The ELLIPTIC CURVE CRYPTOGRAPHY APPLIED FOR (k,n) THRESHOLD SECRET SHARING SCHEME ECC

Main Article Content

Article Sidebar

Published Sep 8, 2021
SUNEETHA CH Ms

Abstract

Invention of Secret Sharing Scheme by Adi Shamir along with the prevalent advancements offers strong protection of the secret key in communication network. Shamir’s scheme which is established using Lagrange Interpolation polynomial. The group manager or dealer of the group splits the secret S to be communicated into n pieces allots all the n pieces to n participants.  A subgroup of t or more participants of the group come together to reconstruct the secret key. Later the cryptanalysis of secret sharing scheme came into picture in the direction of cheater detection whose motivation is to fool the honest participants. The present paper goals to describe a modification to (k,n) threshold secret scheme using elliptic curve cryptography to avoid the dishonest shareholders and faked shares. In this scheme the group manager or dealer distributes the shares among the participants as affine points on the elliptic curve so that the share modification by the participants or faked shares can be easily detected.

How to Cite

CH, S., & CH, N. (2021). The ELLIPTIC CURVE CRYPTOGRAPHY APPLIED FOR (k,n) THRESHOLD SECRET SHARING SCHEME : ECC. SPAST Abstracts, 1(01). Retrieved from https://spast.org/techrep/article/view/222
Abstract 4 |

Article Details

Keywords

Shamir Secret Sharing Scheme, Lagrange Interpolation polynomial, Elliptic curve over finite field, Encryption, Decryption

References
1. A. Shamir, “How to share a secret”, Communications of the ACM, 22(11) : 612-613, 1979.
2. G.R. Blakley et.al. “Safeguarding cryptographic keys”, In proceedings of the national computer conference, Vol. 48, pp.313-317, 1979.
3. M Tompa, H Woll , “How to share a secret with cheaters” journal of Cryptology, 1, pages133–138, 1989, Springer.
4. L Harn - Security and communication networks, 2014 - Wiley Online Library.
5. L Chen, D. Gollman,CJ Mitchell and P. Wild, “Secret sharing with reusable polynomials[A], Proceeding of the second Australian conference on information security and privacy, ACJSP’97[C].
6. R Du, Z Sun, B Wang, D Long, “Quantum secret sharing of secure direct communication using one-time pad” ,International Journal of Theoretical Physics, Springer, volume 51, pages 2727–2736 (2012).
7. CC Yang, TY Chang, MS Hwang, “A (t, n) multi-secret sharing scheme”, J of Applied Mathematics and Computation, Elsevier, Volume 151, Issue 2, 5 April 2004, pages 483-490.
8. J Shao and Z. Cao, “A new efficient (t,n) verifiable multi secret sharing (vmss) based on Ych scheme”, Applied mathematics and computation, 168(1): 135-140,2005.
9. VP. Binu and A. Sreekumar, “Threshold multi secret sharing using elliptic curve and pairing”, Wireless Personal Communications, 2017 – Springer, 92, pages1531–1543(2017).
10. E Dawson, D Donovan, “The breadth of Shamir's secret-sharing scheme”, Journal of Computers & Security, Volume 13, Issue 1, February 1994, pages 69-78.
11. M Franklin, R Cramer, B Schoenmakers, “Multi-authority secret-ballot elections with linear work”LNCS Vol. 1070, 1996.
12. A Basu, I Sengupta, JK Sing, “Secured hierarchical secret sharing using ECC based signcryption”, https://doi.org/10.1002/sec.370.
13. Koblitz N., “Elliptic curve cryptosystems, mathematics of computation”,Vol. 48, No.177, pp. 203-209, January 1987.
14. 2. Miller V., “Uses of elliptic curves in cryptography”. In advances in Cryptography (CRYPTO 1985), Springer LNCS, 1985, vol. 218, pp 417-4 26.
15. Menzes A., and Vanstone S. “Hand book of applied cryptography”, The CRC-Press series of Discrete Mathematics and its Applications CRC-Press, 1997.
16. Miyaji , Nakabayashi and Takano “Elliptic curves with low embedding degree”, Journal of Cryptology, 2006, Volume 19, Number 4, Pages 553-562.
17. Maurer U., A. Menzes and E. Teske, “Analysis of GHS weil decent attack on the ECDLP over characteristic two fields of composite degree”. LMS journal of computation and Mathematics, 5:127-174, 2002.
18. Arron Blumenfeld, “Discrete logarithms on Elliptic curves”, 2011.
Section
GE3- Computers & Information Technology