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checking that H 2 , 0 computed from the
P
ath c 1
matches H 2 , 0 included in the
D
igest,
H root = H 2 , 0 = h ( h ( h ( c 1 )
|
H 0 , 0 )
|
H 1 , 1 ) .
(4)
Remark 2. Notice that the MHT can be built by a TTP and distributed to a
repository because a leaf cannot be added or deleted to Φ without modifying
H root
2 which is included in the
D
igest and as the
D
igest is signed, it cannot be
forged by a non-TTP.
The 2-3 Tree.
In the AD, a 2-3 tree is chosen to build the MHT. In a 2-3 tree, each internal node
has two or three children ( t
). The main advantage of this type of tree
is that performing management tasks such as searching, adding and removing
a leaf can be performed in o ( log ( n )) [1] where n is the number of leaves. Each
leaf within the tree represents a certificate; certificates are distinguished by their
serial number and leaves are ordered by serial number. The leaves' order is
essential to prove that a certain certificate, identified by serial number c target ,
is not revoked ( c target
∈{
2 , 3
}
Φ ). To do so, it is enough to demonstrate the existence
of two adjacent leaves : a minor adjacent leaf and a major adjacent leaf which
fulfill that c minor ∈ Φ , c major ∈ Φ and c minor <c target <c major .
/
5 Status Checking Protocol
We have developed a JAVA implementation of the AD called AD-MHT 3 . Next,
we briefly describe the fields that contain the two main JAVA classes of our
implementation:
- The TwoThreeTree class contains the following fields: the number of levels,
the RDI ID , a reference to the private key used to sign the
igest, the validity
period for the current H root and a reference to the root node.
- The Node class contains the following fields: a reference to the left child,
a reference to the middle child, a reference to the right child (this child
only exists if the node has 3 children), the biggest element of the subtree
that descends from this node denoted by max , the smallest element of the
subtree that descends from this node denoted by min and the cryptographic
value of this node ( H i,j ).
D
Fig. 3 shows a sample 2-3 that represents a set of revoked certificates Φ =
{
. Notice that leaves on the left represent smaller serial num-
bers than leaves on the right.
2 To do such a thing, an attacker needs to find a pre-image of a OWHF which is
computationally infeasible by definition.
3 The software for the AD-MHT client and the AD-MHT server can be downloaded
from http://isg.upc.es/cervantes
2 , 5 , 7 , 8 , 12 , 16 , 19
}
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