-
Previous Article
The secrecy capacity of the arbitrarily varying wiretap channel under list decoding
- AMC Home
- This Issue
- Next Article
Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields
1. | Department of Information and Communication Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan |
2. | Department of Mathematical Sciences, Aalborg University, Denmark |
The first construction of strongly secure quantum ramp secret sharing by Zhang and Matsumoto had an undesirable feature that the dimension of quantum shares must be larger than the number of shares. By using algebraic curves over finite fields, we propose a new construction in which the number of shares can become arbitrarily large for fixed dimension of shares.
References:
[1] |
G. R. Blakley and C. Meadows, Security of ramp schemes, in Advances in Cryptology-CRYPTO'84, vol. 196 of Lecture Notes in Computer Science, Springer-Verlag, 1985, 242-269.
doi: 10.1007/3-540-39568-7_20. |
[2] |
A. Bogdanov, S. Guo and I. Komargodski, Threshold secret sharing requires a linear size alphabet, in Theory of Cryptography (eds. M. Hirt and A. Smith), Springer Berlin Heidelberg,
Berlin, Heidelberg, 9986 (2016), 471-484.
doi: 10.1007/978-3-662-53644-5_18. |
[3] |
I. Cascudo, R. Cramer and C. Xing,
Bounds on the threshold gap in secret sharing and its applications, IEEE Trans. Inform. Theory, 59 (2013), 5600-5612.
doi: 10.1109/TIT.2013.2264504. |
[4] |
I. Cascudo, J. Skovsted Gundersen and D. Ruano, Improved bounds on the threashold gap in ramp secret sharing, 2018, Cryptology ePrint Archive 2018/099. |
[5] |
H. Chen and R. Cramer, Algebraic geometric secret sharing schemes and secure multi-party
computations over small fields, in Advances in Cryptology - CRYPT 2006 (ed. C. Dwork),
vol. 4117 of Lecture Notes in Computer Science, Springer-Verlag, 2006, 521-536.
doi: 10.1007/11818175_31. |
[6] |
H. Chen, R. Cramer, R. de Haan and I. Cascudo Pueyo, Strongly multiplicative ramp schemes
from high degree rational points on curves, in Advances in Cryptology - EUROCRYPT 2008 (ed. N. Smart), vol. 4965 of Lecture Notes in Computer Science, Springer-Verlag, 2008, 451-470
doi: 10.1007/978-3-540-78967-3_26. |
[7] |
R. Cleve, D. Gottesman and H.-K. Lo,
How to share a quantum secret, Phys. Rev. Lett., 83 (1999), 648-651.
doi: 10.1103/PhysRevLett.83.648. |
[8] |
D. Gottesman,
Theory of quantum secret sharing, Phys. Rev. A, 61 (2000), 042311.
doi: 10.1103/PhysRevA.61.042311. |
[9] |
M. Iwamoto and H. Yamamoto,
Strongly secure ramp secret sharing schemes for general
access structures, Inform. Process. Lett., 97 (2006), 52-57.
doi: 10.1016/j.ipl.2005.09.012. |
[10] |
R. Matsumoto,
Coding theoretic construction of quantum ramp secret sharing, IEICE Trans. Fundamentals, E101-A (2018), 1215-1222.
doi: 10.1587/transfun.E101.A.1215. |
[11] |
R. Matsumoto,
Strong security of the strongly multiplicative ramp secret sharing based on
algebraic curves, IEICE Trans. Fundamentals, E98-A (2015), 1576-1578.
doi: 10.1587/transfun.E98.A.1576. |
[12] |
R. J. McEliece and D. V. Sarwate,
On sharing secrets and Reed-Solomon codes, Comm. ACM, 24 (1981), 583-584.
doi: 10.1145/358746.358762. |
[13] |
T. Ogawa, A. Sasaki, M. Iwamoto and H Yamamoto,
Quantum secret sharing schemes and reversibility of quantum operations, Phys. Rev. A, 72 (2005), 032318.
doi: 10.1103/PhysRevA.72.032318. |
[14] |
A. Shamir,
How to share a secret, Comm. ACM, 22 (1979), 612-613.
