Identity Theft Prevention using Aggregated Proof of Knowledge

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Identity Theft Prevention usingAggregated Proof
of Knowledge

• Elisa Bertino, Abhilasha Bhargav-Spantzel,
• Anna Squicciarini,
• Rui Xue

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What is Identity Theft?

• Identity Theft is the use of personally
  identifying information belonging to one
  individual by another individual for financial or
  personal gain.

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Multi-Factor Identity Verification
Require additional identity information as
proof to qualify to be the owner of the identity
attribute being used.
Example Real Life Scenario Requirement for
additional proofs of identity
I will use my credit card to pay
To use your credit card please show your drivers
license and an additional photo id for
verification of your identity
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Overview of our Approach

• We have a logical entity called the registrar
  which establishes and maintains identity
  commitments used to establish proof of knowledge
  of strong identifiers used later for multifactor
  identity verification.
• Two main Phases
• Enrollment or Registration User commits his
  strong identifiers to be used later as proofs of
  identity.
• Usage Before revealing the actual value of a
  required attribute one has to verify the
  commitments of other attributes as proofs of
  identity.

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Example
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Preliminary Concepts

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Example of ZK Proof system
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Pedersen Commitment ZK Proveknow how to open

• Public commitment c gxhr (mod p)
• Private knowledge x,r
• Protocol
• P picks random y, s in 1..q, sends d gyhs
  mod p
• V sends random challenge e in 1..q
• P sends uyex, vser (mod q)
• 4. V accepts if guhv dce (mod p)

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Bilinear Maps

• Let G1, G2, and Gt be cyclic groups of the same
  order.

Bilinear maps are called pairings because they
associate pairs of elements from G1 and G2 with
elements in Gt.
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Aggregated signatures (Boneh, et al.)

• Signatures on different messages by multiple
  signers can be combined into one small signature.
• Scheme requires bilinear map (in Gap DH groups)
• BGLS Details

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Preliminary Concepts

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Proving aggregated signature on committed values
To prove the knowledge of multiple identifiers.
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Proving aggregated signature on committed values
and open
To open in clear multiple sensitive identifiers.
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Proving aggregated signature on some committed
values and opening some
To prove u values and open v
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Integrating the zero-knowledge proof into the
verification
To prove the knowledge of secret commitments.
Note that the only information sent by the
principal is s, while in the previous protocol
the tags and the commitments were also sent.
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Zero-knowledge proof the aggregated signature
To prove the possession of signature.
The final submitted value is independent of any
of the actual signatures. Principal remains
unlinkable and anonymous even if it had initially
revealed its strong identifiers and commitments
to the verifying SP.
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Efficiency Analysis

• Our signatures on commitments are short and the
  storage complexity is smaller than the ones
  computed with existing techniques Camenisch et.
  Al.04
• Our approach is more flexible in that whenever n
  messages are committed for a user, the user is
  able to to prove 2n-1 many combinations of them
  which does not appear possible in the existing
  schemes

Comparison of the number of exponentiations for
proving t factors
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Conclusion

• Identity theft is a major problem
• Our approach supports the strong verification of
  identity attributes, which is a component of
  comprehensive solutions against identity theft

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