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QCrypt 2018: On the possibility of classical client blind quantum - - PowerPoint PPT Presentation

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Motivations QFactory Security QCrypt 2018: On the possibility of classical client blind quantum computing Alexandru Cojocaru, L eo Colisson, Elham Kashefi, Petros Wallden August 30, 2018 A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

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SLIDE 1

Motivations QFactory Security

QCrypt 2018: On the possibility of classical client blind quantum computing

Alexandru Cojocaru, L´ eo Colisson, Elham Kashefi, Petros Wallden August 30, 2018

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 1 / 15

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SLIDE 2

Motivations QFactory Security Main Goal UBQC in a nutshell

Robin Hood

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 2 / 15

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SLIDE 3

Motivations QFactory Security Main Goal UBQC in a nutshell

Main Goal

N =?×?

10011 11010

Figure: (Blind) Quantum Computing

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 3 / 15

slide-4
SLIDE 4

Motivations QFactory Security Main Goal UBQC in a nutshell

Main Goal

N =?×?

p, q

Figure: (Blind) Quantum Computing

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 3 / 15

slide-5
SLIDE 5

Motivations QFactory Security Main Goal UBQC in a nutshell

Main Goal

N =?×?

p, q

Figure: (Blind) Quantum Computing

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 3 / 15

slide-6
SLIDE 6

Motivations QFactory Security Main Goal UBQC in a nutshell

Main Goal

N =?×?

10011

Figure: (Blind) Quantum Computing

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 3 / 15

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SLIDE 7

Motivations QFactory Security Main Goal UBQC in a nutshell

Main Goal

N =?×?

10011

?

Figure: (Blind) Quantum Computing

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 3 / 15

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SLIDE 8

Motivations QFactory Security Main Goal UBQC in a nutshell

Our solution

Universal Blind Quantum Computing (UBQC) [A. Broadbent, J. Fitzsimons, E. Kashefi]

+

QFactory

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 4 / 15

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SLIDE 9

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC UA UB UC

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 10

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 11

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 12

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 13

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 14

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 15

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 16

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 17

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 18

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

slide-19
SLIDE 19

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 20

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 21

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

UA UB UC = |+

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 5 / 15

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SLIDE 22

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 23

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 24

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 25

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 26

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 27

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 28

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 29

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 30

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 31

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 32

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 33

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 34

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 35

Motivations QFactory Security Main Goal UBQC in a nutshell

UBQC in a nutshell

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 6 / 15

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SLIDE 36

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

QFactory: description

10011

Figure: QFactory gadget: simulate quantum channel

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 7 / 15

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SLIDE 37

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

QFactory: description

10011

QFactory

01101

Figure: QFactory gadget: simulate quantum channel

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 7 / 15

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SLIDE 38

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

QFactory: description

QFactory θ $ ← − {0, π

4 , . . . , 7π 4 }

θ |+θ Figure: QFactory: ideal functionality

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 8 / 15

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SLIDE 39

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Cryptographic assumptions

Functions {fk} One-way

This function is hard to invert. . .

Trapdoor

. . . except if you have the trapdoor tk associated to the function index k.

Collision resistant

Without trapdoor tk, hard to find x = x′ such that fk(x) = fk(x′)

2-Regular

2 preimages for all elements in Im(fk)

y x x′

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 9 / 15

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SLIDE 40

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Cryptographic assumptions

Functions {fk} One-way

This function is hard to invert. . .

Trapdoor

. . . except if you have the trapdoor tk associated to the function index k.

