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Table 1 Notations used in the proposed protocol

From: Lightweight authentication protocol in edge-based smart grid environment

Notations

Descriptions

SM

Smart meter

\(ES_j\)

\(j{\mathrm{th}}\) edge node

TA

Trusted authority

\(E_p(a,b),p\)

Elliptic curve cryptosystem, \(E_p:y^3=x^3+ax+b(mod\,p)\) is an elliptic curve over prime field \(F_p\), p is a prime, where \(x,y,a,b\in F_p\) and \((4a^3+27b^2) mod\,p\ne 0\)

kG

\(kG=G+G+\cdots +G(k times,k\in F_p)\),Scalar multiplication in elliptic curve Cryptosystem

\(r_i\)

The register parameters generated by trusted authority

Adv

Adversary

s

Secret key of TA

\(SK_{ij},SK_{ji}\)

Session key by SMs and edge nodes

\(n_i,n_j\)

Random number chosen by SMs and edge nodes

\(H(\cdot )\)

Cryptographic one-way hash function

||

Concatenation

\(\oplus\)

Bitwise XOR operation