D:\User\sbornik_38_pdf\23.DVI


Mathematical Problems of Computer Science 38, 56{58, 2012.

I nfor mation-T heor etic Appr oach to B iometr ic

I denti¯cation P r oblem

Ma r ia m E . H a r o u t u n ia n , L ilit A . Te r -V a r d a n ya n

Institute for Informatics and Automation Problems of the National Academy
of Sciences of the Republic of Armenia

armar@ipia.sci.am, lilit@sci.am

N o wa d a ys p e o p le live in t h e e r a o f la r g e -s c a le c o m p u t e r n e t wo r ks c o n n e c t in g h u g e
n u m b e r s o f e le c t r o n ic d e vic e s . Th e s e d e vic e s e xe c u t e a p p lic a t io n s t h a t u s e n e t wo r ks fo r e x-
c h a n g in g in fo r m a t io n . S o m e t im e s t h e in fo r m a t io n t h a t is t r a n s m it t e d wit h in t h e s e n e t wo r ks
a n d s t o r e d b y t h e d e vic e s is s e n s it ive t o m is u s e . Mo r e o ve r , t h e n e t wo r ks a n d d e vic e s c a n n o t
a lwa ys b e t r u s t e d . A ls o ille g a l c o p yin g o f c o p yr ig h t e d c o n t e n t , ille g a l u s e o f e -p a ym e n t s ys -
t e m s , a n d id e n t it y t h e ft c a n b e fo r e s e e n . Tr a d it io n a l s ys t e m s fo r a c c e s s c o n t r o l, wh ic h a r e
b a s e d o n t h e p o s s e s s io n o f s e c r e t kn o wle d g e ( p a s s wo r d , s e c r e t ke y, e t c .) . Mo r e o ve r , p a s s wo r d
c a n o ft e n b e g u e s s e d , s in c e t e n d t o u s e p a s s wo r d s wh ic h a r e e a s y t o r e m e m b e r .

B io m e t r ic s is t h e t e c h n o lo g y t h a t is u s e d t o u n iqu e ly id e n t ify a s p e c ī c h u m a n b e in g . It
is p r im a r ily u s e d t o p r o vid e s e c u r it y fo r p e r s o n a l o r b u s in e s s a s s e t s . A b io m e t r ic s s ys t e m
m u s t ¯ r s t s t o r e a p e r s o n 's b io m e t r ic d a t a . Th e n , wh e n s o m e o n e t r ie s t o a c c e s s a p e r s o n a l o r
b u s in e s s s ys t e m , t h e s t o r e d b io m e t r ic d a t a is c o m p a r e d t o t h e d a t a o f t h e p e r s o n c u r r e n t ly
a c c e s s in g t h e s ys t e m . If t h e d a t a m a t c h e s u p , t h e p e r s o n c a n h a ve a c c e s s t o t h e p r o t e c t e d
in fo r m a t io n .

B io m e t r ic s ys t e m s o ®e r a s o lu t io n t o m o s t o f t h e p r o b le m s m e n t io n e d a b o ve . Th e y c o u ld
e it h e r s u b s t it u t e d fo r t r a d it io n a l s ys t e m s o r u s e d t o r e in fo r c e t h e m . B io m e t r ic s ys t e m s a r e
b a s e d o n p h ys ic a l o r b e h a vio r a l c h a r a c t e r is t ic s o f h u m a n b e in g s , like fa c e s , ¯ n g e r p r in t s , vo ic e ,
ir is e s . Th e r e s u lt s o f t h e m e a s u r e m e n t o f t h e s e c h a r a c t e r is t ic s a r e c a lle d b io m e t r ic d a t a . B io -
m e t r ic d a t a h a ve t h e a d va n t a g e t h a t p o t e n t ia lly t h e y a r e u n iqu e id e n t ī e r s o f h u m a n b e in g .
A b io m e t r ic s s ys t e m m u s t ¯ r s t s t o r e a p e r s o n 's b io m e t r ic d a t a . Th e n , wh e n s o m e o n e t r ie s t o
a c c e s s a p e r s o n a l o r b u s in e s s s ys t e m , t h e s t o r e d b io m e t r ic d a t a is c o m p a r e d t o t h e d a t a o f t h e
p e r s o n c u r r e n t ly a c c e s s in g t h e s ys t e m . If t h e d a t a m a t c h e s u p , t h e p e r s o n c a n h a ve a c c e s s t o
t h e p r o t e c t e d in fo r m a t io n . Th e a t t r a c t ive p r o p e r t y o f u n iqu e n e s s , t h a t h o ld s fo r b io m e t r ic s ,
a ls o r e s u lt s in it s m a jo r we a kn e s s . U n like p a s s wo r d s , b io m e t r ic in fo r m a t io n , if c o m p r o m is e d
o n c e , c a n n o t b e c a n c e le d a n d e a s ily r e p la c e d b y o t h e r b io m e t r ic in fo r m a t io n , s in c e p e o p le
o n ly h a ve lim it e d r e s o u r c e s o f b io m e t r ic d a t a . R e qu ir e m e n t s fo r b io m e t r ic s ys t e m s s h o u ld
in c lu d e s e c u r e s t o r a g e a n d s e c u r e c o m m u n ic a t io n o f b io m e t r ic d a t a in t h e a p p lic a t io n s wh e r e
t h e y a r e u s e d .

