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Lossy Trapdoor Functions

Lossy Trapdoor Functions. Definition and applications. Lossy Trapdoor Functions. Definition [PW08]. Invertible. Lossy. Lossy Trapdoor Functions. Implications. [BKPW12] What about the IB setting ?. Lossy Trapdoor Functions. Constructing a primitive. Setup. Encrypt. Decrypt. Gen.

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Lossy Trapdoor Functions

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  1. Lossy Trapdoor Functions Definition and applications

  2. Lossy Trapdoor Functions Definition [PW08] Invertible Lossy

  3. Lossy Trapdoor Functions Implications [BKPW12] Whataboutthe IB setting?

  4. Lossy Trapdoor Functions Constructing a primitive Setup Encrypt Decrypt Gen Evalpk Invert Game 1 Secure! IND Setup Encrypt Decrypt? Gen’ Evalpk’ Game 2 C hides M!

  5. Identity-Based Lossy Trapdoor Function[BKPW12] Working towards a definition

  6. Identity-Based Lossy Trapdoor Functions IBE - Functionality Constructed with an IB-LTDF uses: IBE [Sha84,BF01] consistsof:

  7. Identity-Based Lossy Trapdoor Functions Functional requirements Invertible

  8. Identity-Based Lossy Trapdoor Functions IBE – Security Game / Reduction Using IB-LTDF can try toinvert. should be lossy

  9. Identity-Based Lossy Trapdoor Functions Towards defining sec. requirements Invertible Sec. Requirement? Lossy

  10. Identity-Based Lossy Trapdoor Functions [BKPW12] limitations

  11. Identity-Based Lossy Trapdoor Functions [BKPW12] limitations

  12. Identity-Based Lossy Trapdoor Function New Definition and Hierarchical Extension

  13. Identity-Based Lossy Trapdoor Functions Our definition (I) Lossy Experiment Real Experiment L I has small range has full range

  14. Identity-Based Lossy Trapdoor Functions Our definition (II) Extra Cond. #1: big enough Extra Cond. #2: indep. from guess

  15. Identity-Based Lossy Trapdoor Functions [EHLR14] implications *Also in [XXZ12]

  16. Identity-Based Lossy Trapdoor Functions [EHLR14] implications *Also in [XXZ12]

  17. Identity-Based Lossy Trapdoor Function Construction

  18. Identity-Based Lossy Trapdoor Functions Construction similar to [PW08] • Matrix-vector paradigm Building block: a new Hierarchical Predicate Encryption • Hidden Predicate defines Injective or Lossy To evaluate the function for an identity: • Homomorphically evaluate the Predicate for the Identity • Obtain a matrix of HIBE ciphertexts • Compute the matrix-vector product in the exponent Our construction

  19. Identity-Based Lossy Trapdoor Function Conclusion

  20. Identity-Based Lossy Trapdoor Functions Wegive a new definition Wegive a hierarchicalextension of thedefinition Ourdefinitionimpliesnew primitiveswithadaptivesecurity: • One-way HIB TrapdoorFunctions • HIB DeterministicEncryption • HIB HedgedEncryption • Forward SecureDeterministicEncryption • Forward SecureHedgedEncryption Wegive a constructionwhichsatisfiesthe extended definition Ourcontributions

  21. THANK YOU!

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