Eff Efficient Entr icient Entropy opy Est Estimation imation for - - PowerPoint PPT Presentation

▶
eff efficient entr icient entropy opy est estimation
SMART_READER_LITE
LIVE PREVIEW

Eff Efficient Entr icient Entropy opy Est Estimation imation for - - PowerPoint PPT Presentation

Mar 23, 2024 603 likes •873 views

Efficient entropy estimation for MIA using B-splines Eff Efficient Entr icient Entropy opy Est Estimation imation for for Mutua Mutual l Information Information Analys Analysis is using using B-splines splines Alexandre VENELLI IML

slide-1
SLIDE 1

Efficient entropy estimation for MIA using B-splines

Eff Efficient Entr icient Entropy

  • py Est

Estimation imation for for Mutua Mutual l Information Information Analys Analysis is using using B-splines splines

Alexandre VENELLI

ATMEL Secure Microcontroller Solutions Rousset, FRANCE IML – ERISCS Université de la Méditerranée Marseille, FRANCE

slide-2
SLIDE 2

Efficient entropy estimation for MIA using B-splines

Outl Outline ine

 Differential side-channel attacks – Power analysis  Mutual Information Analysis  Proposed B-splines estimation technique  Experimental results  Conclusion

2 WISTP 2010

slide-3
SLIDE 3

Efficient entropy estimation for MIA using B-splines

Di Differen fferenti tial al side side-channel channel attac attack workflow workflow

WISTP 2010 3

slide-4
SLIDE 4

Efficient entropy estimation for MIA using B-splines

Po Power wer an analysis alysis and and leak leakag age mod model el

WISTP 2010 4

time power consumption

 Messerges et al. 1999

  • Linear relation between

power consumption and Hamming Weight of a processed data.

b M H a t P   ) ( . ) (

slide-5
SLIDE 5

Efficient entropy estimation for MIA using B-splines

Some Some statisti statistica cal tests tests use used in p in prac racti tice ce ( (1) 1)

 Kocher et al. 1999

  • Simplified T-Test (distance of means)

 Brier et al. 2004

  • Pearson correlation factor,
  • Correlation Power Analysis (CPA)

WISTP 2010 5

slide-6
SLIDE 6

Efficient entropy estimation for MIA using B-splines

Some Some statisti statistica cal tests tests use used in p in prac racti tice ce ( (2) 2)

 Gierlichs et al. 2008

  • Mutual Information Analysis (MIA) + histograms

 Veyrat-Charvillon et al. 2009

  • Cramér-von Mises test (nonparametric)

 This presentation

  • MIA + B-splines estimation (nonparametric)

WISTP 2010 6

slide-7
SLIDE 7

Efficient entropy estimation for MIA using B-splines

Remaind Remainder er on

  • n i

info nformation rmation the theory

  • ry

 Let X be a random variable with MX possible states Xi with i = {1…MX}.  Entropy of X:  Mutual information:

  • WISTP 2010

7

X

M i i i

X p X p X H

1

)) ( log( ) ( ) (

) ( ) ( ) ; ( Y X H X H Y X I   ) , ( ) ( ) ( ) ; ( Y X H Y H X H Y X I   

slide-8
SLIDE 8

Efficient entropy estimation for MIA using B-splines

Prob Problem lem : : estimating estimating mutua mutual information information

 Mutual Information:

  • very powerful,
  • yet difficult to estimate.

 Using the definition of entropy, the density has to be estimated.  Goal: estimate a density given a finite number of data points drawn from that density function.  Different approaches:

  • histograms, kernel density estimation, …

WISTP 2010 8

slide-9
SLIDE 9

Efficient entropy estimation for MIA using B-splines

Hi Histog stogram ram ba base sed estimation estimation

WISTP 2010 9

  • Easy to calculate and

understand.

  • Systematic errors due

to the finite size of the dataset.

slide-10
SLIDE 10

Efficient entropy estimation for MIA using B-splines

MIA MIA vs vs CPA CPA

 Figure taken from : Moradi A, Mousavi N, Paar C, Salmasizadeh M. A Comparative Study of Mutual Information Analysis under a Gaussian

  • Assumption. Information Security Applications. 2009:193–205.

