Securing Cloud Data - Cloud Computing with e-Science Applications - page 50

Let Y be the set of leaf nodes of A. The ciphertext is given by

( )

( )

y ()

( )

()

()

P

α s

s P 0

CT = A, CMeggChC = , , = , = gCHatt y , =

y

y y

KeyGen ( MK , S ): Let S be the set of attributes of the receiver. The AA
chooses r ∈ at random and r j ∈ , ∀ j ∈ S . The secret key SK is

p p

given by

( )

== ∀∈ = () =

( α ,

r

+ r r r

SK Dg jSDgHj :

j

, Dg

j

j j

Decrypt ( CT , SK , S ): Let i = att ( x ) be a leaf node. If i ∈ S , then

( )

eD C
eD C

,
,

( ) =

i x

DecryptNode CT SK x , ,

)

(3.5)

(

i x

( )

()

r

()

P 0

egHi

r

i

, g

x

= (3.6)

( )

()

()

P 0

r

eg Hi ,

x

i

()

= (

)

rP x 0

egg , (3.7)

If i ∉ S , then DecryptNode ( CT , SK , x ) = NULL .

We consider the case when x is a nonleaf node; the following steps are carried
out: Let S x be the set of child nodes of x . If there are no such sets, then return
NULL. Else, F x is calculated. Lagrange's coefficient is ∆ ,

xj
ij

−
−

() =

x Π

.

iS jSji ∈ ,

()

() =

{

( ) ∈

}

0

F = Π F , wherei = indexz Sindex z , : zS x (3.8)

tSx ,

x z Sz ∈ x

x

( )

()

0

()

tS x ,

( )

rP 0

z

= Π zS egg , (3.9)

∈

x

()

( )

0

()

tSx ,

( )

rP indexz

()

= Π zS egg ,

parentz

(3.10)

∈

x

() ()

( )

rP i 0

z t S x ,

= Π zS egg , (3.11)

∈

x

= (

)

()

rP x 0

egg , (3.12)