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 DTCSS-A scheme |
N | Number of potential thresholds in DTCSS-B 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 two-variable one-way 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}, ${\left[h\right(x\left)\right]}_{k}={\sum}_{i=0}^{k-1}{a}_{i}{x}^{i}$. |
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