Notation  Meaning 

n  Number of participants 
t  Threshold value 
P_{i}  Participant i 
P  Participant set, P = {P_{1}, P_{2},⋯, P_{n}} 
q  A big prime number randomly chosen by the dealer, q > n 
S  Domain of the secret, S = GF(q) 
s  Secret, s ∈ S 
S_{i}  Domain of participant P_{i}’s secret shadow, S_{i} = GF(q) 
s_{i}  Participant P_{i}’s secret shadow, s_{i} ∈ S_{i} 
T  Domain of potential threshold 
t′  New threshold in DTCSSA scheme 
N  Number of potential thresholds in DTCSSB scheme 
h(x)  A polynomial 
h(x_{i})  Value of polynomial h(x) in a given x_{i} 
${y}_{i}^{j}$  Participant P_{i}’s j^{th} advance secret shadow 
ψ_{i}  Participant P_{i}’s secret shadow updating function 
f(r, s)  A twovariable oneway function 
deg(⋅)  Operator is used for computing the degree of the polynomial 
[x^{k}]  Coefficient operator. If h(x) = ∑_{i≥0}a_{i}x^{i}, then [x^{k}] h(x) = a_{k}. 
[⋅]_{k}  Polynomial operator. If h(x) = ∑_{i≥0}a_{i}x^{i}, ${\left[h\right(x\left)\right]}_{k}={\sum}_{i=0}^{k1}{a}_{i}{x}^{i}$. 
TCSSA  DTCSSA  TCSSB  DTCSSB  

NTL  t < t′  t_{min} ≤ t′ ≤ t_{max}  t′ ∈ {t_{1}, t_{2},⋯, t_{N}} (0 < t_{i + 1} − t_{i} < t_{1})  t′ ∈ {t_{1}, t_{2},⋯, t_{N}} 
NCP  t′ − t + 1  1  N  1 
NRP  $\frac{{t}^{\prime}t+2}{2}$  1  $\frac{N+1}{2}$  1 
SSS  (t′ − t + 1) log q  log q  N log q  log q 
BCS  log q  log q  $\frac{N+1}{2}logq$  (n + 1) log q 
Verbal autopsy only  Cause of death on death certificate  

Causes  Vasc  Resp  Neop  Infect  Unsp  Other Sp  Total 
1. Vascular disease (Vasc)  2114  196  19  11  947  129  3416 
2. Respiratory diseases including pulmonary TB (Resp)  94  571  6  8  204  35  918 
3. Neoplasm (Neop)  85  36  462  22  158  37  800 
4. Infection (except Resp) (Infect)  51  29  4  203  111  53  451 
5. Unspecified medical (unsp)  30  12  8  1  114  11  176 
6.Other specific medical illness(Other Sp.)  219  67  11  45  319  892  1553 
Total  2593  911  510  290  1853  1157  7314 


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