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Lec 14: PAKE Based on SPHF

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Recap: SPHF

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From SPHF to PAKE [KV11]

 

 

 

 

 

 

 

 

 

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  • Everyone computes (the product of) 2 SPHF values
    • My hash key on (our password and) your ciphertext → can compute because I know my hash key
    • Your hash key on (our password and) my ciphertext → can compute because I know your projection key and witness (randomness) for my ciphertext

 

 

 

 

 

 

 

 

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Game-based security proof [KV 11, Thm 1]

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Discussion

  • Do not need statistical smoothness; can relax to “computational SPHF”
  • More discussion next time…

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References

  • [KV11] Jonathan Katz and Vinod Vaikuntanathan. Round-Optimal Password-Based Authenticated Key Exchange. In TCC 2011.