Optimal Information Rate Calculation Based on a Class of Graph Access Structure

doi:10.3969/j.issn.1671-1122.2022.04.009

Abstract

Abstract:

Secret sharing provides a very effective way for key management and the information rate of access structure provides a theoretical guarantee for the design of efficient secret sharing scheme. In this paper, by using the relationship between access structure and connected graph, a class of access structure with 8 participants is transformed into a class of 63 graph access structures with 8 vertices, 9 edges and a maximum vertex degree of 3. The accurate value or upper and lower bounds of the optimal information rate of these 63 graph access structures are calculated by splitting construction method, entropy method, vertex degree theorem, decomposition construction method and weighted decomposition method. The accurate values of the optimal information rates of 30 graph access structures and the upper and lower bounds of the optimal information rates of the other 33 graph access structures are obtained.

Key words: graph access structure, optimal information rate, secret sharin scheme, decomposition of graphs

CLC Number:

TP309

LYU Kaixin, LI Zhihui, HEI Jiliao, SONG Yun. Optimal Information Rate Calculation Based on a Class of Graph Access Structure[J]. Netinfo Security, 2022, 22(4): 77-85.

Figures/Tables 7

存取结构名称	存取结构	存取结构名称	存取结构
G1	AB+AC+AF+BD+BE+ CD+CE+DG+FH	G33	AB+AD+AH+BC+BE+ CD+CF+EG+FG
G2	AB+AC+AF+BC+BE+ CD+DE+DG+EH	G34	AB+AD+AH+BC+BD+ CE+CF+EG+FG
G3	AF+AG+AH+BC+BD+ BF+CD+CE+DE	G35	AB+AD+AH+BE+BF+ CE+CF+CG+DG
G4	AB+AG+AH+BC+BD+ CE+CF+DE+DF	G36	AB+AD+AH+BC+BE+ CE+CF+DG+FG
G5	AB+AG+AH+BC+BE+ CD+CF+DE+DF	G37	AB+AC+AH+BD+BE+ CD+CF+EG+FG
G6	AB+AG+AH+BC+BD+ CD+CE+DF+EF	G38	AB+AD+AH+BC+BE+ CF+CG+DE+FG
G7	AB+AE+AG+BC+BF+ CD+CF+DE+DH	G39	AB+AD+AH+BC+BE+ CF+CG+DG+EF
G8	AB+AE+AG+BC+BD+ CE+CF+DF+DH	G40	AB+AC+AH+BD+BE+ CF+CG+DF+EG
G9	AE+AF+AG+BC+BD+ BE+CD+CF+DH	G41	AB+AC+AH+BD+BE+ CF+CG+DE+FG
G10	AB+AE+AG+BC+BF+ CD+CE+DF+DH	G42	AB+AC+AH+BC+BD+ CE+DF+EG+FG
G11	AB+AE+AG+BC+BE+ CD+CF+DF+DH	G43	AB+AD+AE+BF+BG+ CE+CF+CG+DH
G12	AB+AE+AG+BD+BF+ CD+CE+CF+DH	G44	AB+AC+AD+BE+BF+ CE+CF+DG+GH
G13	AB+AE+AG+BC+BH+ CD+CF+DE+DF	G45	AD+AE+AF+BC+BE+ BG+CF+CG+DH
G14	AB+AE+AG+BD+BH+ CE+CF+DE+DF	G46	AC+AD+AE+BC+BE+ BF+CF+DG+GH
G15	AB+AE+AG+BC+BD+ CD+CF+DH+EF	G47	AB+AC+AD+BE+BF+ CF+CG+EG+DH
G16	AB+AC+AG+BC+BD+ CH+DE+DF+EF	G48	AB+AD+AE+BC+BF+ CE+CG+FG+DH
G17	AB+AC+AG+BD+BE+ CD+CF+DH+EF	G49	AB+AD+AE+BC+BF+ CF+CG+EG+DH
G18	AB+AC+AG+BD+BH+ CD+CE+DF+EF	G50	AB+AD+AE+BC+BE+ CF+CG+FG+DH
G19	AB+AE+AG+BC+BD+ CD+CF+DE+FH	G51	AB+AC+AD+BC+BE+ CE+DF+FG+GH
G20	AB+AE+AG+BC+BD+ CD+CF+DF+EH	G52	AB+AC+AD+BC+BE+ CF+DG+EF+GH
G21	AB+AC+AG+BC+BD+ CE+DE+DF+FH	G53	AB+AC+AD+BC+BE+ CF+EG+FG+DH
G22	AB+AC+AG+BD+BE+ CD+CF+DF+EH	G54	AC+AD+AE+BC+BD+ BF+EG+FH+GH
G23	AB+AC+AG+BD+BE+ CD+CE+DF+FH	G55	AC+AD+AE+BC+BF+ BG+DH+EH+FG
G24	AB+AC+AG+BC+BD+ CD+DE+EF+FH	G56	AC+AD+AE+BC+BF+ BG+DH+EG+FH
G25	AB+AC+AE+BC+BD+ CD+DF+EG+FH	G57	AB+AC+AD+BC+BE+ DH+EF+FG+GH
G26	AD+AE+AH+BC+BD+ BE+CF+CG+FG	G58	AB+AC+AD+BE+BF+ CG+DG+EH+FH
G27	AD+AE+AH+BD+BF+ BG+CE+CF+CG	G59	AB+AC+AD+BE+BF+ CG+EG+DH+FH
G28	AD+AE+AH+BC+BD+ BF+CE+CG+FG	G60	AC+AD+AE+BF+BG+ BH+CG+DH+EF
G29	AD+AE+AH+BC+BD+ BF+CF+CG+EG	G61	AC+AD+AE+BF+BG+ BH+CE+DG+FH
G30	AB+AD+AH+BE+BF+ CE+CF+CG+FG	G62	AB+AC+AD+BE+BF+ CG+DH+EF+GH
G31	AB+AD+AH+BE+BF+ CD+CF+CG+EG	G63	AB+AC+AD+BE+BG+ CF+DG+EH+FH
G32	AB+AD+AH+BD+BE+ CE+CF+CG+FG	—	——