WISTP 2010 10

slide-11
SLIDE 11

Efficient entropy estimation for MIA using B-splines

Wha What are are B B-sp spli line ne fun function ctions ? (1) ? (1)

WISTP 2010 11

Degr Degree ee-0 0 basis basis fun functions ctions

1.5

slide-12
SLIDE 12

Efficient entropy estimation for MIA using B-splines

WISTP 2010 12

Wha What are are B B-sp spli line ne fun function ctions ? (2) ? (2)

Degr Degree ee-1 1 basis basis fun functions ctions

1.5

slide-13
SLIDE 13

Efficient entropy estimation for MIA using B-splines

WISTP 2010 13

Wha What are are B B-sp spli line ne fun function ctions ? (3) ? (3)

Degr Degree ee-2 2 basis basis fun functions ctions

1.5

slide-14
SLIDE 14

Efficient entropy estimation for MIA using B-splines

B-sp spli line nes for MI estimation for MI estimation

 Idea proposed by Daub et al. 2004 in the context of medical studies.  Instead of using a step function with histograms, a polynomial B-spline function is used to weight a data point.  Hence, data points can be in one or several intervals.

WISTP 2010 14

slide-15
SLIDE 15

Efficient entropy estimation for MIA using B-splines

MI MI estimation estimation i in n the the pre prese senc nce of no

  • f noise

ise

WISTP 2010 15

His Histogr tograms ams

1.5 2.5

slide-16
SLIDE 16

Efficient entropy estimation for MIA using B-splines

WISTP 2010 16

MI MI estimation estimation i in n the the pre prese senc nce of no

  • f noise

ise

Degr Degree ee-2 2 B-spline spline fun functions ctions

1.5 2.5

slide-17
SLIDE 17

Efficient entropy estimation for MIA using B-splines

B-sp spli line nes for MI estimation for MI estimation

WISTP 2010 17

  • Better efficiency than

histograms

  • Interesting propriety

for side-channel

  • Slower to compute

than histograms

slide-18
SLIDE 18

Efficient entropy estimation for MIA using B-splines

Cr Cramé amér-vo von Mi Mise ses s wi with th B-sp spli line nes

 Cramér-von Mises test in Veyrat-Charvillon et al. 2009.  Its needs cumulative density functions.  B-splines can be used to estimate these density functions.

WISTP 2010 18

slide-19
SLIDE 19

Efficient entropy estimation for MIA using B-splines

Exp Experimental erimental resu result lts

 Metrics to measure the efficiency of side-channel attacks by Standaert et al. 2008:

  • first order success rate: given a number of traces, the

probability that the correct hypothesis is the first best hypothesis of an attack.

  • guessed entropy: average position of the correct hypothesis

in the sorted hypothesis vector of an attack

 Attacks efficiency tested with 2 different setups:

  • on « DPA Contest 2008/2009a » power curves of a DES,
  • on power curves acquired on a Atmel STK600 board with a

ATmega2560 chip of a multiprecision multiplication.

WISTP 2010 19

a: HTTP://WWW.DPACONTEST.ORG

slide-20
SLIDE 20

Efficient entropy estimation for MIA using B-splines

DES DES – DPA DPA Contes Contest 20 2008 08/200 /2009 First First ord

  • rder

er su succ cces ess rate rate

WISTP 2010 20

slide-21
SLIDE 21

Efficient entropy estimation for MIA using B-splines

DES DES – DPA DPA Contes Contest 20 2008 08/200 /2009 Gue Guess ssed ed En Entrop tropy

WISTP 2010 21

slide-22
SLIDE 22

Efficient entropy estimation for MIA using B-splines

Multi Multiplication plication – ST STK600 K600 / / At Atmeg mega 2560 2560 First First ord

  • rder

er su succ cces ess rate rate

WISTP 2010 22

slide-23
SLIDE 23

Efficient entropy estimation for MIA using B-splines

Multi Multiplication plication – ST STK600 K600 / / At Atmeg mega 2560 2560 Gue Guess ssed ed en entrop tropy

WISTP 2010 23

slide-24
SLIDE 24

Efficient entropy estimation for MIA using B-splines

Conc Conclusion lusion

 B-splines offer a lot more efficiency than classical histograms for an acceptable computational overhead.  However MIA still is not as performant as CPA on most platforms.  A New Hope:

  • Other efficient entropy estimators,
  • Higher order side-channel analysis.

WISTP 2010 24

slide-25
SLIDE 25

Efficient entropy estimation for MIA using B-splines

Ques Questi tion

  • ns

s ?

WISTP 2010 25