Table 1 Notations and their corresponding meanings

G ₁, G ₂

Groups

ê

Bilinear paring operation

H ₁

Hash function

PK

System public parameters

MK

System master key

AA

Attribute authority

U

Global attribute set

A _i

Attribute i

D _i

Private key of attribute i

M

Plaintext

T _i

Access structure

x

Node in the access tree

Δ _i,S(x)

Lagrange interpolation function

q _x

Polynomial defined by AA

p _x

Polynomial defined by signer

v

Signature to be verified

id _l

Identity of user l