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存取结构名称	最优信息率	存取结构名称	最优信息率	存取结构名称	最优信息率	存取结构名称	最优信息率
G1	3/5	G17	1/2~3/5	G33	4/7~3/5	G49	4/7~3/5
G2	1/2~3/5	G18	1/2~3/5	G34	2/3	G50	4/7~3/5
G3	1/2~3/5	G19	1/2~3/5	G35	3/5	G51	2/3
G4	3/5	G20	1/2~3/5	G36	4/7~3/5	G52	1/2~3/5
G5	2/3	G21	3/5	G37	1/2~3/5	G53	1/2~3/5
G6	4/7~3/5	G22	1/2~3/5	G38	3/5	G54	2/3
G7	3/5	G23	1/2~3/5	G39	3/5	G55	2/3
G8	5/9~3/5	G24	1/2~3/5	G40	1/2~3/5	G56	3/5
G9	4/7~3/5	G25	3/5~2/3	G41	3/5	G57	3/5
G10	1/2~3/5	G26	3/5~2/3	G42	3/5	G58	2/3
G11	5/9~3/5	G27	2/3	G43	3/5	G59	3/5
G12	1/2~3/5	G28	3/5~2/3	G44	2/3	G60	3/5
G13	1/2~3/5	G29	3/5~2/3	G45	3/5	G61	2/3
G14	1/2~3/5	G30	4/7~3/5	G46	3/5	G62	3/5
G15	1/2~3/5	G31	4/7~3/5	G47	1/2~3/5	G63	3/5
G16	1/2~3/5	G32	3/5	G48	3/5	——	——