Collision resistant

Without trapdoor tk, hard to find x = x′ such that fk(x) = fk(x′)

2-Regular

2 preimages for all elements in Im(fk)

y x x′

⇒ Candidate based on [MP11]

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 9 / 15

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SLIDE 41

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 42

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 43

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 44

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi)

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 45

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 46

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 47

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m⇒

x |x|0⊗m

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-48
SLIDE 48

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-49
SLIDE 49

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 50

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 51

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

|0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 52

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

⇒ Produces |+θ |0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-53
SLIDE 53

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

⇒ Produces |+θ y, (bi) |0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-54
SLIDE 54

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

⇒ Produces |+θ y, (bi) (x, x′) := Inv(tk, y) |0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-55
SLIDE 55

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

⇒ Produces |+θ y, (bi) (x, x′) := Inv(tk, y) θ := (−1)xn n−1

i=1 (xi − x′ i)(biπ + αi)

|0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

slide-56
SLIDE 56

Motivations QFactory Security Description of the QFactory gadget Cryptographic assumptions Construction

Construction

tk, k (αi

$

← − {0, π

4 . . . 7π 4 })n−1 i=1

k, (αi) Compute circuit |0 |0 |0 |0 |0 . . . . . . n m . . . . . . H H H Ufk . . . ⇒ y

α1

. . .

αn−1

b1 bn−1

⇒ Produces |+θ y, (bi) (x, x′) := Inv(tk, y) θ := (−1)xn n−1

i=1 (xi − x′ i)(biπ + αi)

⇒ Gets θ |0⊗n|0⊗m⇒

x |x|0⊗m⇒ x |x|fk(x)= y(|x + |x′) ⊗ |y⇒ (|x + |x′) ⊗ |y⇒ ( i |bi) ⊗ |+θ ⊗ |y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 10 / 15

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SLIDE 57

Motivations QFactory Security Hardcore function and Honest-but-curious model Intuition of proof

Hardcore function and Honest-but-curious model

Adversary

k, y, (αi), (bi)

θ′

?

= θ Cannot be better than random guess: θ hard-core function. Security Blindness of the output θ. Corollary: QFactory is secure in the honest-but-curious model. If adversary: follows the protocol can only access classical registers ⇒ he cannot determine θ

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 11 / 15

slide-58
SLIDE 58

Motivations QFactory Security Hardcore function and Honest-but-curious model Intuition of proof

Intuition of proof

θ is a hardcore function: proof based on Goldreich-Levin Theorem: Theorem If f is a one-way function, then the predicate hc(x, r) = xiri mod 2 cannot be distinguished from a random bit, given r and f(x). Recall, in our case: f(x) ≈ y and θ ≈

  • (xi − x′

i)

ÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜ

Unknown to server

(4bi + αi) ÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜ

Known to server

mod 8

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 12 / 15

slide-59
SLIDE 59

Motivations QFactory Security

Summary and future work

Summary QFactory: simulate quantum channel from classical channel

✭✭✭✭✭✭✭ ✭ ❤❤❤❤❤❤❤ ❤

quantum client → classical clients For now, proof in honest-but-curious model Future work Improve proof of security in Universal Composability model Improve efficiency in blind computing Explore new possible applications, certified qubits (QFactory + Zero Knowledge proof) that could improve MPC, GHZ

  • state. . . . . .
  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 13 / 15

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SLIDE 60

Motivations QFactory Security

Applications of QFactory

Simulate quantum channel

Delegated computing

Blind Verifiable

Multi-Party Computing Quantum money Quantum signature Key dis- tribution Certified qubit ???

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 14 / 15

slide-61
SLIDE 61

Motivations QFactory Security

Questions

Thank you for your attention! arxiv.org/abs/1802.08759

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 15 / 15

slide-62
SLIDE 62

Motivations QFactory Security

Function construction

As0 e As1 e

1

A s2 e2

fA,y((s, e), c) = Ax + e + c × y

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 15 / 15

slide-63
SLIDE 63

Motivations QFactory Security

Comparison with other works

Paper

Classical Homo- morphic Encryption for Quantum Circuits On the possibility

  • f

blind quantum computing Classical Verifica- tion

  • f

Quantum Computations

Blind input Blind algorithm Verifiability Non-Interactive Efficiency/Requirements FHE UBQC/VBQC, Linear Post-hoc, poly degree 9?

  • A. Cojocaru, L. Colisson, E. Kashefi, P. Wallden

QFactory and classical blind quantum computing 15 / 15