Efficient log authentication for Forensic Computing

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• Efficient log authentication for Forensic
  Computing
• Nobutaka Kawaguchj, Naohiro Obata, Shintaro
  Ueda, Yusuke Azuma, Hirashi Shigeno and Kenichi
  Okada
• ??????
• ???????

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SUMMARY

• In this paper, an efficient log
  authentication scheme for Forensic Computing is
  proposed.
• To conduct reliable Forensic Computing, it is
  required that the logs as digital evidences be
  verified, To verify them, digital signatures
  issued by authorities are needed . However, if
  many logging hosts connect to the server that
  issues the signatures, the traffic of the server
  will increase. And this paper propose a scheme to
  solve this problem by using distributed Merkle
  Tree Algorithm .

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PROPOSAL

• When many logging nodes connect to the Sign
  Server , the traffic of the server will increase.
• There is an efficient signing scheme that
  reduces the traffic of the Sign Server by
  constructing distributed Merkle Tree composed of
  logging hosts.

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• In distributed Merkle Tree, hosts construct a
  tree topology. Next, hashes of all hosts are
  accumulated and sent to the Sign Server from the
  root node. The root node is the only host, which
  communicates directly with the Sign Server.
• Therefore , traffic of the server can be
  reduced to a remarkable degree and the traffic
  increase of the logging hosts is minimized.

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Disrributed Merkle Tree
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• Each logging host connects with each other
  similar to a P2P network. And In this model, hash
  values, signature and authentication information
  are transmitted between logging hosts and Sign
  Server.

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Computation of hash values

• Each logging host computes the hash value of
  the logs as soon as the logs are generated. the
  logging host positioned at the leaf node of the
  tree constructs a binary Merkle Tree. The tree is
  constructed by the hash values. Finally the
  logging host sends the root hash to the parent
  node. In the case when the node does not generate
  any log within a signature interval time, a dummy
  hash (e.g., all the bit is set to zero) is sent
  to the parent node.

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Transmission of hashes to the parent node
(1)The parent node receives the hashes from the
child nodes
(2)Using the hashes received from the child nodes
to compute the hash , and a Merkle Tree is
constructed. The root hash of the tree is sent to
the parent node's parent node.
(3) The hashes used for constructing the tree are
stored temporarily for later use
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Computation of the signature by the Sign Server

• The root node in the distributed Merkle Tree
  communicates with the Sign Server. On receiving
  the hash from the root node, the Sign Server
  concatenates the hash with the current timestamp
  and signs the concatenated value.

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Reception of the signature andauthentication
information from the Sign Server

• Each logging host needs to receive the
  signature and authentication information
  corresponding to the hash that the host sent to
  the parent node and verifies the signature.
• We call the signature and authentication
  information as the authdata.

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The format of the authdata sent by both the Sign
Server and the parent nodes to the child nodes.
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Each entry in the format is composed of the
data to reconstruct a Merkle Tree. Using the
authdata, the hash sent to the parent node before
is verified as follows.

• (1) Using the root hash which was stored
  temporally when the hash is sent to the parent
  node and entry 1 in the format, Merkle Tree is
  constructed. The index in entry 1 indicates the
  position of the root hash of entry 1 in the
  Merkle Tree.

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• (2) Using the hash computed as the root hash of
  the Merkle Tree constructed in (1) and the entry
  2, a new Merkle Tree is constructed again. The
  process is continued until all the entries are
  consumed to construct the tree.
• (3) Finally the root hash of the final Merkle
  Tree and the timestamp is verified by the
  signature.

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Transmission of the signature and authdatato the
child nodes

• On sending the authdata, hashes and index to
  compute the root hash stored temporally is
  appended to the authentication information as new
  entry 1. The appended new entry for each child
  node is distinct. Finally the new authdata are
  sent to the child nodes.

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Iv. EVALUATION AND DISCUSSION

• Theoretical Analysiswe call our proposed scheme
  as the tree connection scheme and the scheme in
  which all logging node connects to the Sign
  Server directly as the direct connection scheme.
• Comparison in the condition where the
  signature delay time of two schemes are
  equivalent

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Signature delay time

• In direct connection, since logging hosts
  connect to the Sign Server directly, signature
  delay time is equivalent of one RTT (Round-Trip
  Time?????????????), therefore O (1) . On the
  other hand, in tree connection, from each logging
  node, it takes O (logdN ) hops (the height of the
  tree) to the Sign Server. N is the number of
  logging hosts and d is the degree of the
  distributed Merkle Tree.

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Sending rate of Sign Server

• In direct connection, the Sign Server
  communicates with all logging hosts , so in
  Tree-Linking protocol a Merkle Tree is
  constructed by the Sign Server using the hashes
  received in one signature interval time.
• The size of authentication information required
  to verify a hash is O(log2N). Therefore, the
  sending rate of the Sign Server required to send
  the authdata to N hosts is O (N log2N).

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• On the other hand, in tree connection, since
  the Sign Server only communicates to the root
  node of the tree, the Sign Server only sends one
  signature. Therefore, the sending rate is O(1).

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Receiving rate of Sign Server

• In direct connection, the Sign Server is
  required to receive the hashes from all logging
  hosts. Therefore, the receiving rate is O(N) .
• On the other hand, in tree connection, the Sign
  Server only receives a hash from the root node.
  Therefore, the receiving rate is O(1)

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Sending rate of logging host

• In direct connection, each host only sends the
  hash values. Therefore, the sending rate is O(1).
  But in tree connection, the sending rate of the
  leaf nodes is different from that of the internal
  nodes. Because the leaf node only sends the hash
  to the parent node. , the sending rate is O(1).
  The internal node sends the authdata to the child
  nodes. Since the authentication information size
  is O(log2 N ) and each internal node has d child
  nodes, the sending rate is
• O (d log2 N) ,

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Receiving rate of logging host

• In both direct connection and tree
  connection, the receiving rate of the logging
  host is O(log2 N) .

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• It is obvious that the tree connection scheme
  reduces the traffic of the Sign Server compared
  with the direct connection scheme . On the other
  hand, the tree connection scheme increases the
  signature delay time and the sending rate of the
  logging host.

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Comparison in the condition where the signature
delay time of two schemes are equivalent

• First, the following parameters are defined.
• (1) Dd Signature delay time of the direct
  connection
• scheme
• (2) Dt Signature delay time of the tree
  connection scheme
• (3) Dlink R TT between a parent node and a child
  node of
• a node.
• (4) Id Signature interval time of the direct
  connection scheme
• (5) It Signature interval time of the tree
  connection scheme
• (6) Sd , Rd Sending rate and receiving rate of
  the Sign Server of the direct connection scheme
  respectively
• (7) St , Rt Sending rate and receiving rate of
  the Sign Server of the tree connection scheme
  respectively
• (8) d Degree of the Merkle Tree
• (9) h Height of the Merkle Tree

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If Dd Dt and Rrecv gt 1 is true, it is easily
seen that the tree connection scheme is more
effective than the direct connection scheme in
the condition where the signature delay time of
the two schemes are equivalent. And This means
that if the signature delay time is too short, it
is impossible to make the tree connection scheme
more effective than the direct connection scheme.
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CONCLUSION AND FUTURE WORK

• Our scheme is scalable in terms of logging host
  traffic versus number of hosts. One of our future
  works is to define the protocols and methods that
  efficiently construct the distributed Merkle
  Tree. In this paper, we do not consider the
  effect of malicious hosts, compromise of the Sign
  Server and network failure. So, we will improve
  our scheme to counter these problems.

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• The End