doi: 10.1145/359168.359176. |
[15] |
A. D. Smith, Quantum secret sharing for general access structures, 2000, arXiv:quant-ph/0001087, |
[16] |
H. Stichtenoth,
Algebraic Function Fields and Codes, vol. 254 of Graduate Texts in Mathematics, 2nd edition, Springer-Verlag, Berlin Heidelberg, 2009. |
[17] |
D. R. Stinson, Cryptography Theory and Practice, 3rd edition, Chapman & Hall/CRC, 2006.
![]() ![]() |
[18] |
H. Yamamoto, Secret sharing system using (k; l; n) threshold scheme, Electronics and Communications in Japan (Part I: Communications), 69 (1986), 46-54, (the original Japanese
version published in 1985)
doi: 10.1002/ecja.4410690906. |
[19] |
P. Zhang and R. Matsumoto,
Quantum strongly secure ramp secret sharing, Quantum Information Processing, 14 (2015), 715-729.
doi: 10.1007/s11128-014-0863-2. |
show all references
References:
[1] |
G. R. Blakley and C. Meadows, Security of ramp schemes, in Advances in Cryptology-CRYPTO'84, vol. 196 of Lecture Notes in Computer Science, Springer-Verlag, 1985, 242-269.
doi: 10.1007/3-540-39568-7_20. |
[2] |
A. Bogdanov, S. Guo and I. Komargodski, Threshold secret sharing requires a linear size alphabet, in Theory of Cryptography (eds. M. Hirt and A. Smith), Springer Berlin Heidelberg,
Berlin, Heidelberg, 9986 (2016), 471-484.
doi: 10.1007/978-3-662-53644-5_18. |
[3] |
I. Cascudo, R. Cramer and C. Xing,
Bounds on the threshold gap in secret sharing and its applications, IEEE Trans. Inform. Theory, 59 (2013), 5600-5612.
doi: 10.1109/TIT.2013.2264504. |
[4] |
I. Cascudo, J. Skovsted Gundersen and D. Ruano, Improved bounds on the threashold gap in ramp secret sharing, 2018, Cryptology ePrint Archive 2018/099. |
[5] |
H. Chen and R. Cramer, Algebraic geometric secret sharing schemes and secure multi-party
computations over small fields, in Advances in Cryptology - CRYPT 2006 (ed. C. Dwork),
vol. 4117 of Lecture Notes in Computer Science, Springer-Verlag, 2006, 521-536.
doi: 10.1007/11818175_31. |
[6] |
H. Chen, R. Cramer, R. de Haan and I. Cascudo Pueyo, Strongly multiplicative ramp schemes
from high degree rational points on curves, in Advances in Cryptology - EUROCRYPT 2008 (ed. N. Smart), vol. 4965 of Lecture Notes in Computer Science, Springer-Verlag, 2008, 451-470
doi: 10.1007/978-3-540-78967-3_26. |
[7] |
R. Cleve, D. Gottesman and H.-K. Lo,
How to share a quantum secret, Phys. Rev. Lett., 83 (1999), 648-651.
doi: 10.1103/PhysRevLett.83.648. |
[8] |
D. Gottesman,
Theory of quantum secret sharing, Phys. Rev. A, 61 (2000), 042311.
doi: 10.1103/PhysRevA.61.042311. |
[9] |
M. Iwamoto and H. Yamamoto,
Strongly secure ramp secret sharing schemes for general
access structures, Inform. Process. Lett., 97 (2006), 52-57.
doi: 10.1016/j.ipl.2005.09.012. |
[10] |
R. Matsumoto,
Coding theoretic construction of quantum ramp secret sharing, IEICE Trans. Fundamentals, E101-A (2018), 1215-1222.
doi: 10.1587/transfun.E101.A.1215. |
[11] |
R. Matsumoto,
Strong security of the strongly multiplicative ramp secret sharing based on
algebraic curves, IEICE Trans. Fundamentals, E98-A (2015), 1576-1578.
doi: 10.1587/transfun.E98.A.1576. |
[12] |
R. J. McEliece and D. V. Sarwate,
On sharing secrets and Reed-Solomon codes, Comm. ACM, 24 (1981), 583-584.
doi: 10.1145/358746.358762. |
[13] |
T. Ogawa, A. Sasaki, M. Iwamoto and H Yamamoto,
Quantum secret sharing schemes and reversibility of quantum operations, Phys. Rev. A, 72 (2005), 032318.
doi: 10.1103/PhysRevA.72.032318. |
[14] |
A. Shamir,
How to share a secret, Comm. ACM, 22 (1979), 612-613.