Th e p r o b le m o f b io m e t r ic id e n t i¯ c a t io n is t r a n s fe r r e d t o in fo r m a t io n -t h e o r e t ic a l m o d e l
b y W ille m s e t a l [1 ]. Th e m o d e l o f a b io m e t r ic s ys t e m is s h o wn in Fig u r e 1 .

5 6



M. Haroutunian, L. Ter-Vardanyan 5 7

E nr olling phase

I denti¯cation phase

Figur e. 1. M odel of biometr ic identi¯cation system

B io m e t r ic a l id e n t i¯ c a t io n in g e n e r a l in vo lve s t wo p h a s e s . In a n e n r o llm e n t p h a s e a ll in -
d ivid u a ls a r e o b s e r ve d a n d fo r e a c h in d ivid u a l a r e c o r d is a d d e d t o a d a t a b a s e . Th is r e c o r d
c o n t a in s e n r o llm e n t -d a t a , i.e . a n o is y ve r s io n o f t h e b io m e t r ic a l d a t a c o r r e s p o n d in g t o t h e
in d ivid u a l. In t h e id e n t i¯ c a t io n p h a s e a n u n kn o wn in d ivid u a l is o b s e r ve d a g a in . Th e r e -
s u lt in g id e n t ī c a t io n -d a t a , a n o t h e r n o is y ve r s io n o f t h e b io m e t r ic a l d a t a o f t h e u n kn o wn
in d ivid u a l, is c o m p a r e d t o ( a ll) t h e e n r o llm e n t -d a t a in t h e d a t a b a s e a n d t h e s ys t e m h a s t o
c o m e u p wit h a n e s t im a t e o f t h e in d ivid u a l. E s s e n t ia l in t h is p r o c e d u r e is t h a t b o t h in t h e
e n r o llm e n t -p h a s e a n d in t h e id e n t ī c a t io n -p h a s e n o is y ve r s io n s o f t h e b io m e t r ic a l d a t a a r e
o b t a in e d . Th e a c t u a l b io m e t r ic a l d a t a o f e a c h in d ivid u a l r e m a in u n kn o wn .

W ille m s e t a l [1 ] in ve s t ig a t e d t h e fu n d a m e n t a l p r o p e r t ie s o f b io m e t r ic id e n t ī c a t io n s ys -
t e m . It h a s b e e n s h o wn t h a t it is n o t p o s s ib le t o id e n t ify r e lia b ly m o r e p e r s o n s t h a n c a p a c it y
wh ic h is a n in h e r e n t c h a r a c t e r is t ic o f a n y id e n t i¯ c a t io n s ys t e m . Th e y d e r ive d t h e c a p a c it y
o f s u c h s ys t e m .

