One way encryption system

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One way encryption system

• by
• Adi Sashkis
• and
• Yehezkel Horowitz
• Advisor
• Prof. Shlomi Dolev

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Out line

• Base concept
• Lattice Shortest Vector problem
• System definition
• Mathematical research
• Questions

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Goal one way encryption system

• No pre-shared knowledge (only IP and port).
• Establish a secure tunnel with individuals (in
  spite of the fact that all can listen and no one
  answers).
• Sounds impossible?

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Solution one way encryption system

• The encryption power computation gap.
• We assume that our system can perform the task
  faster than the advisory.
• This will give us a gap of time to pass the data
  in secure way.
• How?

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Encryption system concept

• Generate randomly a sequence of independent
  problems.
• Solve them one by one.
• Encrypt each problem with the solution of the
  previous problem.
• Thus, only who solve all the previous problems
  can start solve the current problem.

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Lattice Shortest Vector Problem

• We need to randomly choose puzzles that are hard
  in average.Worst case-average case equivalence.
• Lattice Shortest Vector Problem is an NP problem
  in the average case Ajtai97.
• Given matrix mn above Zq find a vector such
  that ltmatrixgtltvectorgtltzero vectorgt.
• Notes
• The solution cant be the zero vector.

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The system modes

• Symmetric mode minimal solution
• Asymmetric mode build-in solution

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Symmetric mode

• Both sides solve the problem generated by the
  encryptor.
• There is only lexicographically first among the
  minimal solutions .
• Both sides need to have powerful resources to
  satisfy the componential gap.

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Asymmetric mode

• Only the decryptor solve the problem generated by
  the encryptor.
• The encryptor dont need powerful resources.
• How the encryptor know the solution?

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Asymmetric mode cont.

• The encryptor have a build-in solution.
• No guarantee that this is the minimal solution,
  we can have more than one solution.
• How the decryptor will know which solution to
  choose?

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Asymmetric mode cont.

• The decryptor will build a tree-form database to
  manage all possible solutions and their derived
  decrypted problems.
• This can be huge task!

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Asymmetric mode cont.

• Mathematical research can minimize the solutions
  amount.
• Choose the matrix size and Zq wisely.
• The vector amount in the matrix have impact
  (exponentially) on the problem hardness.
• The vector length q have impact on the solution
  amount.
• Need to choose m,n,q such that 2m ltlt qn

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One way encryption system

• To fine tune the parameters, we run automated
  test program this take a lot of time
• The results we received matched our researchs
  estimations.

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Questions?
More information about our project you can find
at http//www.cs.bgu.ac.il/adihen/finalProject.h
tm
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The End

• Thank you for listening us.