Two-fet based PUF

A Simple and Reliable Cell for Single Bit

Physically Unclonable Constants

Riccardo Bernardini and Roberto Rinaldo

DIEG–University of Udine

{riccardo.bernadini, rinaldo}@uniud.it

Extended journal version:

http://ieeexplore.ieee.org/document/7539631/

https://doi.org/10.1109/TIFS.2016.2599008

February 1, 2017

http://ieeexplore.ieee.org/document/7539631/

https://doi.org/10.1109/TIFS.2016.2599008

A Simple and Reliable Cell for Single Bit Physically Unclonable Constants

Outline

• Motivation and Introduction

– An example: SRAM

– Double randomness and reliability

• Our proposal

– Description

– Analytic results

– Simulation results

• Conclusions & the Future

1

DIEGM University of Udine


Motivation

So, tell me,what is a PUC?

A Physically UnclonableConstant, a secret word, impossible to reproduceeven for the chip maker

What is used for? Chip authentication,

private keys,stuff like that…

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Motivation

Wouldn't a NVM suffice?

No, the secret word mustexist only when the chipis "alive"…

To avoid "offline"attacks, you see…Hmm… I see.

How do you that?By exploitingconstruction-timerandom variationsLet me use an example…

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An example: SRAM

It is an SRAM! Yes, just readit without initializing it…

But you'll get a random value!

Well… Yes and no…

V1(t)V2(t)

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An example: SRAM

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

10

x

1

V1

(V)

V2

(V)

V1(t)V2(t)

The cell will neverbe exactly symmetric,so there will be a preferred outcome

How much"preferred"depends onthe cell symmetry

noiseless

noisy

noise

5



Double randomness

DeviceProduction

Device

Measurement StabilizerRawdata

Key

Building-timerandomness

Run-timerandomness

Off-line On-line

The bit you read isa random variablewhose "randomness"is selected at production time

Like drawing a coinfrom a bag and then throwing the coin..

Exactly! And we want thecoins in the bag as unfairas possible…

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Double randomness and stabilizers

DeviceProduction

Device

MeasurementRawdata

Key

Building-timerandomness

Run-timerandomness

Off-line On-line

S0, an ideal PUC is a random constant. What ifis it not "really" constant?

We use a stabilizer. Manysolutions are possible, but, basically you use some "redundance" to correct the "wrong" bits.Let me guess:

"fair coins" == expensive stabilizers

Right!

Stabilizer

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Measuring reliabilityCan we get a quantitative measure of the "quality" of the "bag"?

Yes, by looking at thedistribution of the reliability.

This is the caseof SRAM [1]

[1] R. Maes et al., “A soft decision helper data algorithm for SRAM PUFs,” ISIT 2009.

0.15 0.5 1.010

−4

10−3

10−2

10−1

100

Reliability = 2 | p(T)-1/2 |

F r

p(T) = 1 or 0(random constant)

p(T) = p(F) = 0.5(fair coin)

p(T) = 0.5 ± 0.075

Ideal

Curve

SRAM

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What is wrong with SRAM?

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

10

x

1

You see, the problem isthat the SRAM has twostable states. This is finefor a memory, but it makes an unreliable PUC.

You want something more similar to a balance: a single equilibrium point that depends on the asymmetry

Right

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Our proposal

Q1

Q2

C IcI1

I2+-

Vc

Vraw

V0

V0

This is our idea…

Cool, how does it work?

Transistors Q1 and Q2are nominally matched,so that nominally |VT1| = |VT2|, ϐ1 = ϐ2, I1 = I2 and Ic=0

So, nominally, Vraw = V0 for ever…But Q1 and Q2 willnot be exactly matched

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Our proposal: qualitative analysis

Q1

Q2

C Ic

I1

I2+-

Vc

Vraw

V0

V0

Right! We are exactlygoing to exploit this!

Right, suppose now that Q2 conductsa bit more so thatIc < 0 and Vc decreases…

Vc=0, so Q1 and Q2 are in saturation…

I 2

VDS2

V0t=0

… and VDS2 decreases…

I1 Ic

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Q1

Q2

C Ic

I1

I2+-

Vc

Vraw

V0

V0

As long as VDS2 is large enough nothingchanges: Q2 remainsin saturation Ic remains constant and Vc decreases linearlywith time…

I 2

VDS2

t=t1

…until VDS2 reaches V0+VT2

VDS2(t1)

I1 Ic

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Q1

Q2

C Ic

I1

I2+-

Vc

Vraw

V0

V0

Exactly! At that timeQ2 enters the trioderegion and I2 gets smaller. MeanwhileQ1 remains in saturation,so I1 does not change

I 2

VDS2

t=t2

Therefore, Ic gets smallerand the charging slows down…

VDS2(t2)

I1 Ic

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Q1

Q2

C Ic=0

I1

I2+-

Vc

Vraw

V0

V0

…until the process endswhen I2=I1. At thattime Ic=0 and the equilibrium (stable)is reached.

I 2

VDS2

t=∞

Cool, since at eq. Q2 must bein triode region, Vraw cannot be in the shadowed area.

VDS2(∞)

I1

VT

Discontinuous

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Our proposal: theoretical analysis

Nice, but can you be more analytic?

−2 −1 0 1 2−2

−1.5

−1

−0.5

0

0.5

1

1.5

2x 10

−5

Perfect Match

I c(A

)

Vc

(V)

Q1 stronger

Q2 stronger

dVc/dt ∝ Ic

Q2 slightly stronger

Negative slope ⇒

Stable equilibrium

Sure, justcheck thisfigure

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Variations

What do wehave here? Q1

Q2

C

+-

Vc

V0

V0

Q1

Q2

C

+-

Vc

V0

V0

Two variations of thebasic scheme: the topscheme "forces" theoutput of the cellto VH/VL

In the bottomscheme the SRAMcell stores theresult, so that the PUC can beturned off

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Simulations

10 000 Random variations

VTi ∼ N(V T,nom, σ2Vi) σ2Vi = Kv

Li Wi

[2]

βi ∼ N(βnom, σ2βi) σ2β= βnom Kβ

Li Wi[2]

[2] P. Kinget, “Device mismatch and tradeoffs in the design of analog circuits,” IEEE Journal of Solid-State Circuits, June 2005

Sample at time t=ton + 0.5 ms

We also runsome simulationsby randomly changing theparameters

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Simulation results

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120

Vraw

(V)

# O

ccur

ence

s

Temperature = 25 ° C

0 0.5 1 1.5 2 2.5 30

500

1000

1500

2000

2500

3000

Vout

(V)#

Occ

uren

ces

Temperature = 25 ° C, Prob(1)=0.4988

Prob ≈ 0.5-1.2 ⋅ 10-3

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Simulation results

0 0.5 1 1.5 2 2.5 30

20

40

60

80

100

120

Vraw

(V)

# O

ccur

ence

s

Temperature = 0 ° C

0 0.5 1 1.5 2 2.5 30

500

1000

1500

2000

2500

3000

Vout

(V)#

Occ

uren

ces

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Simulation results

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Simulation results

0 0.2 0.4 0.6 0.8 1 1.2 1.410

−4

10−3

10−2

10−1

100

Reliability (R)

F r

Proposed 25° CProposed −30° CSRAM

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Conclusions

• A very simple cell for binary PUC has been proposed

• Theoretical analysis and simulations show that

– The cell is unbiased

– The cell is very reliable, pratically ideal

– The cell works on a very large range of temperatures

• Stabilizer may be unnecessary

• Future directions

– Understanding the “eye closing”

– Experimental results on a prototype

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Two-fet based PUF

Engineering

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