1. Ilya Mironov, Omkant Pandey, Omer Reingold, Gil Segev Microsoft Research

2. Incremental Deterministic Public-Key Encryption

3. Deterministic Public-Key Encryption

5. Deterministic Public-Key Encryption: PRIV1-IND [Bellare, Boldyreva, O’Neill CRYPTO’07] E pk [ ]

6. Is It Secure? Computational assumptions Min-entropy of the source Secure Deterministic Encryption Long, unpredictable plaintext: -digital photograph -MS Word document -entire database -full disk -search -de-duplication -deterministic KEM

7. security efficiency Length of the plaintext

8. Incrementality -Incrementality with access to plaintext: setting bit -Incrementality without access to plaintext: flipping bit

9. Incremental Deterministic Public-Key Encryption

10. Our results  Two schemes 1. Generic Solution 2. DDH-based solution tight up to polylog factors incrementality min-entropy Deterministic Encryption Incremental Deterministic Encryption

11. Naïve Generic Solution min-entropy ? EEE … E: deterministic encryption scheme

12. Sample-then-extract [Nisan,Zuckerman’96][Vadhan’04] min-entropy similar min-entropy rate

13. Generic Solution min-entropy Partition input into random subsets PRIV-IND  PRIV1-IND with Incrementality

14. Standard Model DDH  PRIV1-IND with Incrementality

15. Lossy Trapdoor Functions [Peikert, Waters STOC’08] Injective mode: Lossy mode:

16. Smooth Trapdoor Functions Injective mode: Smooth mode: statistically close

17. Smooth Trapdoor Functions  PRIV1-IND Security injective mode: smooth mode:

18. Construction of PRIV1-IND Lossy Trapdoor FunctionPairwise-independent permutation Smooth Trapdoor Function [Boldyreva, Fehr, O’Neill CRYPTO’08] Deterministic Public-Key Encryption

19. Construction of PRIV1-IND Lossy Trapdoor FunctionPairwise-independent permutation Smooth Trapdoor Function [Boldyreva, Fehr, O’Neill CRYPTO’08] Deterministic Public-Key Encryption Incremental

20. Construction of Lossy TDF [Freeman, Goldreich, Kiltz, Rosen, Segev PKC’10] [Brakerski, Segev CRYPTO’11] Key generation Encryption Decryption

21. Security Argument: Lossy TDF rank 1

22. Towards Incremental Smooth TDF rank ℓ sparse

23. Towards Incremental Smooth TDF  Sample-then-extract + Leftover Hash Lemma

24. Towards Incremental Smooth TDF 

25. 

26. Smooth vs Injective Mode full rank

27. Incrementality 

28. Open Problems Incremental Deterministic Encryption:  Stronger security: PRIV-IND (multiple messages)  Length-preserving in the standard model Deterministic Encryption:  Relaxing the definition to allow dependency on the public key