Table 1 Notations

\({\varvec{I}\varvec{n}\varvec{f}\varvec{o}}_{\varvec{X}}\)

The registration information of all participants in the system

\({\varvec{S}\varvec{K}}_{\varvec{X}}\), \({\varvec{P}\varvec{K}}_{\varvec{X}}\)

public-private key pairs of\(X\)

\(\varvec{G}\)

A generator for the elliptic group

\({\varvec{C}\varvec{e}\varvec{r}\varvec{t}}_{\varvec{X}}\)

\(X\)‘s digital certificate

\({\varvec{r}\varvec{o}\varvec{l}\varvec{e}}_{\varvec{X}}\)

\(X\)‘s attribute

\(\varvec{f}\left(\varvec{m}\right)\)

The function \(f(\cdot)\) for the elliptic curve that embeds the message\(m\)

\({\varvec{P}}_{\varvec{m}}\)

\(m \text{E}\text{m}\text{b}\text{e}\text{d}\text{d}\text{i}\text{n}\text{g} \text{d}\text{a}\text{t}\text{a} \text{i}\text{n}\text{t}\text{o} f(\cdot)\)

\({\varvec{f}}^{-1}\left(\bullet \right)\)

The inverse function of\(f\left(\cdot \right)\)

\({\varvec{J}}_{\varvec{P}\varvec{i}}\)

Patient P’s transaction information in the chain

\(\varvec{t}\varvec{i}\varvec{m}\varvec{e}\varvec{s}\varvec{t}\varvec{a}\varvec{m}\varvec{p}\)

Current timestamp

\({\varvec{M}}_{\varvec{P}\varvec{i}}\)

Patient information and corresponding encrypted EMR

\(({\varvec{C}}_{\varvec{A}}, {\varvec{C}}_{\varvec{B}})\)

User ciphertext encrypted with encryption key

\(({\varvec{C}\varvec{'}}_{\varvec{A}},{ \varvec{C}\varvec{'}}_{\varvec{B}})\)

User ciphertext encrypted with re-encryption key

\(({\varvec{Q}}_{\varvec{X}\varvec{j}}, {\varvec{T}}_{\varvec{X}\varvec{j}})\)

The \(jth\) signature generated by user\(X\)

\(({\varvec{x}}_{\varvec{i}}, {\varvec{y}}_{\varvec{i}})\)

A random point on an elliptic curve

\(\stackrel{-}{{\varvec{x}}_{\varvec{i}}}\)

Point \(({x}_{i}, {y}_{i})\) convert \({x}_{i}\) to an integer

\({\varvec{H}}_{\varvec{X}\varvec{j}}\)

The \(jth\) hash generated by user\(X\)

\({\varvec{r}\varvec{K}}_{\varvec{A}\to \varvec{B}}\)

\(\varvec{n}\)

\(\varvec{e}\)

Proxy re-encryption key generated from \(A\) to\(B\)

the elliptic curve of order

Bilinear mapping