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Dual System Encryption: Realizing IBE and HIBE from Simple Assumptions

Dual System Encryption: Realizing IBE and HIBE from Simple Assumptions. Brent Waters. Identity-Based Encryption [S84,BF01,C01]. MSK. Public Params. ID. ID’. Authority. Decrypt iff ID’ = ID. 2. IBE Security [BF01]. Public Params. ID Q. ID 1. ID 1. ID Q. Challenger. Attacker. ….

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Dual System Encryption: Realizing IBE and HIBE from Simple Assumptions

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  1. Dual System Encryption:Realizing IBE and HIBE from Simple Assumptions Brent Waters

  2. Identity-Based Encryption [S84,BF01,C01] MSK Public Params ID ID’ Authority Decrypt iff ID’ = ID 2

  3. IBE Security [BF01] Public Params IDQ ID1 ID1 IDQ Challenger Attacker … M0, M1, ID* IDi(challenge ID) b Enc(Mb , PP, ID*) b’ Adv = Pr[b’=b] -1/2

  4. IBE Security Proofs ID Space Priv. Key Space • 2 Goals: • Answer Attacker Queries • Use Attacker Response • “Partitioning” [BF01, C01, CHK03, BB04, W05] Attacker Simulator Challenge Space

  5. Partitioning and Aborts ID Space Priv. Key Space Challenge Space Abort and try again ID1 ID2… … IDQ ID*(challenge ID) Simulator Attacker 

  6. Finding a Balance ID Space Priv. Key Space • Aborts effect security loss • Challenge Space -> “right size” • C.S. = 1/Q (for Q queries ) => 1/Q no abort Simulator Challenge Space

  7. Structure gives problems! • Hierarchical IBE • Q queries per HIBE level => (1/Q)depth loss • Attribute-Based Encryption similar Partitioning won’t work! :gov :edu

  8. The Gentry Approach [G06,GH09] • Ready for both • Shove degree Q poly into Short params => Complex Assumption

  9. Our Results • IBE (w/ short parameters) • HIBE • Broadcast Encryption • Full Security • Simple Assumption: Decision Linear Given: g, u, v, ga , ub, Dist: va+b from R

  10. Dual System Encryption ID ID ID ID • 2 types of Keys & CTs Normal Used in real system Semi-Functional   Normal  Semi-Functional • Types are indist. (with a caveat)

  11. Principles • No aborts I’m ready for anything! Simulator • Change things slowly • Hybrid over keys form • Goal: Everything Semi Functional

  12. Proof Overview – 3 Steps ID1 ID2 IDQ ID1 ID2 IDQ ID* ID Challenge CT  Semi Func. Keys  Semi. Func. (one at a time!!) Argue Security Simulator …

  13. Problem: Simulator can test keys! ? • Create S.F. CT for “Bob” and unknown key for “Bob” • Decryption works iff key is normal Simulator “Bob” “Bob”

  14. Resolution: Tweak Semantics • Add “tags” tc , tk to C.T. and Key • Decrypt iff IDc = IDkAND tc tk • Negl. correctness error (can patch) • SW08 revocation IDc , tc IDK , tK

  15. Problem: Simulator can test keys! ? • Sim. Picks A, B 2 Zp : F(ID) = A ¢ ID + B • Challenge CT and unknown key tags  F(ID) Simulator “Bob” , tk =x “Bob” , tc =x • Dec. Fails regardless of Semi Functionality! • 2 different IDs look independent • Hybrid  simple assumption

  16. How it is built p1 p2 p3 ID ID ID ID • Subgroup version N= p1 p2 p3 Normal S.F. Normal S.F.

  17. Glimpse of Subgroup Construction Setup: KeyGen(ID): Encrypt(ID,M): • Similarities to Boneh-Boyen04 • D. Linear same concepts, more messy

  18. Conclusions and Speculation • Dual Encryption: Change Forms First! • One by one  Small Assumptions • HIBE, B.E. became easier • Prediction: ABE + Functional Enc. • Need new techniques • Prediction: Simple Assumptions & Full Security

  19. Dual Interpretation Interpretation 1: Selective Security + Assumptions were bad • Not ultimately necessary Alternative: They lead us in the right directions • Full secure schemes “look like” selective • Gentry06 beyond partitioning

  20. Thank you 20

  21. The Gentry Approach [G06,GH09] • Ready for both • Simulator 1-key per identity – always looks good • Shove degree Q poly into Short params => Complex Assumption

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