yaole
28 lines
648 B
Markdown
28 lines
648 B
Markdown
# 判断标识，用户私钥和主公钥的一致性
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Let $h_1 = H_1(ID||hid, N)$, for the user sign key $ds$,
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$$
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ds = \left[ \frac{ks}{h_1+ks} \right]\cdot P_1,
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$$
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and $P_{pubs} = [ks]\cdot P_2$, we have
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$$
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\begin{array}{rcl}
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& & e(ds, P_{pubs} + [h_1]\cdot P2) \\
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&=& e(\left[ \frac{ks}{h_1+ks} \right]\cdot P_1, [ks+h_1]\cdot P_2)\\
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&=& e(P_1, P_{2})^{ks} \\
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&=& e(P_1, P_{pubs}).
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\end{array}
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$$
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Thus, we need to compute if the following equation holds:
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$$
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e(ds, P_{pubs} + [h_1]\cdot P_2) \overset{?}{=} e(P_1, P_{pubs}).
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$$
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The same for encryption user key $de$:
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$$
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e(P_{pube} + [h_1]\cdot P_1, de) \overset{?}{=} e(P_{pube}, P_2).
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$$
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