A Brief Story of - PowerPoint Presentation

Slide1

A Brief Story of Computing on Private Data

Ten H Lai

Ohio State UniversitySlide2

AgendaComputing on private dataFully

homomorphic

encryption

(FHE)

Gentry’s bootstrapping theorem

Our resultSlide3

FHE: The Holy Grail of CryptographySlide4

Cloud Computing

Servers

Storages

Networks

ApplicationsSlide5

天上有多少星星

城裡有多少姑娘

但人間只有一個妳

天上只有一顆月亮Slide6

Cloud Computing

6

Cloud

server

Internet

EncryptSlide7

Computing on private data

7

Cloud

server

Internet

EncryptSlide8

Computing on private

data

Cloud

8

A question proposed by

Rivest

,

Aldeman

,

Dertouzos

in 1978 (one year after RSA was invented). Slide9

C-HomomorphismSlide10

C

-homomorphicSlide11

RSA is multiplicatively homomorphicSlide12

Fully

Homomorphic

Encryption (FHE)Slide13
Slide14
Slide15

15Slide16

16Slide17

17Slide18

18

BootstrappingSlide19

19

m

m

sk

A

Decrypt

m

encrypted under a pink key

pk

A

Evaluate

Decrypt

mSlide20

m

m

sk

A

m

sk

A

m

Decrypt

Evaluate

Decrypt

20

Encrypt under a blue key

pk

B

Evaluate

DecryptSlide21

Decrypt

Decrypt

sk

A

sk

A

NAND

m

1

NAND

m

2

NAND-augmented Decrypt circuit:

21

m

1

m

2Slide22

Decrypt

Decrypt

sk

A

c

1

sk

A

c

2

NAND

m

1

NAND

m

2

Evaluate

22

fresh

m

1

m

2Slide23

23

m

1

NAND

m

2

23

fresh

m

1

m

2

sk

A

Under a pink key

PK

A

Under a blue key

PK

BSlide24

24

24

m

1

m

2

m

1

NAND

m

2

Increased noiseSlide25

25Slide26

sk

A

m

1

m

2

m

1

NAND

m

2

Evaluate

Decrypt-NAND

sk

A

m

3

m

4

m

3

NAND

m

4

Evaluate

Decrypt-NAND

m

1

NAND

m

2

m

3

NAND

m

4

Evaluate

Decrypt-NAND

sk

B

(m

1

NAND

m

2

)

NAND

(m

3

NAND

m

4

)

26Slide27

sk

A

m

1

m

2

m

1

NAND

m

2

Evaluate

Decrypt-NAND

sk

A

m

3

m

4

m

3

NAND

m

4

Evaluate

Decrypt-NAND

m

1

NAND

m

2

m

3

NAND

m

4

Evaluate

Decrypt-NAND

sk

B

(m

1

NAND

m

2

)

NAND

(m

3

NAND

m

4

)

27Slide28

28

Decrypt

Decrypt

NANDSlide29

29Slide30

30

Encryption key

Decryption key

Evaluation keySlide31

31

Decrypt

DecryptSlide32

32Slide33

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Encryption key

Decryption key

Evaluation keySlide34

34Slide35

35Slide36

…

level d level 1

36Slide37

…

Decrypt circuits

level

d

level 1

37Slide38

Decrypt circuits

…

38Slide39

39Slide40

40Slide41

41

Encryption key

Decryption key

Evaluation keySlide42

42Slide43

43Slide44

44

Decrypt

Decrypt

NANDSlide45

45Slide46

46

Secret-key independent ,

Computationally intensive,

Done with encryption

Secret-key

dependent

Decryption algorithmSlide47

47Slide48

48

FHE is still in its infantrySlide49

Multi-Key/Multi-Scheme FHESlide50

Single-key FHE

50Slide51

Is Multi-key

FHE Possible?

51Slide52

Is Multi-scheme

FHE Possible?

52Slide53

53Slide54

54Slide55

55Slide56

56Slide57

Evaluate circuit

C

Evaluate(

C

)

ProblemSlide58

Eval

(

C

)

If under

pk

1

CSlide59

Eval

(

C

)

Eval

(

Eval

(

C

)

)

Under

pk

2

CSlide60

Evaluate(

C

)

?

CSlide61

?Slide62

62Slide63

Trivial encryptionsSlide64

Eval

(

C

)

Eval

(

Eval

(

C

)

)

Summary

of ideas

CSlide65

65

CSlide66
Slide67
Slide68
Slide69

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