doi: 10.1145/359168.359176. |
[15] |
A. D. Smith, Quantum secret sharing for general access structures, 2000, arXiv:quant-ph/0001087, |
[16] |
H. Stichtenoth,
Algebraic Function Fields and Codes, vol. 254 of Graduate Texts in Mathematics, 2nd edition, Springer-Verlag, Berlin Heidelberg, 2009. |
[17] |
D. R. Stinson, Cryptography Theory and Practice, 3rd edition, Chapman & Hall/CRC, 2006.
![]() ![]() |
[18] |
H. Yamamoto, Secret sharing system using (k; l; n) threshold scheme, Electronics and Communications in Japan (Part I: Communications), 69 (1986), 46-54, (the original Japanese
version published in 1985)
doi: 10.1002/ecja.4410690906. |
[19] |
P. Zhang and R. Matsumoto,
Quantum strongly secure ramp secret sharing, Quantum Information Processing, 14 (2015), 715-729.
doi: 10.1007/s11128-014-0863-2. |
[1] |
Bagher Bagherpour, Shahrooz Janbaz, Ali Zaghian. Optimal information ratio of secret sharing schemes on Dutch windmill graphs. Advances in Mathematics of Communications, 2019, 13 (1) : 89-99. doi: 10.3934/amc.2019005 |
[2] |
Stefka Bouyuklieva, Zlatko Varbanov. Some connections between self-dual codes, combinatorial designs and secret sharing schemes. Advances in Mathematics of Communications, 2011, 5 (2) : 191-198. doi: 10.3934/amc.2011.5.191 |
[3] |
Adriana Navarro-Ramos, William Olvera-Lopez. A solution for discrete cost sharing problems with non rival consumption. Journal of Dynamics and Games, 2018, 5 (1) : 31-39. doi: 10.3934/jdg.2018004 |
[4] |
Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169 |
[5] |
Dan Mangoubi. A gradient estimate for harmonic functions sharing the same zeros. Electronic Research Announcements, 2014, 21: 62-71. doi: 10.3934/era.2014.21.62 |
[6] |
Rafael Bravo De La Parra, Luis Sanz. A discrete model of competing species sharing a parasite. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2121-2142. doi: 10.3934/dcdsb.2019204 |
[7] |
Osman Palanci, Mustafa Ekici, Sirma Zeynep Alparslan Gök. On the equal surplus sharing interval solutions and an application. Journal of Dynamics and Games, 2021, 8 (2) : 139-150. doi: 10.3934/jdg.2020023 |
[8] |
Jong Soo Kim, Won Chan Jeong. A model for buyer and supplier coordination and information sharing in order-up-to systems. Journal of Industrial and Management Optimization, 2012, 8 (4) : 987-1015. doi: 10.3934/jimo.2012.8.987 |
[9] |
João Correia-da-Silva, Joana Pinho. The profit-sharing rule that maximizes sustainability of cartel agreements. Journal of Dynamics and Games, 2016, 3 (2) : 143-151. doi: 10.3934/jdg.2016007 |
[10] |
I-Lin Wang, Chen-Tai Hou. A crowdsourced dynamic repositioning strategy for public bike sharing systems. Numerical Algebra, Control and Optimization, 2022, 12 (1) : 31-46. doi: 10.3934/naco.2021049 |
[11] |
Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165 |
[12] |
Alar Leibak. On the number of factorizations of $ t $ mod $ N $ and the probability distribution of Diffie-Hellman secret keys for many users. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021029 |
[13] |
Shiyong Li, Wei Sun, Quan-Lin Li. Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1099-1117. doi: 10.3934/jimo.2018194 |
[14] |
Xue-Yan Wu, Zhi-Ping Fan, Bing-Bing Cao. Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1999-2027. doi: 10.3934/jimo.2019040 |
[15] |
Daniele Bartoli, Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco. A 3-cycle construction of complete arcs sharing $(q+3)/2$ points with a conic. Advances in Mathematics of Communications, 2013, 7 (3) : 319-334. doi: 10.3934/amc.2013.7.319 |
[16] |
Xiaomei Li, Renjing Liu, Zhongquan Hu, Jiamin Dong. Information sharing in two-tier supply chains considering cost reduction effort and information leakage. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021200 |
[17] |
Guoqiang Shi, Yong Wang, Dejian Xia, Yanfei Zhao. Information sharing when competing manufacturers adopt asymmetric channel in an e-tailer. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021207 |
[18] |
Constanza Riera, Matthew G. Parker, Pantelimon Stǎnicǎ. Quantum states associated to mixed graphs and their algebraic characterization. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021015 |
[19] |
Rich Stankewitz, Toshiyuki Sugawa, Hiroki Sumi. Hereditarily non uniformly perfect sets. Discrete and Continuous Dynamical Systems - S, 2019, 12 (8) : 2391-2402. doi: 10.3934/dcdss.2019150 |
[20] |
Maura B. Paterson, Douglas R. Stinson. Splitting authentication codes with perfect secrecy: New results, constructions and connections with algebraic manipulation detection codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021054 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]