Advances in Functional Encryption for Secure Data Handling

Explore the evolution from Cryptomania to Obfustopia through Secret-Key Functional Encryption, Public-Key Encryption, and the power of Secret-Key Functional Encryption. Discover the significance of different encryption schemes such as Public-Key Functional Encryption, Secret-Key Functional Encryption, and more in ensuring data security and privacy.

• Functional Encryption
• Data Security
• Cryptography
• Encryption Schemes

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1. From Cryptomania to Obfustopia through Secret-Key Functional Encryption Nir Bitansky Ryo Nishimaki Alain Passel gue Daniel Wichs (MIT) (NTT) (ENS) (NEU)

2. public-key encryption ?????? ??????(?) ?? ? 1/19

3. functional encryption [SW 05] ?????? ? ?????(?) ??? ??? ?(?) ?(?) = 1/19

4. secret-key functional encryption [SW 05] ?????? ??????(?) ??? ??? ?(?) ?(?) = - FE:????(???) independent of ? ,#??? - weak FE: grows with either or both 1/19

5. the power of secret-key functional encryption 2/19

6. minicrypt cryptomania obfustopia weak PKFE, restricted PKFE weak SKFE PKFE [AJ 15] [BV 15] [GPSZ 16] [SS 10] [GVW 12] [SS 10] [GPSW 06] ... ? ? ? SKFE 3/19

7. minicrypt cryptomania obfustopia weak PKFE, restricted PKFE weak SKFE PKFE [AJ 15] [BV 15] [GPSZ 16] [SS 10] [GVW 12] [SS 10] [GPSW 06] ... evidences [AS 15] constructions SKFE 3/19

8. this work iO [AJ 15] [BV 15] [GPSZ 16] public-key functional encryption (plain) secret-key + public-key encryption functional encryption 4/19

9. 5/19

10. ? 6/19

11. its all about the size [BV15], [AJ15], [LPST16], [Lin16] ? compression, compression, compression... 7/19

12. exponentially-efficient iO (XiO) [LPST 16] ?(0?) ?(1?) XiO ? ? 2? 1 ? ? = poly ? for any ? = (1), XiO + LWE PKFE 8/19

13. exponentially-efficient iO (XiO) [LPST 16] ?(0?) ?(1?) XiO ? ? 2? 1 ? ? = poly ? for any ? = (1), XiO + LWE PKFE 8 /19

14. for any ? = (1), XiO + LWE PKFE 1-key succinct PKFE for Boolean functions [GKPVZ 13] 1-key sublinear PKFE for ?/???? [AJ 15],[BV 15] ? ? = ? ?1 ? ? ??? ?????(?) ?1 ? 9 /19

15. Boolean function ?????? ? ?? ?????(?,?) |???| = |?| 9 /19

16. Boolean function ?????? ? ?? ???[?] ? ??????,? |???| XiO ???1 ?= ?1 ? security follows immediately from that PKFE for Boolean functions and XiO via standard hybrid gymnastic... 9 /19

17. two steps [LPST 16] PKFE from XiO + LWE step 1: XiO from SKFE corollary: PKFE from SKFE and LWE 10 /19

18. two steps [LPST 16] PKFE from XiO + LWE step 1: XiO from SKFE step 2: (plain) PKE instead of LWE main result: corollary: PKFE from SKFE and (plain) PKE PKFE from SKFE and LWE 10 /19

19. XiO from SKFE ?: 0,1? {0,1} ?: 0,1?/2 0,1?/2 {0,1} ? ? ?(?||?) 2?/2 ?(?) 11 /19

20. XiO from SKFE ?: 0,1?/2 0,1?/2 {0,1} ? ?????(?) overall size: 2?/2 ???? ? ???( ||?) ? ?(?||?) 11/19

21. XiO from SKFE ?: 0,1?/2 0,1?/2 {0,1} ?????(?) ?????(?(?||.)) ?????(? (?||.)) ? ? overall size: 2?/2 ???? ? ???( ||?) ???? ?(?||?) ? (?| ? = ?(?||?) ??? = ?(?) 11 /19

22. two steps [LPST 16] LWE PKFE from XiO + LWE 1-key succinct PKFE for Boolean functions [GKPVZ 13] step 1: XiO from SKFE corollary: PKFE from SKFE and LWE 12/19

23. two steps [LPST 16] LWE PKFE from XiO + LWE step 2: 1-key succinct PKFE for Boolean functions 1-key succinct PKFE for Boolean functions [GKPVZ 13] from XiO and (plain) PKE step 1: XiO from SKFE corollary: main result: PKFE from SKFE and LWE PKFE from SKFE and (plain) PKE 12 /19

24. construction [SS 10] less weak PKFE weak PKFE from PKE XiO ?1 ? ????(1) ???? ??? |?| sufficient [AJ 15],[BV 15] 13/19

25. ? ?(?) ? ? 14 /19

26. ? ?(?) ? ? ?? ? 14 /19

27. ?????(?) ??? 0??1 0?1 0?2 1 1 ??1 ?1 ?1 ?2 ??1 0??2 ?2 1 1 ??2 ??2 ~ ? = ? ? ?? ?? 0?? 1 ?? ???0???1 ?? ??? encrypted labels ?? 14 /19

28. ?????(?) input garbler ??? circuit garbler 0??1 0?1 0?2 1 1 ??1 ?1 ?1 ?2 ??1 0??2 ?2 1 1 ??2 ??2 ~ ? = ? ?? 0?? 1 ?? ???0???1 ?? ??? encrypted labels ?? garbled circuits are decomposable! 14 /19

29. input garbler circuit garbler 0??1 0?1 0?2 1 1 ??1 ?1 ?2 XiO 0??2 1 1 ??2 ~ ?~ ?? ?? ? ?? ? ?,? ?? ?? 0?? 1 ?? ?? ???0???1 encrypted labels ?? garbled circuits are decomposable! 14 /19

30. input garbler circuit garbler 0??1 1 ??1 XiO 0??2 1 ?? ??2 ? (?,?) ??? ?~ ? ?? ?? ? ?,? ?? ?? ?? ?? ???0???1 encrypted labels ?? garbled circuits are decomposable! 14 /19

31. ?????(?) ??? what about security? ?1 ? if good enough XiO built from ?(1)-input SKFE (obtained from 1-input SKFE via [BKS 16]) ? 2?/? ? = ?(1) 1-input SKFE 2-input SKFE 2?/2 ??? 2?/3 ??? 15 /19 2?/3 ??? 2?/2 ???

32. ?????(?) ?????(? ) ? ??? ??? ? ? = ?(? ) to rely on XiO security: need ???? have ???? ? ??? ? ? ? ??? ? ? ? want to rely on indistinguishability of decomposable GC 16 /19

33. problem: compressing garbled circuit hybrids related: succinct randomized encodings compress to ????? (or ???? ) [BGLPT 15] too much: ???? |?| ?? |?| other SREs [KLW 15, CH 16, ] not with XIO solution: strategy from adaptive garbled circuits compress to ???? ?????? [HJOSW 16] 17 /19

34. two steps step 2: 1-key succinct PKFE for Boolean functions from XiO and (plain) PKE step 1: XiO from SKFE main result: PKFE from SKFE and (plain) PKE 18 /19

35. on removing PKE negative result: [AS 15] - no black-box construction from SKFE to PKE - even assuming subexponential SKFE... positive result: [this work] - PKE from subexponential SKFE and OWF - only quasi-polynomially secure... (not enough for iO) - non-black box transform [BKS 16] 19 /19

36. thank you!