An innovative Policy-based Cross Certification methodology for Public Key Infrastructures

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An innovative Policy-based Cross Certification
methodologyfor Public Key Infrastructures

• V.Casola, A.Mazzeo, N.Mazzocca, M. Rak
• University of Naples Federico II, Italy

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Outline

• Motivation
• Cross-certification as a policy evaluation issue.
• The proposed approach to automate policy
  evaluation
• A quantitative approach to evaluate security
  through policies,
• A methodology to build a Reference Evaluation
  Model to compare and evaluate policies.
• The REM components.
• Methodology applicability through case studies.
• Conclusions and Future Works.

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Motivation

• Certificate policies in PKI are widely used to
  expresses the set of practices a CA enforces for
  certificates management.
• Different CAs need to reach an explicit agreement
  in order to extend trust among each other (cross
  certification).
• The cross-certification is based on manual
  evaluation of the involved policies and mutual
  agreement from experts of the two CAs.
• This process is not automatic and often ambiguous
  and expensive
• (it requires technical and organizational people
  to reach an agreement)
• In the cooperation of different un-trusted
  domains services do not have the possibility to
  cooperate until an off-line agreement has been
  reached.

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Methodology target and applicability context

• We have defined a Methodology to
• Express security through a semi-formal and not
  ambiguous policy
• Evaluate the security level that a security
  infrastructure is able to guarantee by comparing
  its policy against a Reference Evaluation Model.

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Methodology core the REM

• The methodology core is the REM definition
• REM ltFormalization, Technique, Reference
  Levelsgt
• These components address the following needs
• policies should be described in a rigorous way in
  order to (automatically) compare different
  security policies. The REM should propose a
  formalization to translate informal policies in a
  way suitable for the adopted technique.
• How to quantify the system security? The REM
  should define evaluation techniques and a
  security metrics.
• Usually a CA expresses security through a set of
  "security levels" which are related to different
  classes of certificates. The REM should help in
  defining this levels, and in assigning a given
  level to a policy.

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The REM components

• Formalization represents the formal
  (semi-formal) representation of the policy. The
  chosen formalization will affect final
  evaluation, and will be built by taking into
  account the adopted PKI architecture for the
  evaluation
• Technique represents the evaluation technique
  that can be applied to compare policies the
  evaluation technique strictly depends on the
  policy formal representation.
• Reference Levels are instances of policies,
  which represent different security levels. This
  REM component is optional, because not always the
  evaluation will be expressed in terms of security
  levels.

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Policy Formalization (1)

• Policy formalization needs to be
• Not ambiguous, (this is a problem for high level
  languages semantically reach),
• Correct respect to the described system,
• Complete !!!
• RFC3647 is widely used to write a policy. We have
  chosen its main provisions and its tree structure
  for the first steps of our formalization.
• Textual provisions have been refined in a more
  fine-grain and a grammar of enumerative
  data-types has been proposed, so reducing
  semantical complexity

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Policy Formalization (2)

• The defined data-structures are new atomic or
  enumerative types and a total order relation
  among their values has been defined
• We have associated a Local Security Level to each
  provision instance.
• Example
• Data-type Key Protection mechanism
• Ordered values
• No Protection lt Protection on Floppy lt
  Protection on Smart Card lt Protection on Smart
  Card with Biometric Sensor

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Policy Formalization (3)

• The proposed structure is a hierarchical tree
  represented by an XML document
• Tree nodes identify complex security provisions,
  leaves identify simple security provisions.

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Evaluation Techniques

• We have introduced two different evaluation
  techniques
• The first one is based on fuzzy theory to
  represent and evaluate policies.
• The second technique is based on the definition
  of a metric policy space and a distance criterium
  by which we could represent policies and compare
  different policies.

