I. N., “On near-MDS codes”, Proc. IEEE Int. Symp. Inf. Theory, 1994, 427

[16] Chabot C., “Recognition of a code in a noisy environment”, Proc. IEEE Int. Symp. Inf. Theory, 2007, 2211–2215

[17] Ding P., Key J. D., “Minimum-weight codewords as generators of generalized Reed–Muller codes”, IEEE Trans. Inf. Theory, 46:6 (2000), 2152–2157 | DOI | MR

[18] Blake I. F., Mullin R. C., The Mathematical Theory of Coding, Academic Press, N.Y., 1975, 368 pp. | MR | Zbl

[19] Kosolapov Yu. V., “Verkhnyaya granitsa ierarkhii vesov regulyarnykh slaboplotnykh kodov spetsialnogo vida”, Mezhvuz. sb. nauch. tr., Integro-diff. operatory i ikh pril., 8, 2008, 72–80

[20] Barg S., “Nekotorye novye NP-polnye zadachi kodirovaniya”, Problemy peredachi informatsii, 30:3 (1994), 23–28

[21] Bouyukliev I., Bakoev V., “A method for efficiently computing the number of codewords of fixed weights in linear codes”, Discr. Appl. Math., 156:15 (2008), 2986–3004 | DOI | MR | Zbl

[22] Zubkov A. M., Kruglov V. I., “Statisticheskie kharakteristiki vesovykh spektrov sluchainykh lineinykh kodov na $\mathrm{GF}(p)$”, Matematicheskie voprosy kriptografii, 5:1 (2014), 27–38 | Zbl