W e in ve s t ig a t e t h e e xp o n e n t ia lly h ig h r e lia b ilit y c r it e r io n in b io m e t r ic id e n t i¯ c a t io n s ys -
t e m s . In o t h e r wo r d s we in t r o d u c e a n e w p e r fo r m a n c e c o n c e p t o f b io m e t r ic id e n t i¯ c a t io n
E-c a p a c it y, wh ic h t a ke s in t o a c c o u n t a s t r o n g e r r e qu ir e m e n t o n id e n t i¯ c a t io n fa u lt e ve n t s
wit h e xt r e m e ly s m a ll p r o b a b ilit y ( 2 ¡NE in s t e a d o f " ) . In t e r m s o f p r a c t ic a l a p p lic a t io n s a n
e xp o n e n t ia l d e c r e a s e in e r r o r p r o b a b ilit y ( n a m e ly, in u n wa n t e d id e n t i¯ c a t io n fa u lt s ) is m o r e
d e s ir a b le . W e in ve s t ig a t e t h e E-c a p a c it y fu n c t io n , wh ic h is t h e g e n e r a liz a t io n o f t h e c a p a c it y,
a s it t e n d s t o c a p a c it y, wh e n E t e n d s t o 0 . U p p e r a n d t h e lo we r b o u n d s fo r id e n t i¯ c a t io n
E-c a p a c it y fo r m a xim a l a n d a ve r a g e e r r o r p r o b a b ilit ie s a r e c o n s t r u c t e d in [3 ]. W h e n E ! 0
we d e r ive u p p e r a n d lo we r b o u n d s o f t h e c h a n n e l c a p a c it y, wh ic h c o in c id e wit h t h e c a p a c it y
o b t a in e d in [1 ]. W h e n E ! 0 we d e r ive t h e lo we r a n d u p p e r b o u n d s o f t h e c h a n n e l c a p a c it y,
wh ic h c o in c id e wit h t h e c a p a c it y o b t a in e d in [1 ].

A s im ila r r e s u lt is o b t a in e d fo r t h e b io m e t r ic id e n t ī c a t io n s ys t e m wit h r a n d o m p a r a m -
e t e r , wh ic h is m o r e r e a lis t ic fo r a p p lic a t io n s .



5 8 Information-Theoretic Approach to Biometric Identi¯cation Problem

R e fe r e n c e s

[1 ] F. W ille m s , T. K a lke r , J. Go s e lin g , a n d J.-P . L in n a r t z , \ On t h e c a p a c it y o f a b io m e t r ic a l
id e n t i¯ c a t io n s ys t e m " , International Symposium on Information Theory, Y o ko h a m a ,
Ja p a n , p . 8 2 , 2 0 0 3 .

[2 ] S . P a n ka n t i, R . M. B o lle a n d A . Ja in , \ B io m e t r ic s -Th e Fu t u r e o f Id e n t i¯ c a t io n " , IE E E
Computer, vo l. 3 3 , n o . 2 , p p . 4 6 4 9 , Fe b r u a r y, 2 0 0 2 .

[3 ] M. H a r o u t u n ia n , A . Mu r a d ya n a n d L . Te r - V a r d a n ya n , " U p p e r a n d lo we r b o u n d s o f
b io m e t r ic id e n t i¯ c a t io n E - c a p a c it y" , Transactions of IIAP of NAS of R A, M athematical
P roblems of Computer Science,v3 6 , p p .1 -1 0 , 2 0 1 2 .

[4 ] E . A . H a r o u t u n ia n , \ On b o u n d s fo r E-c a p a c it y o f D MC" , IE E E Transactions on Infor-
mation Theory, vo l. 5 3 , n o . 1 1 , p p . 4 2 1 0 -4 2 2 0 , 2 0 0 7 .

[5 ] E . A . H a r o u t u n ia n , M. E . H a r o u t u n ia n a n d A . N . H a r u t yu n ya n , " R e lia b ilit y c r it e r ia
in in fo r m a t io n t h e o r y a n d in s t a t is t ic a l h yp o t h e s is t e s t in g " , F oundations and Trends in
Communications and Information Theory, vo l. 4 , n o 2 -3 , p p . 9 7 -2 6 3 , 2 0 0 8 .

[6 ] M. E . H a r o u t u n ia n , \ E s t im a t e s o f E-c a p a c it y a n d c a p a c it y r e g io n s fo r m u lt ip le -a c c e s s
c h a n n e l wit h r a n d o m p a r a m e t e r " , L ecture Notes in Computer Science, vo l. 4 1 2 3 ,
S p r in g e r V e r la g , p p . 1 9 6 -2 1 7 , 2 0 0 6 .

[7 ] M. E . H a r o u t u n ia n , S . A . To n o ya n , \ R a n d o m c o d in g b o u n d o f in fo r m a t io n h id in g E-
c a p a c it y" , P roc. of IE E E International Symposium on Information Theory, p . 5 3 6 , U S A ,
Ch ic a g o , 2 0 0 4 .

[8 ] T. M. Co ve r a n d J. A . Th o m a s , E lements of Information Theory, W ile y, N e w Y o r k,
1 9 9 1 .

[9 ] I. Cs is z ¶a r a n d J. K Äo r n e r , Information Theory: Coding Theorems for D iscrete M emory-
less Systems, A c a d e m ic P r e s s , N e w Y o r k, 1 9 8 1 .