Lecture10 – More on Physically Unclonable Functions (PUFs)

Rice ELEC 528/ COMP 538

Farinaz Koushanfar

Spring 2009

Outline

• Implementations on silicon

• Applications– Cryptographic keys– Authentication– Details of RFID applications

• Issues with nonstability

Existing Approaches

Sensors to detect attacks

Expensive

Continually battery-powered

Tamper-Proof Package: IBM 4758

Trusted Platform Module (TPM)

A separate chip (TPM) for security functions

Decrypted “secondary” keys can be read out from the bus

Problem

EEPROM/ROM

ProcessorProbe

• Adversaries can physically extract secret keys from EEPROM while processor is off

• Trusted party must embed and test secret keys in a secure location

• EEPROM adds additional complexity to manufacturing

Storing digital information in a device in a way that is resistant to physical attacks is difficult and expensive.

Our Solution:Physical Random Functions (PUFs)• Generate keys from a complex physical system

• Security Advantage– Keys are generated on demand No non-volatile

secrets– No need to program the secret– Can generate multiple master keys

• What can be hard to predict, but easy to measure?

Physical System

Processor

Challenge (c-bits)

configure

characterize

Response (n-bits) Use as a secret

Can generate many secrets by changing the challenge

Hard to fully characterize or predict

PUF Experiments

• Fabricated 200 “identical” chips with PUFs in TSMC 0.18on 5 different wafer runs

Security

– What is the probability that a challenge produces different responses on two different PUFs?

Reliability

– What is the probability that a PUF output for a challenge changes with temperature?

– With voltage variation?

0 5 10 15 20 25 30 35 400

0.05

0.1

0.15

0.2

0.25

Hamming Distance (# of different bits, out of 100)

Pro

ba

bili

ty D

en

sity

Fu

nct

ion

Measurement NoiseInter-Chip Variation

Inter-Chip Variation• Apply random challenges and observe 100

response bitsMeasurement noise for Chip X = 0.9 bits

Distance between Chip X and Yresponses = 24.8 bits

Can identifyindividual ICs

0 5 10 15 20 25 30 35 400

0.05

0.1

0.15

0.2

0.25

Hamming Distance (# of different bits, out of 100)

Pro

ba

bili

ty D

en

sity

Fu

nct

ion

Measurement NoiseInter-Chip VariationVoltage Variation NoiseTemp Variation Noise

Environmental Variations• What happens if we change voltage and

temperature?

Measurement noise at 125C(baseline at 20C) = 3.5 bits

Measurement noise with 10% voltage variation = 4 bitsEven with environmental variation,

we can still distinguish two different PUFs

Reliable PUFs

PUFn

Challenge

PUFs can be made more secure and reliable by adding extra control logic

c

Response

k

One-WayHash

Function

New Response

• Hash function (SHA-1,MD5) precludes PUF “model-building” attacks since, to obtain PUF output, adversary has to invert a one-way function

SyndromeBCH

Encoding n - k

• Error Correcting Code (ECC) can eliminate the measurement noise without compromising security

BCHDecoding

Syndrome

For calibrationFor Re-generation

Ring-Oscillator (RO) PUF

• The structure relies on delay loops and counters instead of MUX and arbiters

• Better results on FPGA – more stable

RO PUFs (cont’d)

• Easy to duplicate a ring oscillator and make sure the oscillators are identical– Much easier than ensuring the racing paths

with equal path segments

• How many bits can we generate from the scheme in the previous page?– There are N(N-1)/2 distinct pairs, but the

entropy is significantly smaller: log2(N!)– E.g., 35 ROs can produce 133 bits, 128 can

produce 716, and 1024 can produce 8769

Reliability enhancement

• Environmental changes have a large impact on the freq. (and even relative ones)

RO PUFs

• ROs whose frequencies are far are more stable than the ones with closer f’s

• Possible advantage: do not use all pairs, but only the stable ones

• It is easy to watch the distance in the counter and pick the very different ones

• The new question is how many ring oscillators do we need to accomplish having B stable bits?

• What are the other comparative advantages/ disadvantages compared to delay-based PUFs?

• Can we use this structure to generate many challenge-response pairs?

Applications -- Authentication

• Challenges should never be used to prevent the man-in-the-middle attacks

• Is this practical?

Application – Cryptographic Key Generation

• The unstability is a problem• Some crypto protocols (e.g., RSA) require specific

mathematical properties that random numbers generated by PUFs do not have

• How can we use PUFs to generate crypto keys?– Error correction process: initialization and regeneration– There should be a one-way function that can generate the key

from the PUF output

Crypto Key Generation

• Initialization: a PUF output is generated and error correcting code (e.g., BCH) computes the syndrome (public info)

• Regeneration: PUF uses the syndrome from the initial phase to correct changes in the output

• Clearly, the syndrome reveals information about the circuit output and introduces vulnerabilities

Vulnerabilities Caused by ECC

• Given a b-bit syndrome, the attackers can learn at most b-bits about the PUF output

• Thus, to have k secret bits after error correction, we generate n=k+b bits at PUF

• How much area / power overhead do we get for the RO implementation?

Experiments with RO PUFs

• Experiments done on 15 Xilinx Virtex4 LX25 FPGA (90nm)

• They placed 1024 ROs in each FPGA as a 16-by-64 array

• Each RO consisted of 5 INVs and 1 AND, implemented using look-up tables

• The goal is to know if the PUF outputs are unique (for security) and reproducible (for reliability and security)

Reliability and Security Metrics

The Probability Distribution for Inter-chip Variations

• 128 bits are produced from each PUF• x-axis: number of PUF o/p bits different b/w two FPGAs;

y-axis: probability• Purple bars show the results from 105 pair-wise

comparisons• Blue lines show a binomial distribution with fitted

parameters (n=128, p =0.4615)• Average intra-chip variations 0.4615 ~ 0.5

The Probability Distribution for Intra-chip Variations

• PUF o/p are generated at two different conditions and compared

• Changing the temperature from 20C to 120C and the core voltage from 1.2 to 1.08 altered the PUF o/p by ~0.6 bits (0.48%)

• Intra-chip variations is much lower than inter-chip – the PUF o/p did not change fro small to moderate environmental changes

False Positive (FP) and Negative (FN) Experiments

• If we allow up to 10 bits out of 128 to be different, FP rate ~2.1x10-21, and FN rate is less than 5x10-11

• Assumption: inter-chip and intra-chip follow binomial distributions

• The same experiments could be used to compute the reliability of PUF-based crypto keys

Physically Unclonable Function–Based Security and Privacy

in RFID Systems

Leonid Bolotnyy and Gabriel RobinsDept. of Computer Science

University of Virginia

www.cs.virginia.edu/robins

Contribution and MotivationContribution• Privacy-preserving tag identification algorithm• Secure MAC algorithms• Comparison of PUF with digital hash functions

Motivation• Digital crypto implementations require 1000’s of gates• Low-cost alternatives

– Pseudonyms / one-time pads– Low complexity / power hash function designs– Hardware-based solutions

PUF-Based Security

• Physical Unclonable Function (PUF) [Gassend et al 2002]• PUF Security is based on

– wire delays– gate delays– quantum mechanical fluctuations

• PUF characteristics– uniqueness– reliability– unpredictability

• PUF Assumptions– Infeasible to accurately model PUF– Pair-wise PUF output-collision probability is constant– Physical tampering will modify PUF

Privacy in RFID

• Privacy

A B C

Alice was here: A, B, C

privacy

Private Identification Algorithm

• Assumptions– no denial of service attacks (e.g., passive adversaries, DoS

detection/prevention mechanisms)– physical compromise of tags not possible

• It is important to have – a reliable PUF– no loops in PUF chains– no identical PUF outputs

ID

Requestp(ID)

ID

Database

ID1, p(ID1), p2(ID1), …, pk(ID1)

...IDn, pn(IDn), pn

2(IDn), …, pnk(IDn)

Improving Reliability of Responses• Run PUF multiple times for same ID & pick majority

μm(1-μ)N-m )kR(μ, N, k) ≥ (1 - ∑

N Nm

N+12

m=

number of runs

chain lengthunreliabilityprobability

overallreliability

R(0.02, 5, 100) ≥ 0.992

• Create tuples of multi-PUF computed IDs &identify a tag based on at least one valid position value

∞expected numberof identifications

S(μ, q) = ∑ i [(1 – (1-μ)i+1)q - (1 – (1-μ)i)q]i=1

tuple size

S(0.02, 1) = 49, S(0.02, 2) = 73, S(0.02, 3) = 90

(ID1, ID2, ID3)

Privacy Model

1. A passive adversary observes polynomially-many rounds of reader-tag communications with multiple tags

2. An adversary selects 2 tags

3. The reader randomly and privately selects one of the 2 tags and runs one identification round with the selected tag

4. An adversary determines the tag that the reader selected

Experiment:

Definition: The algorithm is privacy-preserving if an adversary can notdetermine reader selected tag with probability substantially greater than ½

Theorem: Given random oracle assumption for PUFs,an adversary has no advantage in the above experiment.

PUF-Based MAC Algorithms

• MAC based on PUF– Motivation: “yoking-proofs”, signing sensor data– large keys (PUF is the key)– cannot support arbitrary messages

• MAC = (K, τ, υ)

K

K

• valid signature σ : υ (M, σ) = 1• forged signature σ’ : υ (M’, σ’) = 1, M = M’

• Assumptions– adversary can adaptively learn poly-many (m, σ) pairs– signature verifiers are off-line– tag can store a counter (to protect against replay attacks)

Large Message Space

σ (m) = c, r1, ..., rn, pc(r1, m), ..., pc(rn, m)

Assumption: tag can generate good random numbers (can be PUF-based)

Signature verification• requires tag’s presence• password-based or in radio-protected environment (Faraday Cage)• learn pc(ri, m), 1 ≤ i ≤ n• verify that the desired fraction of PUF computations is correct

To protect against hardware tampering• authenticate tag before MAC verification• store verification password underneath PUF

Key: PUF

Choosing # of PUF Computations

α < probv ≤ 1 and probf ≤ β ≤ 1

0 ≤ t ≤ n-1

i=t+1

μi(1-μ)n-iprobv(n, t, μ) = 1 - ∑

nni

j=t+1

τj(1-τ)n-jprobf(n, t, τ) = 1 - ∑

nnj

probv(n, 0.1n, 0.02)

probf(n, 0.1n, 0.4)

Theorem

Given random oracle assumption for a PUF, the probability that an adversary could forge a signature for a message is bounded from above by the tag impersonation probability.

Small Message SpaceAssumption: small and known a priori message space

Key[p, mi, c] = c, pc(1)(mi), ..., pc

(n) (mi)

PUFmessage

counter

σ(m) = c, pc(1)(m), ..., pc

(n) (m),

..., c+q-1, pc+q-1

(1)(m), pc+q-1(n)(m)

sub-signature

Verify that the desired number of sub-signatures are valid

PUF reliability is again crucial

Theorem

Given random oracle assumption for a PUF, the probability that an adversary could forge a signature for a message is bounded by the tag impersonation probability times the number of sub-signatures.

Attacks on MAC Protocolsoriginal clone

• Impersonation attacks– manufacture an identical tag– obtain (steal) existing PUFs

• Hardware-tampering attacks– physically probe wires to learn the PUF– physically read-off/alter keys/passwords

• Side-channel attacks– algorithm timing– power consumption

• Modeling attacks– build a PUF model to predict PUF’s outputs

Comparison of PUF With Digital Hash Functions

• Reference PUF: 545 gates for 64-bit input– 6 to 8 gates for each input bit– 33 gates to measure the delay

• Low gate count of PUF has a cost– probabilistic outputs– difficult to characterize analytically– non-unique computation– extra back-end storage

• Different attack target for adversaries– model building rather than key discovery

• Physical security– hard to break tag and remain undetected

MD4

7350

MD5

8400

SHA-256

10868

Yuksel

1701

PUF

545

AES

3400

algorithm

# of gates

PUF Design• Attacks on PUF

– impersonation– modeling– hardware tampering– side-channel

• Weaknesses of existing PUF

• New PUF design– no oscillating circuit– sub-threshold voltage

• Compare different non-linear delay approaches

reliability

Conclusions and Future Work

• Develop theoretical framework for PUF• Design new sub-threshold voltage based PUF• Manufacture and test PUFs

– varying environmental conditions– motion, acceleration, vibration, temperature, noise

• Design new PUF-based security protocols– ownership transfer– recovery from privacy compromise– PUFs on RFID readers

} in progress

• PUF: hardware primitive for RFID security• Identification and MAC algorithms based on PUF• PUFs protect tags from physical attacks• PUFs is the key

Thank You

Questions ?

Leonid Bolotnyylbol@cs.virginia.edu

Dept. of Computer ScienceUniversity of Virginia

PUF-Based Ownership Transfer

• Ownership Transfer

• To maintain privacy we need– ownership privacy– forward privacy

• Physical security is especially important

• Solutions– public key cryptography (expensive)– knowledge of owners sequence– trusted authority– short period of privacy

s2,4

s1,2

s3,9

s2,5

s3,10s3,8

Using PUF to Detect and Restore Privacy of Compromised System

1. Detect potential tag compromise2. Update secrets of affected tags

s1,0

s2,0

s1,1

s2,1

s3,1

s2,2 s2,3

s3,0 s3,4 s3,5s3,2 s3,3 s3,7s3,6