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Table 1 Defines the used annotations

From: Ensuring user authentication and data integrity in multi-cloud environment

PU, PRPublic key, private key
M, COriginal message, encrypted massage
Ai,Aj (i,jϵ(1,n))User identity
F()Stands for encryption
F′()Stands for decryption
Φ(n)The totient of n
PR(A)A’s private key
PU(A)A’s public key
PU(B)B’s public key
PR(B)B’s private key
p, qTwo different primes