TY - GEN
T1 - Two matrices for Blakley's secret sharing scheme
AU - Hei, Xiali
AU - Du, Xiaojiang
AU - Song, Binheng
PY - 2012
Y1 - 2012
N2 - The secret sharing scheme was invented by Adi Shamir and George Blakley independently in 1979. In a (k, n)-threshold linear secret sharing scheme, any k-out-of-n participants could recover the shared secret, and any less than k participants could not recover the secret. Shamir's secret sharing scheme is more popular than Blakley's even though the former is more complex than the latter. The reason is that Blakley's scheme lacks determined, general and suitable matrices. In this paper, we present two matrices that can be used for Blakley's secret sharing system. Compared with the Vandermonde matrix used by Shamir's scheme, the elements in these matrices increase slowly. Furthermore, we formulate the optimal matrix problem and find the lower bound of the minimal maximized element for k=2 and upper bound of the minimal maximized element of matrix for given k.
AB - The secret sharing scheme was invented by Adi Shamir and George Blakley independently in 1979. In a (k, n)-threshold linear secret sharing scheme, any k-out-of-n participants could recover the shared secret, and any less than k participants could not recover the secret. Shamir's secret sharing scheme is more popular than Blakley's even though the former is more complex than the latter. The reason is that Blakley's scheme lacks determined, general and suitable matrices. In this paper, we present two matrices that can be used for Blakley's secret sharing system. Compared with the Vandermonde matrix used by Shamir's scheme, the elements in these matrices increase slowly. Furthermore, we formulate the optimal matrix problem and find the lower bound of the minimal maximized element for k=2 and upper bound of the minimal maximized element of matrix for given k.
KW - Pascal matrix
KW - linear secret sharing
KW - linear threshold cryptography
UR - http://www.scopus.com/inward/record.url?scp=84871977842&partnerID=8YFLogxK
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U2 - 10.1109/ICC.2012.6364198
DO - 10.1109/ICC.2012.6364198
M3 - Conference contribution
AN - SCOPUS:84871977842
SN - 9781457720529
T3 - IEEE International Conference on Communications
SP - 810
EP - 814
BT - 2012 IEEE International Conference on Communications, ICC 2012
T2 - 2012 IEEE International Conference on Communications, ICC 2012
Y2 - 10 June 2012 through 15 June 2012
ER -