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Lec 13: Smooth Projective Hash Functions

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Motivation: PAKE without idealized model

  • All PAKEs we’ve seen (EKE, OEKE, SPAKE2) rely on RO/IC
  • Can we do PAKE without idealized model?
    • Today and next time: PAKE with CRS (“standard model”)
    • Can also do PAKE even without CRS (“plain model”); super inefficient, no standard security (adversary can launch >1 online guessing attack per instance)

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  • 2-step construction
    • 1. Construct SPHF for a given language (SPHF is language-specific) → today
    • 2. For any SPHF, construct PAKE → next time

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SPHF

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SPHF Examples

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Example 1: ElGamal

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Example 2: Naor-Yung [KV11]

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Example 3: Cramer-Shoup

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References

  • [GL03] Rosario Gennaro and Yehuda Lindell. A Framework for Password-Based Authenticated Key Exchange. In EUROCRYPT 2003.
  • [KV11] Jonathan Katz and Vinod Vaikuntanathan. Round-Optimal Password-Based Authenticated Key Exchange. In TCC 2011.