Securing Cloud Data - Cloud Computing with e-Science Applications - page 53

in the LSSS to the actual set of attributes. For each message M , the ciphertext
C is calculated per Equations (3.16) and (3.17). Ciphertext C is then stored in
the cloud.
When a user U u requests a ciphertext from the cloud, the cloud transfers
the requested ciphertext C using the ssh protocol. The decryption algorithm
returns plaintext message M if the user has a valid set of attributes.

System initialization : Select a prime p , generator g of G , groups G and G T
of order p , a map e : G × G → G T , and a hash function H : {0, 1}* → G
that maps the identities of users to G . Each AA A j ∈A has a set of
attributes L j . The attributes disjoint ( L i ∩ L j = φ for i ≠ j ). Each AA
also chooses two random exponents α i

y , ∈ . The secret key of

i q

AA A j is

{ }

SK j = α , y , iL ∈ . (3.13)

i i j

The public key of AA A j is published:

{ }

( )

α

i

y

PK j = e gg , , gi , ∈ L . (3.14)

i

j

Key generation and distribution by KDCs : User U u receives a set of attri-
butes I [ j , u ] from AA A j and corresponding secret key sk i , u for each
i ∈ I [ j , u ]:

()

y

α

sk = gHu

i

, (3.15)

i

iu ,

where α i , y i ∈ SK [ j ]. Note that all keys are delivered to the user
securely using the user's public key, such that only that user can
decrypt it using its secret key.
Encryption by sender : The sender decides about the access tree and
encrypts message M as follows:

h
∈ , with
s as its first entry; h is the number of leaves in the access tree
(equal to the number of rows in the corresponding matrix R ).

1. Choose a random seed s ∈ and a random vector v

q q

2. Calculate λ x = R x · v , where R x is a row of R.

h
∈ with 0 as the irst entry.

3. Choose a random vector w

q

4. Calculate ω x = R x · w

5. For each row R x of R , choose a random ρ x ∈ .

q

6. The following parameters are calculated: