Lecture 3: Power Analysis

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Lecture 3: Power Analysis

Information Security – Theory vs. Reality

0368-4474-01, Winter 2011

Guest Lecturer: Yossi Oren

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Required Reading

http://www.dpabook.orghttp://www.springerlink.com/content/g01q1k

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Fundamentals

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Fundamentals

AES Circuit Design Statistics Introduction to Power Analysis

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The AES Cipher

Plaintext Ciphertext

Key

AES

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The AES Cipher (2)

Source: http://www.moserware.com/2009/09/stick-figure-guide-to-advanced.html

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The AES Cipher (3)void RijndaelEncrypt( u8 input[16], u8 output[16] )

{[…] for (r=1; r<=9; r++) { ByteSub(state); ShiftRow(state); MixColumn(state); KeyAdd(state, roundKeys, r); }[…]

Source: http://users.ece.utexas.edu/~gerstl/ee382v-ics_f09/soc/tutorials/System_C_Code_Examples_2/date04_examples/cosimulate/sw_only/

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Statistics 101

⇐ Low Variance

High ⇒ Variance

⇐ Low Correlati

on

High ⇒ Correlati

on

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PowerVib

ratio n

Timing

Soun

dHeatEM

Side Channel Attacks

Plaintext Ciphertext

Radiation

Crypto Device

KeyBad Inputs Errors

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Theory of power analysis

Power consumption is variable Power consumption depends on

instruction Power consumption depends on

data

q

Power consumption

Vdd

GND

a q

A

P1C1

C2N1

The power consumption of a CMOS gate depends on the data:

q: 0->0 virtually no power cons.q: 1->1 virtually no power cons.

q: 0->1 high power cons. (proportional to C2) q: 1->0 high power cons. (proportional to C1)

Power Consumption is Variable?

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Power Consumption is Variable!

Source: DPA Book

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Power Depends on Instruction

Source: DPA Book

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Power Depends on Data

Source: DPA Book

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Q&A (Fundamentals)

•AES•Circuit Design•Statistics

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Correlation Power Analysis (CPA)

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Correlation Power Analysis Simple Power Analysis Warm-up Correlation Power Analysis Full Correlation Power Analysis

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Power Analysis Attack Scenario Plaintexts and ciphertexts may be

chosen, known or unknown

Power

Plaintexts CiphertextsCrypto Device

Key

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Theory of power analysis

Power consumption is variable Power consumption depends on

instruction Power consumption depends on

data

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Simple Power Analysis (SPA)

Pros: Small amount of traces

Cons: Detailed reverse engineering Long manual part

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Differential Power Analysis (DPA) Use statistical properties of traces to

recover key Pros:

Very limited reverse engineering Harder to confuse

Cons: Large amount of traces

Two main types of DPA: Difference of means (traditional DPA) Correlation power analysis (CPA)

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CPA Basics

We want to discover the correct key value (ck) and when it is used (ct)

Idea: On the correct time, the power

consumption of all traces is correlated with the correct key

On other times and other keys the traces should show low correlation

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Warm-up CPA

Assume plaintext and correct key are known but correct time is unknown

Form hypothesis and test it Good hypothesis:

Depends on known plaintext Depends on small amount of key bits Non-linear – sensitive to small

changes Maps to power consumption using a

model

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Warm-up CPA in Numbers1000 traces, each consisting of 1

million points Each trace uses a different known

plaintext – 1000 plaintexts1 known key Hypothesis is vector of 1000

hypothetical power values Output of warm-up CPA: vector of 1

million correlation values with peak at ct

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Warm-up CPA in Pictures

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Full CPA

Plaintext is known, but correct key and correct time unknown

Idea: run warm-up CPA many times in parallel

Create many competing hypotheses

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Full CPA in Numbers

1000 traces, each consisting of 1 million points

Each trace uses a different known plaintext – 1000 plaintexts

Key is unknown – 256 guesses for first byte

Hypothesis is matrix of 1000X256 hypothetical power values

Output of full CPA: matrix of 1,000,000X256 correlation values with peak at (ck,ct)

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Full CPA in Pictures

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Q&A (CPA)

•Simple Power Analysis•Warm-up Correlation Power Analysis•Full Correlation Power Analysis