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The Fuzzy Technique - 1

• All provisions of the policy are translated into
  a fuzzy judgment which expresses the Local
  Security Level of each provision
• A fuzzy judgment can be represented by a pair
  (p,s), where p is the ordinal position of the
  label in the chosen scale of judgment and s is
  the number of labels considered by the scale i.e.
  the number of LSL for that provision.
• The pairs are translated into fuzzy numbers with
  triangular shapes characterized by these points

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The Fuzzy Technique - 2
orness variable graphics

• A policy is characterized by the aggregation of
  fuzzy judgments on structured provisions through
  the OFNWA (Ordered Fuzzy Number Weighted
  Averaging) aggregation technique.
• The result of aggregation is the global judgment
  of the policy and it is a fuzzy number, too.
• It is represented by a triangular membership
  function, where xM expresses the Global Security
  Level of the policy under evaluation while the
  distance between xL and xR gives a measure of the
  evaluation uncertainty.

GSL
uncertainty
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The metrical space Technique - 1

• After the policy formalization, each provision
  is represented by an enumerative data-type the
  type-values are ordered.
• The policy space is made homogeneous thanks to
  threshold functions (F-functions) which allow to
  associate a Local Security Level to each
  provision
• The policy space is represented by a n x 4
  matrix
• The distance criterium for the definition of
  the metric space is the Euclidean distance among
  matrices, defined as
• d(A,B) v( s (A-B,A-B))
• where s (A,B) Tr (ABT)

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The metrical space Technique the policy matrix

• The policy space is represented by a n x 4 matrix
  (total number of provisions for the number of
  Local Security Levels)

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Reference Levels

• The last component of the REM is the set of
  reference security levels that could be used as a
  reference scale for the numerical evaluation of
  security.
• Note that when references are not available, the
  REM is used for direct comparison among two or
  more policies.

• Example evaluation of the 4 security levels for
  the Government of Canada PKI

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The reference levels and the metric function

• Evaluation of the 4 security levels for
  the Government of Canada PKI with the metrical
  technique

The metric function for the evaluation of the
GSL of Px
if dX0 d10 gt LPX L0, if d10 lt
dX0 lt d20 gt LPX L1, if d20 lt dX0 lt
d30 gt LPX L2, if d30 lt dX0 lt d40
gt LPX L3, if d40 dX0 gt LPX L4,
d10 d(GofC1, ? ) 7,07 d20 d(GofC2, ?
) 11,18 d30 d(GofC3, ? ) 12 d40
d(GofC4, ? ) 12,65
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Techniques comparison

• Fuzzy technique is very flexible and easy to use
  it gives as a result a judgment and some
  parameters on which the evaluator could play to
  locate critical points thanks to a graphical
  representation of orness-variable results.
• Metrical space technique gives as a result a
  number it is helpful when a root-CA needs to
  associate a leaf-CA to a certain security level
  number.

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CASE 1Example of Fuzzy Formalization
An evaluation graph each provision is structured
and expressed by a fuzzy judgement. Aggregation
takes in count the structure, the judgements and
different weights.
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Application of the Fuzzy technique
Policy evaluation
The target policy
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CASE 2Example of matrix representation
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Application of the metrical technique

• References

Target policy evaluation d(CT, ? ) ?149 e
d30 lt d(CT, ? ) lt d40 so LCT L3.
d10 d(GofC1, ? ) 7,07 d20 d(GofC2, ?
) 11,18 d30 d(GofC3, ? ) 12 d40
d(GofC4, ? ) 12,65
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Conclusions and

• The Cross Certification process is based on the
  evaluation of Certificate policies
• We have proposed a methodology to automatically
  evaluate and compare security policies
• The core of the methodology is the evaluation
  technique with which we could represent
  formalized policies and evaluate them against
  some reference security levels

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Future Works

• We are actually working on the assessment of the
  methodology, in particular
• implementation of an automatic evaluator system
  to apply the methodology in un-trusted domains
• Application of the methodology in different
  stages of a system development
• Application of the methodology for Service Level
  Agreement (SLA) in cooperative services.